id sid tid token lemma pos american_scientific_journal-3454 1 1 118 118 NUM american_scientific_journal-3454 1 2 american american ADJ american_scientific_journal-3454 1 3 scientific scientific ADJ american_scientific_journal-3454 1 4 research research NOUN american_scientific_journal-3454 1 5 journal journal NOUN american_scientific_journal-3454 1 6 for for ADP american_scientific_journal-3454 1 7 engineering engineering NOUN american_scientific_journal-3454 1 8 , , PUNCT american_scientific_journal-3454 1 9 technology technology NOUN american_scientific_journal-3454 1 10 , , PUNCT american_scientific_journal-3454 1 11 and and CCONJ american_scientific_journal-3454 1 12 sciences science NOUN american_scientific_journal-3454 1 13 ( ( PUNCT american_scientific_journal-3454 1 14 asrjets asrjet NOUN american_scientific_journal-3454 1 15 ) ) PUNCT american_scientific_journal-3454 1 16 issn issn PROPN american_scientific_journal-3454 1 17 ( ( PUNCT american_scientific_journal-3454 1 18 print print NOUN american_scientific_journal-3454 1 19 ) ) PUNCT american_scientific_journal-3454 1 20 2313 2313 NUM american_scientific_journal-3454 1 21 - - SYM american_scientific_journal-3454 1 22 4410 4410 NUM american_scientific_journal-3454 1 23 , , PUNCT american_scientific_journal-3454 1 24 issn issn PROPN american_scientific_journal-3454 1 25 ( ( PUNCT american_scientific_journal-3454 1 26 online online ADJ american_scientific_journal-3454 1 27 ) ) PUNCT american_scientific_journal-3454 1 28 2313 2313 NUM american_scientific_journal-3454 1 29 - - SYM american_scientific_journal-3454 1 30 4402 4402 NUM american_scientific_journal-3454 1 31 ยฉ ยฉ PROPN american_scientific_journal-3454 1 32 global global ADJ american_scientific_journal-3454 1 33 society society NOUN american_scientific_journal-3454 1 34 of of ADP american_scientific_journal-3454 1 35 scientific scientific ADJ american_scientific_journal-3454 1 36 research research NOUN american_scientific_journal-3454 1 37 and and CCONJ american_scientific_journal-3454 1 38 researchers researcher NOUN american_scientific_journal-3454 1 39 http://asrjetsjournal.org/ http://asrjetsjournal.org/ NOUN american_scientific_journal-3454 1 40 lqr lqr NOUN american_scientific_journal-3454 1 41 and and CCONJ american_scientific_journal-3454 1 42 ๐‡๐‡๐Ÿ๐Ÿ ๐‡๐‡๐Ÿ๐Ÿ PROPN american_scientific_journal-3454 1 43 controllers controller NOUN american_scientific_journal-3454 1 44 design design VERB american_scientific_journal-3454 1 45 using use VERB american_scientific_journal-3454 1 46 state state NOUN american_scientific_journal-3454 1 47 derivative derivative ADJ american_scientific_journal-3454 1 48 feedback feedback NOUN american_scientific_journal-3454 1 49 for for ADP american_scientific_journal-3454 1 50 multivariable multivariable ADJ american_scientific_journal-3454 1 51 systems system NOUN american_scientific_journal-3454 1 52 hazem hazem PROPN american_scientific_journal-3454 1 53 i. i. PROPN american_scientific_journal-3454 1 54 alia alia PROPN american_scientific_journal-3454 1 55 * * PROPN american_scientific_journal-3454 1 56 , , PUNCT american_scientific_journal-3454 1 57 mohammed mohammed PROPN american_scientific_journal-3454 1 58 z. z. PROPN american_scientific_journal-3454 1 59 m. m. PROPN american_scientific_journal-3454 1 60 alib alib PROPN american_scientific_journal-3454 1 61 a a PRON american_scientific_journal-3454 1 62 , , PUNCT american_scientific_journal-3454 1 63 bdepartment bdepartment NOUN american_scientific_journal-3454 1 64 of of ADP american_scientific_journal-3454 1 65 control control NOUN american_scientific_journal-3454 1 66 and and CCONJ american_scientific_journal-3454 1 67 system system NOUN american_scientific_journal-3454 1 68 engineering engineering NOUN american_scientific_journal-3454 1 69 , , PUNCT american_scientific_journal-3454 1 70 university university NOUN american_scientific_journal-3454 1 71 of of ADP american_scientific_journal-3454 1 72 technology technology NOUN american_scientific_journal-3454 1 73 , , PUNCT american_scientific_journal-3454 1 74 baghdad-10001 baghdad-10001 ADJ american_scientific_journal-3454 1 75 , , PUNCT american_scientific_journal-3454 1 76 iraq iraq PROPN american_scientific_journal-3454 1 77 aemail aemail NOUN american_scientific_journal-3454 1 78 : : PUNCT american_scientific_journal-3454 1 79 hazemcontrol2001@yahoo.com hazemcontrol2001@yahoo.com X american_scientific_journal-3454 1 80 bemail bemail NOUN american_scientific_journal-3454 1 81 : : PUNCT american_scientific_journal-3454 2 1 mohammedzuhair29@gmail.com mohammedzuhair29@gmail.com X american_scientific_journal-3454 2 2 abstract abstract ADJ american_scientific_journal-3454 2 3 this this DET american_scientific_journal-3454 2 4 paper paper NOUN american_scientific_journal-3454 2 5 presents present VERB american_scientific_journal-3454 2 6 the the DET american_scientific_journal-3454 2 7 design design NOUN american_scientific_journal-3454 2 8 of of ADP american_scientific_journal-3454 2 9 lqr lqr NOUN american_scientific_journal-3454 2 10 ( ( PUNCT american_scientific_journal-3454 2 11 linear linear ADJ american_scientific_journal-3454 2 12 quadratic quadratic ADJ american_scientific_journal-3454 2 13 regular regular ADJ american_scientific_journal-3454 2 14 ) ) PUNCT american_scientific_journal-3454 2 15 and and CCONJ american_scientific_journal-3454 2 16 h2 h2 NOUN american_scientific_journal-3454 2 17 controller controller NOUN american_scientific_journal-3454 2 18 using use VERB american_scientific_journal-3454 2 19 state state NOUN american_scientific_journal-3454 2 20 derivative derivative ADJ american_scientific_journal-3454 2 21 feedback feedback NOUN american_scientific_journal-3454 2 22 . . PUNCT american_scientific_journal-3454 3 1 this this DET american_scientific_journal-3454 3 2 design design NOUN american_scientific_journal-3454 3 3 is be AUX american_scientific_journal-3454 3 4 solvable solvable ADJ american_scientific_journal-3454 3 5 for for ADP american_scientific_journal-3454 3 6 all all DET american_scientific_journal-3454 3 7 controllable controllable ADJ american_scientific_journal-3454 3 8 systems system NOUN american_scientific_journal-3454 3 9 . . PUNCT american_scientific_journal-3454 4 1 the the DET american_scientific_journal-3454 4 2 state state NOUN american_scientific_journal-3454 4 3 derivative derivative ADJ american_scientific_journal-3454 4 4 feedback feedback NOUN american_scientific_journal-3454 4 5 is be AUX american_scientific_journal-3454 4 6 used use VERB american_scientific_journal-3454 4 7 instead instead ADV american_scientific_journal-3454 4 8 of of ADP american_scientific_journal-3454 4 9 state state NOUN american_scientific_journal-3454 4 10 feedback feedback NOUN american_scientific_journal-3454 4 11 in in ADP american_scientific_journal-3454 4 12 many many ADJ american_scientific_journal-3454 4 13 mechanical mechanical ADJ american_scientific_journal-3454 4 14 systems system NOUN american_scientific_journal-3454 4 15 because because SCONJ american_scientific_journal-3454 4 16 the the DET american_scientific_journal-3454 4 17 main main ADJ american_scientific_journal-3454 4 18 sensors sensor NOUN american_scientific_journal-3454 4 19 of of ADP american_scientific_journal-3454 4 20 vibration vibration NOUN american_scientific_journal-3454 4 21 are be AUX american_scientific_journal-3454 4 22 accelerometers accelerometer NOUN american_scientific_journal-3454 4 23 . . PUNCT american_scientific_journal-3454 5 1 a a DET american_scientific_journal-3454 5 2 multivariable multivariable ADJ american_scientific_journal-3454 5 3 active active ADJ american_scientific_journal-3454 5 4 suspension suspension NOUN american_scientific_journal-3454 5 5 system system NOUN american_scientific_journal-3454 5 6 is be AUX american_scientific_journal-3454 5 7 used use VERB american_scientific_journal-3454 5 8 in in ADP american_scientific_journal-3454 5 9 this this DET american_scientific_journal-3454 5 10 paper paper NOUN american_scientific_journal-3454 5 11 to to PART american_scientific_journal-3454 5 12 show show VERB american_scientific_journal-3454 5 13 the the DET american_scientific_journal-3454 5 14 effectiveness effectiveness NOUN american_scientific_journal-3454 5 15 of of ADP american_scientific_journal-3454 5 16 the the DET american_scientific_journal-3454 5 17 proposed propose VERB american_scientific_journal-3454 5 18 controllers controller NOUN american_scientific_journal-3454 5 19 . . PUNCT american_scientific_journal-3454 6 1 the the DET american_scientific_journal-3454 6 2 obtained obtain VERB american_scientific_journal-3454 6 3 results result NOUN american_scientific_journal-3454 6 4 are be AUX american_scientific_journal-3454 6 5 compared compare VERB american_scientific_journal-3454 6 6 to to ADP american_scientific_journal-3454 6 7 the the DET american_scientific_journal-3454 6 8 same same ADJ american_scientific_journal-3454 6 9 approaches approach NOUN american_scientific_journal-3454 6 10 when when SCONJ american_scientific_journal-3454 6 11 a a DET american_scientific_journal-3454 6 12 state state NOUN american_scientific_journal-3454 6 13 feedback feedback NOUN american_scientific_journal-3454 6 14 is be AUX american_scientific_journal-3454 6 15 used use VERB american_scientific_journal-3454 6 16 . . PUNCT american_scientific_journal-3454 7 1 it it PRON american_scientific_journal-3454 7 2 is be AUX american_scientific_journal-3454 7 3 shown show VERB american_scientific_journal-3454 7 4 that that SCONJ american_scientific_journal-3454 7 5 the the DET american_scientific_journal-3454 7 6 design design NOUN american_scientific_journal-3454 7 7 using use VERB american_scientific_journal-3454 7 8 state state NOUN american_scientific_journal-3454 7 9 derivative derivative ADJ american_scientific_journal-3454 7 10 feedback feedback NOUN american_scientific_journal-3454 7 11 can can AUX american_scientific_journal-3454 7 12 achieve achieve VERB american_scientific_journal-3454 7 13 a a DET american_scientific_journal-3454 7 14 better well ADJ american_scientific_journal-3454 7 15 performance performance NOUN american_scientific_journal-3454 7 16 . . PUNCT american_scientific_journal-3454 8 1 keywords keyword NOUN american_scientific_journal-3454 8 2 : : PUNCT american_scientific_journal-3454 8 3 lqr lqr PROPN american_scientific_journal-3454 8 4 control control NOUN american_scientific_journal-3454 8 5 ; ; PUNCT american_scientific_journal-3454 8 6 h2 h2 NOUN american_scientific_journal-3454 8 7 control control NOUN american_scientific_journal-3454 8 8 ; ; PUNCT american_scientific_journal-3454 8 9 state state NOUN american_scientific_journal-3454 8 10 derivative derivative ADJ american_scientific_journal-3454 8 11 feedback feedback NOUN american_scientific_journal-3454 8 12 ; ; PUNCT american_scientific_journal-3454 8 13 multivariable multivariable ADJ american_scientific_journal-3454 8 14 systems system NOUN american_scientific_journal-3454 8 15 ; ; PUNCT american_scientific_journal-3454 8 16 active active ADJ american_scientific_journal-3454 8 17 suspension suspension NOUN american_scientific_journal-3454 8 18 . . PUNCT american_scientific_journal-3454 9 1 1 1 X american_scientific_journal-3454 9 2 . . X american_scientific_journal-3454 9 3 introduction introduction NOUN american_scientific_journal-3454 9 4 the the DET american_scientific_journal-3454 9 5 state state NOUN american_scientific_journal-3454 9 6 derivative derivative ADJ american_scientific_journal-3454 9 7 feedback feedback NOUN american_scientific_journal-3454 9 8 is be AUX american_scientific_journal-3454 9 9 very very ADV american_scientific_journal-3454 9 10 useful useful ADJ american_scientific_journal-3454 9 11 and and CCONJ american_scientific_journal-3454 9 12 essential essential ADJ american_scientific_journal-3454 9 13 for for ADP american_scientific_journal-3454 9 14 achieving achieve VERB american_scientific_journal-3454 9 15 a a DET american_scientific_journal-3454 9 16 desired desire VERB american_scientific_journal-3454 9 17 specification specification NOUN american_scientific_journal-3454 9 18 for for ADP american_scientific_journal-3454 9 19 some some DET american_scientific_journal-3454 9 20 control control NOUN american_scientific_journal-3454 9 21 problems problem NOUN american_scientific_journal-3454 9 22 . . PUNCT american_scientific_journal-3454 10 1 the the DET american_scientific_journal-3454 10 2 motivation motivation NOUN american_scientific_journal-3454 10 3 of of ADP american_scientific_journal-3454 10 4 using use VERB american_scientific_journal-3454 10 5 state state NOUN american_scientific_journal-3454 10 6 derivative derivative ADJ american_scientific_journal-3454 10 7 feedback feedback NOUN american_scientific_journal-3454 10 8 comes come VERB american_scientific_journal-3454 10 9 from from ADP american_scientific_journal-3454 10 10 controlled control VERB american_scientific_journal-3454 10 11 vibration vibration NOUN american_scientific_journal-3454 10 12 suspension suspension NOUN american_scientific_journal-3454 10 13 of of ADP american_scientific_journal-3454 10 14 mechanical mechanical ADJ american_scientific_journal-3454 10 15 systems system NOUN american_scientific_journal-3454 10 16 where where SCONJ american_scientific_journal-3454 10 17 the the DET american_scientific_journal-3454 10 18 accelerometers accelerometer NOUN american_scientific_journal-3454 10 19 represent represent VERB american_scientific_journal-3454 10 20 the the DET american_scientific_journal-3454 10 21 main main ADJ american_scientific_journal-3454 10 22 sensors sensor NOUN american_scientific_journal-3454 10 23 of of ADP american_scientific_journal-3454 10 24 vibration vibration NOUN american_scientific_journal-3454 10 25 [ [ X american_scientific_journal-3454 10 26 1 1 NUM american_scientific_journal-3454 10 27 ] ] PUNCT american_scientific_journal-3454 10 28 . . PUNCT american_scientific_journal-3454 11 1 different different ADJ american_scientific_journal-3454 11 2 approaches approach NOUN american_scientific_journal-3454 11 3 that that PRON american_scientific_journal-3454 11 4 are be AUX american_scientific_journal-3454 11 5 based base VERB american_scientific_journal-3454 11 6 on on ADP american_scientific_journal-3454 11 7 state state NOUN american_scientific_journal-3454 11 8 feedback feedback NOUN american_scientific_journal-3454 11 9 have have AUX american_scientific_journal-3454 11 10 been be AUX american_scientific_journal-3454 11 11 extended extend VERB american_scientific_journal-3454 11 12 to to PART american_scientific_journal-3454 11 13 be be AUX american_scientific_journal-3454 11 14 designed design VERB american_scientific_journal-3454 11 15 using use VERB american_scientific_journal-3454 11 16 state state NOUN american_scientific_journal-3454 11 17 derivative derivative ADJ american_scientific_journal-3454 11 18 feedback feedback NOUN american_scientific_journal-3454 11 19 . . PUNCT american_scientific_journal-3454 12 1 linear linear ADJ american_scientific_journal-3454 12 2 quadratic quadratic ADJ american_scientific_journal-3454 12 3 regulator regulator NOUN american_scientific_journal-3454 12 4 ( ( PUNCT american_scientific_journal-3454 12 5 lqr lqr PROPN american_scientific_journal-3454 12 6 ) ) PUNCT american_scientific_journal-3454 12 7 is be AUX american_scientific_journal-3454 12 8 considered consider VERB american_scientific_journal-3454 12 9 one one NUM american_scientific_journal-3454 12 10 of of ADP american_scientific_journal-3454 12 11 the the DET american_scientific_journal-3454 12 12 well well ADV american_scientific_journal-3454 12 13 - - PUNCT american_scientific_journal-3454 12 14 known know VERB american_scientific_journal-3454 12 15 approaches approach NOUN american_scientific_journal-3454 12 16 that that PRON american_scientific_journal-3454 12 17 provide provide VERB american_scientific_journal-3454 12 18 practical practical ADJ american_scientific_journal-3454 12 19 feedback feedback NOUN american_scientific_journal-3454 12 20 gains gain NOUN american_scientific_journal-3454 12 21 . . PUNCT american_scientific_journal-3454 13 1 this this DET american_scientific_journal-3454 13 2 method method NOUN american_scientific_journal-3454 13 3 has have AUX american_scientific_journal-3454 13 4 adopted adopt VERB american_scientific_journal-3454 13 5 either either PRON american_scientific_journal-3454 13 6 feedback feedback NOUN american_scientific_journal-3454 13 7 or or CCONJ american_scientific_journal-3454 13 8 derivative derivative ADJ american_scientific_journal-3454 13 9 feedback feedback NOUN american_scientific_journal-3454 13 10 controller controller NOUN american_scientific_journal-3454 13 11 and and CCONJ american_scientific_journal-3454 13 12 it it PRON american_scientific_journal-3454 13 13 provides provide VERB american_scientific_journal-3454 13 14 a a DET american_scientific_journal-3454 13 15 perfect perfect ADJ american_scientific_journal-3454 13 16 stabilization stabilization NOUN american_scientific_journal-3454 13 17 for for ADP american_scientific_journal-3454 13 18 an an DET american_scientific_journal-3454 13 19 active active ADJ american_scientific_journal-3454 13 20 suspension suspension NOUN american_scientific_journal-3454 13 21 system system NOUN american_scientific_journal-3454 14 1 [ [ X american_scientific_journal-3454 14 2 2 2 NUM american_scientific_journal-3454 14 3 ] ] PUNCT american_scientific_journal-3454 14 4 . . PUNCT american_scientific_journal-3454 15 1 the the DET american_scientific_journal-3454 15 2 lqr lqr PROPN american_scientific_journal-3454 15 3 approach approach NOUN american_scientific_journal-3454 15 4 can can AUX american_scientific_journal-3454 15 5 achieve achieve VERB american_scientific_journal-3454 15 6 an an DET american_scientific_journal-3454 15 7 acceptable acceptable ADJ american_scientific_journal-3454 15 8 performance performance NOUN american_scientific_journal-3454 15 9 of of ADP american_scientific_journal-3454 15 10 the the DET american_scientific_journal-3454 15 11 system system NOUN american_scientific_journal-3454 15 12 by by ADP american_scientific_journal-3454 15 13 minimizing minimize VERB american_scientific_journal-3454 15 14 the the DET american_scientific_journal-3454 15 15 performance performance NOUN american_scientific_journal-3454 15 16 index index NOUN american_scientific_journal-3454 15 17 [ [ X american_scientific_journal-3454 15 18 3 3 NUM american_scientific_journal-3454 15 19 ] ] PUNCT american_scientific_journal-3454 15 20 . . PUNCT american_scientific_journal-3454 16 1 based base VERB american_scientific_journal-3454 16 2 on on ADP american_scientific_journal-3454 16 3 lqr lqr PROPN american_scientific_journal-3454 16 4 , , PUNCT american_scientific_journal-3454 16 5 some some PRON american_scientific_journal-3454 16 6 of of ADP american_scientific_journal-3454 16 7 new new ADJ american_scientific_journal-3454 16 8 control control NOUN american_scientific_journal-3454 16 9 algorithms algorithm NOUN american_scientific_journal-3454 16 10 have have AUX american_scientific_journal-3454 16 11 been be AUX american_scientific_journal-3454 16 12 derived derive VERB american_scientific_journal-3454 16 13 such such ADJ american_scientific_journal-3454 16 14 as as ADP american_scientific_journal-3454 16 15 in in ADP american_scientific_journal-3454 16 16 [ [ X american_scientific_journal-3454 16 17 1,4 1,4 NUM american_scientific_journal-3454 16 18 ] ] X american_scientific_journal-3454 16 19 . . PUNCT american_scientific_journal-3454 17 1 ----------------------------------------------------------------------- ----------------------------------------------------------------------- PUNCT american_scientific_journal-3454 18 1 * * PUNCT american_scientific_journal-3454 18 2 corresponding correspond VERB american_scientific_journal-3454 18 3 author author NOUN american_scientific_journal-3454 18 4 . . PUNCT american_scientific_journal-3454 19 1 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-3454 19 2 american american PROPN american_scientific_journal-3454 19 3 scientific scientific PROPN american_scientific_journal-3454 19 4 research research NOUN american_scientific_journal-3454 19 5 journal journal NOUN american_scientific_journal-3454 19 6 for for ADP american_scientific_journal-3454 19 7 engineering engineering NOUN american_scientific_journal-3454 19 8 , , PUNCT american_scientific_journal-3454 19 9 technology technology NOUN american_scientific_journal-3454 19 10 , , PUNCT american_scientific_journal-3454 19 11 and and CCONJ american_scientific_journal-3454 19 12 sciences science NOUN american_scientific_journal-3454 19 13 ( ( PUNCT american_scientific_journal-3454 19 14 asrjets asrjet NOUN american_scientific_journal-3454 19 15 ) ) PUNCT american_scientific_journal-3454 19 16 ( ( PUNCT american_scientific_journal-3454 19 17 2017 2017 NUM american_scientific_journal-3454 19 18 ) ) PUNCT american_scientific_journal-3454 19 19 volume volume NOUN american_scientific_journal-3454 19 20 37 37 NUM american_scientific_journal-3454 19 21 , , PUNCT american_scientific_journal-3454 19 22 no no DET american_scientific_journal-3454 19 23 1 1 NUM american_scientific_journal-3454 19 24 , , PUNCT american_scientific_journal-3454 19 25 pp pp ADV american_scientific_journal-3454 19 26 118 118 NUM american_scientific_journal-3454 19 27 - - SYM american_scientific_journal-3454 19 28 128 128 NUM american_scientific_journal-3454 19 29 119 119 NUM american_scientific_journal-3454 19 30 the the DET american_scientific_journal-3454 19 31 h2 h2 NOUN american_scientific_journal-3454 19 32 is be AUX american_scientific_journal-3454 19 33 used use VERB american_scientific_journal-3454 19 34 to to PART american_scientific_journal-3454 19 35 find find VERB american_scientific_journal-3454 19 36 the the DET american_scientific_journal-3454 19 37 optimal optimal ADJ american_scientific_journal-3454 19 38 gain gain NOUN american_scientific_journal-3454 19 39 matrices matrice VERB american_scientific_journal-3454 19 40 the the DET american_scientific_journal-3454 19 41 achieve achieve VERB american_scientific_journal-3454 19 42 the the DET american_scientific_journal-3454 19 43 desired desire VERB american_scientific_journal-3454 19 44 performance performance NOUN american_scientific_journal-3454 19 45 . . PUNCT american_scientific_journal-3454 20 1 the the DET american_scientific_journal-3454 20 2 h2 h2 PROPN american_scientific_journal-3454 20 3 optimal optimal ADJ american_scientific_journal-3454 20 4 control control NOUN american_scientific_journal-3454 20 5 is be AUX american_scientific_journal-3454 20 6 used use VERB american_scientific_journal-3454 20 7 in in ADP american_scientific_journal-3454 20 8 the the DET american_scientific_journal-3454 20 9 design design NOUN american_scientific_journal-3454 20 10 of of ADP american_scientific_journal-3454 20 11 state state NOUN american_scientific_journal-3454 20 12 feedback feedback NOUN american_scientific_journal-3454 20 13 control control NOUN american_scientific_journal-3454 20 14 by by ADP american_scientific_journal-3454 20 15 minimizing minimize VERB american_scientific_journal-3454 20 16 a a DET american_scientific_journal-3454 20 17 quadratic quadratic ADJ american_scientific_journal-3454 20 18 performance performance NOUN american_scientific_journal-3454 20 19 index index NOUN american_scientific_journal-3454 20 20 of of ADP american_scientific_journal-3454 20 21 the the DET american_scientific_journal-3454 20 22 system system NOUN american_scientific_journal-3454 20 23 and and CCONJ american_scientific_journal-3454 20 24 attenuating attenuate VERB american_scientific_journal-3454 20 25 the the DET american_scientific_journal-3454 20 26 effect effect NOUN american_scientific_journal-3454 20 27 of of ADP american_scientific_journal-3454 20 28 disturbances disturbance NOUN american_scientific_journal-3454 20 29 . . PUNCT american_scientific_journal-3454 21 1 reference reference NOUN american_scientific_journal-3454 21 2 [ [ X american_scientific_journal-3454 21 3 5 5 NUM american_scientific_journal-3454 21 4 ] ] PUNCT american_scientific_journal-3454 21 5 have have AUX american_scientific_journal-3454 21 6 used use VERB american_scientific_journal-3454 21 7 the the DET american_scientific_journal-3454 21 8 state state NOUN american_scientific_journal-3454 21 9 derivative derivative ADJ american_scientific_journal-3454 21 10 feedback feedback NOUN american_scientific_journal-3454 21 11 for for ADP american_scientific_journal-3454 21 12 direct direct ADJ american_scientific_journal-3454 21 13 algorithm algorithm NOUN american_scientific_journal-3454 21 14 for for ADP american_scientific_journal-3454 21 15 the the DET american_scientific_journal-3454 21 16 pole pole NOUN american_scientific_journal-3454 21 17 placement placement NOUN american_scientific_journal-3454 21 18 for for ADP american_scientific_journal-3454 21 19 multi multi ADJ american_scientific_journal-3454 21 20 input input NOUN american_scientific_journal-3454 21 21 linear linear PROPN american_scientific_journal-3454 21 22 system system NOUN american_scientific_journal-3454 21 23 . . PUNCT american_scientific_journal-3454 22 1 reference reference NOUN american_scientific_journal-3454 23 1 [ [ X american_scientific_journal-3454 23 2 6 6 NUM american_scientific_journal-3454 23 3 ] ] PUNCT american_scientific_journal-3454 23 4 used use VERB american_scientific_journal-3454 23 5 state state NOUN american_scientific_journal-3454 23 6 derivative derivative ADJ american_scientific_journal-3454 23 7 feedback feedback NOUN american_scientific_journal-3454 23 8 for for ADP american_scientific_journal-3454 23 9 poleplacement poleplacement NOUN american_scientific_journal-3454 23 10 for for ADP american_scientific_journal-3454 23 11 single single ADJ american_scientific_journal-3454 23 12 input input NOUN american_scientific_journal-3454 23 13 single single ADJ american_scientific_journal-3454 23 14 output output NOUN american_scientific_journal-3454 23 15 systems system NOUN american_scientific_journal-3454 23 16 . . PUNCT american_scientific_journal-3454 24 1 cardim cardim PROPN american_scientific_journal-3454 24 2 and and CCONJ american_scientific_journal-3454 24 3 his his PRON american_scientific_journal-3454 24 4 colleagues colleague NOUN american_scientific_journal-3454 25 1 [ [ X american_scientific_journal-3454 25 2 7 7 X american_scientific_journal-3454 25 3 ] ] PUNCT american_scientific_journal-3454 25 4 used use VERB american_scientific_journal-3454 25 5 state state NOUN american_scientific_journal-3454 25 6 derivative derivative ADJ american_scientific_journal-3454 25 7 feedback feedback NOUN american_scientific_journal-3454 25 8 for for ADP american_scientific_journal-3454 25 9 linear linear PROPN american_scientific_journal-3454 25 10 control control NOUN american_scientific_journal-3454 25 11 systems system NOUN american_scientific_journal-3454 25 12 . . PUNCT american_scientific_journal-3454 26 1 kataria kataria PROPN american_scientific_journal-3454 26 2 and and CCONJ american_scientific_journal-3454 26 3 his his PRON american_scientific_journal-3454 26 4 colleagues colleague NOUN american_scientific_journal-3454 27 1 [ [ X american_scientific_journal-3454 27 2 8 8 NUM american_scientific_journal-3454 27 3 ] ] PUNCT american_scientific_journal-3454 27 4 used use VERB american_scientific_journal-3454 27 5 state state NOUN american_scientific_journal-3454 27 6 derivative derivative ADJ american_scientific_journal-3454 27 7 feedback feedback NOUN american_scientific_journal-3454 27 8 for for ADP american_scientific_journal-3454 27 9 pole pole ADJ american_scientific_journal-3454 27 10 - - PUNCT american_scientific_journal-3454 27 11 placement placement NOUN american_scientific_journal-3454 27 12 problem problem NOUN american_scientific_journal-3454 27 13 . . PUNCT american_scientific_journal-3454 28 1 wang wang PROPN american_scientific_journal-3454 28 2 and and CCONJ american_scientific_journal-3454 28 3 his his PRON american_scientific_journal-3454 28 4 colleagues colleague NOUN american_scientific_journal-3454 29 1 [ [ X american_scientific_journal-3454 29 2 9 9 NUM american_scientific_journal-3454 29 3 ] ] PUNCT american_scientific_journal-3454 29 4 have have AUX american_scientific_journal-3454 29 5 used use VERB american_scientific_journal-3454 29 6 the the DET american_scientific_journal-3454 29 7 state state NOUN american_scientific_journal-3454 29 8 feedback feedback NOUN american_scientific_journal-3454 29 9 h2 h2 NOUN american_scientific_journal-3454 29 10 control control NOUN american_scientific_journal-3454 29 11 with with ADP american_scientific_journal-3454 29 12 regional regional ADJ american_scientific_journal-3454 29 13 pole pole NOUN american_scientific_journal-3454 29 14 assignment assignment NOUN american_scientific_journal-3454 29 15 . . PUNCT american_scientific_journal-3454 30 1 reference reference NOUN american_scientific_journal-3454 30 2 [ [ X american_scientific_journal-3454 30 3 10 10 NUM american_scientific_journal-3454 30 4 ] ] PUNCT american_scientific_journal-3454 30 5 presented present VERB american_scientific_journal-3454 30 6 a a DET american_scientific_journal-3454 30 7 technique technique NOUN american_scientific_journal-3454 30 8 based base VERB american_scientific_journal-3454 30 9 on on ADP american_scientific_journal-3454 30 10 state state NOUN american_scientific_journal-3454 30 11 derivative derivative NOUN american_scientific_journal-3454 30 12 for for ADP american_scientific_journal-3454 30 13 robust robust ADJ american_scientific_journal-3454 30 14 vibration vibration NOUN american_scientific_journal-3454 30 15 control control NOUN american_scientific_journal-3454 30 16 of of ADP american_scientific_journal-3454 30 17 dynamical dynamical ADJ american_scientific_journal-3454 30 18 systems system NOUN american_scientific_journal-3454 30 19 . . PUNCT american_scientific_journal-3454 31 1 in in ADP american_scientific_journal-3454 31 2 this this DET american_scientific_journal-3454 31 3 paper paper NOUN american_scientific_journal-3454 31 4 , , PUNCT american_scientific_journal-3454 31 5 the the DET american_scientific_journal-3454 31 6 design design NOUN american_scientific_journal-3454 31 7 of of ADP american_scientific_journal-3454 31 8 lqr lqr NOUN american_scientific_journal-3454 31 9 and and CCONJ american_scientific_journal-3454 31 10 h2 h2 NOUN american_scientific_journal-3454 31 11 controllers controller NOUN american_scientific_journal-3454 31 12 are be AUX american_scientific_journal-3454 31 13 presented present VERB american_scientific_journal-3454 31 14 using use VERB american_scientific_journal-3454 31 15 state state NOUN american_scientific_journal-3454 31 16 derivative derivative ADJ american_scientific_journal-3454 31 17 feedback feedback NOUN american_scientific_journal-3454 31 18 . . PUNCT american_scientific_journal-3454 32 1 the the DET american_scientific_journal-3454 32 2 proposed propose VERB american_scientific_journal-3454 32 3 controllers controller NOUN american_scientific_journal-3454 32 4 are be AUX american_scientific_journal-3454 32 5 applied apply VERB american_scientific_journal-3454 32 6 to to ADP american_scientific_journal-3454 32 7 a a DET american_scientific_journal-3454 32 8 multivariable multivariable ADJ american_scientific_journal-3454 32 9 active active ADJ american_scientific_journal-3454 32 10 suspension suspension NOUN american_scientific_journal-3454 32 11 . . PUNCT american_scientific_journal-3454 33 1 2 2 X american_scientific_journal-3454 33 2 . . X american_scientific_journal-3454 33 3 controllers controller NOUN american_scientific_journal-3454 33 4 design design VERB american_scientific_journal-3454 33 5 in in ADP american_scientific_journal-3454 33 6 this this DET american_scientific_journal-3454 33 7 section section NOUN american_scientific_journal-3454 33 8 , , PUNCT american_scientific_journal-3454 33 9 the the DET american_scientific_journal-3454 33 10 solutions solution NOUN american_scientific_journal-3454 33 11 of of ADP american_scientific_journal-3454 33 12 lqr lqr NOUN american_scientific_journal-3454 33 13 optimal optimal ADJ american_scientific_journal-3454 33 14 control control NOUN american_scientific_journal-3454 33 15 and and CCONJ american_scientific_journal-3454 33 16 h2 h2 NOUN american_scientific_journal-3454 33 17 robust robust ADJ american_scientific_journal-3454 33 18 control control NOUN american_scientific_journal-3454 33 19 using use VERB american_scientific_journal-3454 33 20 state state NOUN american_scientific_journal-3454 33 21 derivative derivative ADJ american_scientific_journal-3454 33 22 feedback feedback NOUN american_scientific_journal-3454 33 23 are be AUX american_scientific_journal-3454 33 24 presented present VERB american_scientific_journal-3454 33 25 . . PUNCT american_scientific_journal-3454 34 1 2.1 2.1 NUM american_scientific_journal-3454 34 2 . . NUM american_scientific_journal-3454 34 3 lqr lqr VERB american_scientific_journal-3454 34 4 state state PROPN american_scientific_journal-3454 34 5 derivative derivative ADJ american_scientific_journal-3454 34 6 feedback feedback NOUN american_scientific_journal-3454 34 7 problem problem NOUN american_scientific_journal-3454 34 8 formulation formulation NOUN american_scientific_journal-3454 34 9 consider consider VERB american_scientific_journal-3454 34 10 a a DET american_scientific_journal-3454 34 11 continuous continuous ADJ american_scientific_journal-3454 34 12 , , PUNCT american_scientific_journal-3454 34 13 time time NOUN american_scientific_journal-3454 34 14 - - PUNCT american_scientific_journal-3454 34 15 invariant invariant ADJ american_scientific_journal-3454 34 16 , , PUNCT american_scientific_journal-3454 34 17 linear linear ADJ american_scientific_journal-3454 34 18 system system NOUN american_scientific_journal-3454 34 19 : : PUNCT american_scientific_journal-3454 34 20 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 34 21 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 34 22 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 34 23 ๐‘ฅ(๐‘ก๐‘ก)= ๐‘ฅ(๐‘ก๐‘ก)= PUNCT american_scientific_journal-3454 34 24 ๐ด๐ด๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐ด๐ด๐‘ฅ๐‘ฅ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 34 25 ) ) PUNCT american_scientific_journal-3454 35 1 + + NUM american_scientific_journal-3454 35 2 ๐ต๐ต๐ต๐ต(๐‘ก๐‘ก ๐ต๐ต๐ต๐ต(๐‘ก๐‘ก NOUN american_scientific_journal-3454 35 3 ) ) PUNCT american_scientific_journal-3454 35 4 ( ( PUNCT american_scientific_journal-3454 35 5 1 1 X american_scientific_journal-3454 35 6 ) ) PUNCT american_scientific_journal-3454 35 7 the the DET american_scientific_journal-3454 35 8 objective objective NOUN american_scientific_journal-3454 35 9 is be AUX american_scientific_journal-3454 35 10 to to PART american_scientific_journal-3454 35 11 stabilize stabilize VERB american_scientific_journal-3454 35 12 the the DET american_scientific_journal-3454 35 13 system system NOUN american_scientific_journal-3454 35 14 by by ADP american_scientific_journal-3454 35 15 means mean NOUN american_scientific_journal-3454 35 16 of of ADP american_scientific_journal-3454 35 17 a a DET american_scientific_journal-3454 35 18 linear linear ADJ american_scientific_journal-3454 35 19 state state NOUN american_scientific_journal-3454 35 20 derivative derivative ADJ american_scientific_journal-3454 35 21 feedback feedback NOUN american_scientific_journal-3454 35 22 expressed express VERB american_scientific_journal-3454 35 23 by by ADP american_scientific_journal-3454 35 24 : : PUNCT american_scientific_journal-3454 35 25 ๐ต๐ต(๐‘ก๐‘ก ๐ต๐ต(๐‘ก๐‘ก PROPN american_scientific_journal-3454 35 26 ) ) PUNCT american_scientific_journal-3454 35 27 = = SYM american_scientific_journal-3454 35 28 โˆ’๐พ๐พ โˆ’๐พ๐พ NUM american_scientific_journal-3454 35 29 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 35 30 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 35 31 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 35 32 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 35 33 ) ) PUNCT american_scientific_journal-3454 35 34 ( ( PUNCT american_scientific_journal-3454 35 35 2 2 X american_scientific_journal-3454 35 36 ) ) PUNCT american_scientific_journal-3454 35 37 the the DET american_scientific_journal-3454 35 38 control control NOUN american_scientific_journal-3454 35 39 law law NOUN american_scientific_journal-3454 35 40 in in ADP american_scientific_journal-3454 35 41 equation equation NOUN american_scientific_journal-3454 35 42 ( ( PUNCT american_scientific_journal-3454 35 43 2 2 X american_scientific_journal-3454 35 44 ) ) PUNCT american_scientific_journal-3454 35 45 is be AUX american_scientific_journal-3454 35 46 to to PART american_scientific_journal-3454 35 47 stabilize stabilize VERB american_scientific_journal-3454 35 48 the the DET american_scientific_journal-3454 35 49 system system NOUN american_scientific_journal-3454 35 50 with with ADP american_scientific_journal-3454 35 51 a a DET american_scientific_journal-3454 35 52 desired desire VERB american_scientific_journal-3454 35 53 performance performance NOUN american_scientific_journal-3454 35 54 . . PUNCT american_scientific_journal-3454 36 1 the the DET american_scientific_journal-3454 36 2 closed close VERB american_scientific_journal-3454 36 3 - - PUNCT american_scientific_journal-3454 36 4 loop loop NOUN american_scientific_journal-3454 36 5 system system NOUN american_scientific_journal-3454 36 6 dynamics dynamic NOUN american_scientific_journal-3454 36 7 is be AUX american_scientific_journal-3454 36 8 : : PUNCT american_scientific_journal-3454 36 9 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 36 10 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 36 11 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 36 12 ๐‘ฅ(๐‘ก๐‘ก)=๐ด๐ด๐‘๐‘ ๐‘ฅ(๐‘ก๐‘ก)=๐ด๐ด๐‘๐‘ PROPN american_scientific_journal-3454 36 13 ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 36 14 ) ) PUNCT american_scientific_journal-3454 36 15 ( ( PUNCT american_scientific_journal-3454 36 16 3 3 X american_scientific_journal-3454 36 17 ) ) PUNCT american_scientific_journal-3454 36 18 where where SCONJ american_scientific_journal-3454 36 19 ๐ด๐ด๐‘๐‘=(๐ผ๐ผ ๐ด๐ด๐‘๐‘=(๐ผ๐ผ NOUN american_scientific_journal-3454 36 20 + + CCONJ american_scientific_journal-3454 36 21 ๐ต๐ต๐พ๐พ)โˆ’1๐ด๐ด ๐ต๐ต๐พ๐พ)โˆ’1๐ด๐ด NUM american_scientific_journal-3454 36 22 ( ( PUNCT american_scientific_journal-3454 36 23 4 4 NUM american_scientific_journal-3454 36 24 ) ) PUNCT american_scientific_journal-3454 36 25 the the DET american_scientific_journal-3454 36 26 stabilizing stabilizing NOUN american_scientific_journal-3454 36 27 control control NOUN american_scientific_journal-3454 36 28 with with ADP american_scientific_journal-3454 36 29 good good ADJ american_scientific_journal-3454 36 30 dynamic dynamic ADJ american_scientific_journal-3454 36 31 behavior behavior NOUN american_scientific_journal-3454 36 32 is be AUX american_scientific_journal-3454 36 33 achieved achieve VERB american_scientific_journal-3454 36 34 by by ADP american_scientific_journal-3454 36 35 minimizing minimize VERB american_scientific_journal-3454 36 36 a a DET american_scientific_journal-3454 36 37 quadratic quadratic ADJ american_scientific_journal-3454 36 38 cost cost NOUN american_scientific_journal-3454 36 39 or or CCONJ american_scientific_journal-3454 36 40 performance performance NOUN american_scientific_journal-3454 36 41 index index NOUN american_scientific_journal-3454 36 42 of of ADP american_scientific_journal-3454 36 43 the the DET american_scientific_journal-3454 36 44 type type NOUN american_scientific_journal-3454 37 1 [ [ X american_scientific_journal-3454 37 2 1 1 NUM american_scientific_journal-3454 37 3 ] ] X american_scientific_journal-3454 37 4 : : PUNCT american_scientific_journal-3454 37 5 ๐ฝ๐ฝ( ๐ฝ๐ฝ( PROPN american_scientific_journal-3454 37 6 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 37 7 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 37 8 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 37 9 ๐‘ฅ(๐‘ก๐‘ก),๐ต๐ต(๐‘ก๐‘ก)=โˆซ ๐‘ฅ(๐‘ก๐‘ก),๐ต๐ต(๐‘ก๐‘ก)=โˆซ PUNCT american_scientific_journal-3454 37 10 ( ( PUNCT american_scientific_journal-3454 37 11 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 37 12 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 37 13 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 37 14 ๐‘ฅ(๐‘ก๐‘ก)๐‘„๐‘„๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก)๐‘„๐‘„๐‘ฅ๐‘ฅ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 37 15 ) ) PUNCT american_scientific_journal-3454 38 1 + + NUM american_scientific_journal-3454 38 2 ๐ต๐ต๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘…๐‘…๐ต๐ต(๐‘ก๐‘ก))๐‘‘๐‘‘๐‘ก๐‘กโˆž ๐ต๐ต๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘…๐‘…๐ต๐ต(๐‘ก๐‘ก))๐‘‘๐‘‘๐‘ก๐‘กโˆž PROPN american_scientific_journal-3454 38 3 0 0 NUM american_scientific_journal-3454 38 4 ( ( PUNCT american_scientific_journal-3454 38 5 5 5 X american_scientific_journal-3454 38 6 ) ) PUNCT american_scientific_journal-3454 38 7 substituting substitute VERB american_scientific_journal-3454 38 8 equation equation NOUN american_scientific_journal-3454 38 9 ( ( PUNCT american_scientific_journal-3454 38 10 2 2 NUM american_scientific_journal-3454 38 11 ) ) PUNCT american_scientific_journal-3454 38 12 into into ADP american_scientific_journal-3454 38 13 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 38 14 , , PUNCT american_scientific_journal-3454 38 15 the the DET american_scientific_journal-3454 38 16 performance performance NOUN american_scientific_journal-3454 38 17 index index NOUN american_scientific_journal-3454 38 18 is be AUX american_scientific_journal-3454 38 19 : : PUNCT american_scientific_journal-3454 38 20 american american ADJ american_scientific_journal-3454 38 21 scientific scientific ADJ american_scientific_journal-3454 38 22 research research PROPN american_scientific_journal-3454 38 23 journal journal NOUN american_scientific_journal-3454 38 24 for for ADP american_scientific_journal-3454 38 25 engineering engineering NOUN american_scientific_journal-3454 38 26 , , PUNCT american_scientific_journal-3454 38 27 technology technology NOUN american_scientific_journal-3454 38 28 , , PUNCT american_scientific_journal-3454 38 29 and and CCONJ american_scientific_journal-3454 38 30 sciences science NOUN american_scientific_journal-3454 38 31 ( ( PUNCT american_scientific_journal-3454 38 32 asrjets asrjet NOUN american_scientific_journal-3454 38 33 ) ) PUNCT american_scientific_journal-3454 38 34 ( ( PUNCT american_scientific_journal-3454 38 35 2017 2017 NUM american_scientific_journal-3454 38 36 ) ) PUNCT american_scientific_journal-3454 38 37 volume volume NOUN american_scientific_journal-3454 38 38 37 37 NUM american_scientific_journal-3454 38 39 , , PUNCT american_scientific_journal-3454 38 40 no no DET american_scientific_journal-3454 38 41 1 1 NUM american_scientific_journal-3454 38 42 , , PUNCT american_scientific_journal-3454 38 43 pp pp ADV american_scientific_journal-3454 38 44 118 118 NUM american_scientific_journal-3454 38 45 - - SYM american_scientific_journal-3454 38 46 128 128 NUM american_scientific_journal-3454 38 47 120 120 NUM american_scientific_journal-3454 38 48 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 38 49 = = PRON american_scientific_journal-3454 38 50 โˆซ โˆซ PROPN american_scientific_journal-3454 38 51 ( ( PUNCT american_scientific_journal-3454 38 52 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 38 53 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 38 54 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 38 55 ๐‘ฅ๐‘„๐‘„๐‘ฅ๐‘ฅ ๐‘ฅ๐‘„๐‘„๐‘ฅ๐‘ฅ PROPN american_scientific_journal-3454 38 56 + + CCONJ american_scientific_journal-3454 38 57 ( ( PUNCT american_scientific_journal-3454 38 58 ๐พ๐พ ๐พ๐พ PROPN american_scientific_journal-3454 38 59 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 38 60 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 38 61 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 38 62 ๐‘ฅ)๐‘‡๐‘‡๐‘…๐‘…(๐พ๐พ ๐‘ฅ)๐‘‡๐‘‡๐‘…๐‘…(๐พ๐พ SYM american_scientific_journal-3454 38 63 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 38 64 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 38 65 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 39 1 ๐‘ฅ))๐‘‘๐‘‘๐‘ก๐‘ก ๐‘ฅ))๐‘‘๐‘‘๐‘ก๐‘ก VERB american_scientific_journal-3454 39 2 = = SYM american_scientific_journal-3454 39 3 โˆซ โˆซ PROPN american_scientific_journal-3454 39 4 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 39 5 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 39 6 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 39 7 ๐‘ฅ๐‘‡๐‘‡(๐‘„๐‘„ ๐‘ฅ๐‘‡๐‘‡(๐‘„๐‘„ PROPN american_scientific_journal-3454 39 8 + + CCONJ american_scientific_journal-3454 40 1 ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ) ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ) PROPN american_scientific_journal-3454 40 2 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 40 3 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 40 4 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 40 5 ๐‘ฅ๐‘‘๐‘‘๐‘ก๐‘กโˆž ๐‘ฅ๐‘‘๐‘‘๐‘ก๐‘กโˆž NOUN american_scientific_journal-3454 40 6 0 0 NUM american_scientific_journal-3454 40 7 โˆž โˆž NUM american_scientific_journal-3454 40 8 0 0 NUM american_scientific_journal-3454 40 9 ( ( PUNCT american_scientific_journal-3454 40 10 6 6 NUM american_scientific_journal-3454 40 11 ) ) PUNCT american_scientific_journal-3454 40 12 suppose suppose VERB american_scientific_journal-3454 40 13 that that SCONJ american_scientific_journal-3454 40 14 a a DET american_scientific_journal-3454 40 15 constant constant ADJ american_scientific_journal-3454 40 16 positive positive ADJ american_scientific_journal-3454 40 17 semidefinite semidefinite NOUN american_scientific_journal-3454 40 18 symmetric symmetric ADJ american_scientific_journal-3454 40 19 matrix matrix NOUN american_scientific_journal-3454 40 20 ๐‘ƒ๐‘ƒ ๐‘ƒ๐‘ƒ NOUN american_scientific_journal-3454 40 21 that that PRON american_scientific_journal-3454 40 22 satisfy satisfy VERB american_scientific_journal-3454 40 23 equation equation NOUN american_scientific_journal-3454 40 24 ( ( PUNCT american_scientific_journal-3454 40 25 6 6 NUM american_scientific_journal-3454 40 26 ) ) PUNCT american_scientific_journal-3454 40 27 can can AUX american_scientific_journal-3454 40 28 be be AUX american_scientific_journal-3454 40 29 obtained obtain VERB american_scientific_journal-3454 40 30 , , PUNCT american_scientific_journal-3454 40 31 thus thus ADV american_scientific_journal-3454 40 32 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 40 33 ฬ‡ ฬ‡ VERB american_scientific_journal-3454 40 34 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 40 35 ๐‘ฅ๐‘‡๐‘‡(๐‘„๐‘„ ๐‘ฅ๐‘‡๐‘‡(๐‘„๐‘„ PROPN american_scientific_journal-3454 40 36 + + CCONJ american_scientific_journal-3454 41 1 ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ) ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ) PROPN american_scientific_journal-3454 41 2 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 41 3 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 41 4 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 41 5 ๐‘ฅ=โˆ’ ๐‘ฅ=โˆ’ NUM american_scientific_journal-3454 41 6 ๐‘‘๐‘‘ ๐‘‘๐‘‘ VERB american_scientific_journal-3454 41 7 ๐‘‘๐‘‘๐‘‘๐‘‘ ๐‘‘๐‘‘๐‘‘๐‘‘ NOUN american_scientific_journal-3454 41 8 ( ( PUNCT american_scientific_journal-3454 41 9 ๐‘ฅ๐‘ฅ๐‘‡๐‘‡๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ ๐‘ฅ๐‘ฅ๐‘‡๐‘‡๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ PROPN american_scientific_journal-3454 41 10 ) ) PUNCT american_scientific_journal-3454 41 11 = = SYM american_scientific_journal-3454 41 12 โˆ’ โˆ’ PROPN american_scientific_journal-3454 41 13 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 41 14 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 41 15 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 41 16 ๐‘ฅ๐‘‡๐‘‡๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ ๐‘ฅ๐‘‡๐‘‡๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ VERB american_scientific_journal-3454 41 17 โˆ’ โˆ’ PROPN american_scientific_journal-3454 41 18 ๐‘ฅ๐‘ฅ๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘ฅ๐‘ฅ๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 41 19 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 41 20 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 41 21 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 41 22 ๐‘ฅ ๐‘ฅ PROPN american_scientific_journal-3454 41 23 ( ( PUNCT american_scientific_journal-3454 41 24 7 7 NUM american_scientific_journal-3454 41 25 ) ) PUNCT american_scientific_journal-3454 41 26 then then ADV american_scientific_journal-3454 41 27 , , PUNCT american_scientific_journal-3454 41 28 equation equation NOUN american_scientific_journal-3454 41 29 ( ( PUNCT american_scientific_journal-3454 41 30 7 7 X american_scientific_journal-3454 41 31 ) ) PUNCT american_scientific_journal-3454 41 32 can can AUX american_scientific_journal-3454 41 33 be be AUX american_scientific_journal-3454 41 34 rewritten rewrite VERB american_scientific_journal-3454 41 35 as as ADP american_scientific_journal-3454 41 36 : : PUNCT american_scientific_journal-3454 41 37 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 41 38 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 41 39 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 41 40 ๐‘ฅ๐‘‡๐‘‡(๐‘„๐‘„ ๐‘ฅ๐‘‡๐‘‡(๐‘„๐‘„ PROPN american_scientific_journal-3454 41 41 + + CCONJ american_scientific_journal-3454 42 1 ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ) ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ) PROPN american_scientific_journal-3454 42 2 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 42 3 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 42 4 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 42 5 ๐‘ฅ ๐‘ฅ NOUN american_scientific_journal-3454 42 6 = = PUNCT american_scientific_journal-3454 42 7 โˆ’ โˆ’ PROPN american_scientific_journal-3454 42 8 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 42 9 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 42 10 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 42 11 ๐‘ฅ๐‘‡๐‘‡(๐‘ƒ๐‘ƒ๐ด๐ด๐‘๐‘โˆ’1 ๐‘ฅ๐‘‡๐‘‡(๐‘ƒ๐‘ƒ๐ด๐ด๐‘๐‘โˆ’1 NOUN american_scientific_journal-3454 42 12 + + CCONJ american_scientific_journal-3454 42 13 ๐ด๐ด๐‘๐‘โˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ) ๐ด๐ด๐‘๐‘โˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ) PROPN american_scientific_journal-3454 42 14 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 42 15 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 42 16 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 42 17 ๐‘ฅ ๐‘ฅ PROPN american_scientific_journal-3454 42 18 ( ( PUNCT american_scientific_journal-3454 42 19 8) 8) NUM american_scientific_journal-3454 42 20 where where SCONJ american_scientific_journal-3454 42 21 ๐ด๐ด๐‘๐‘โˆ’1 ๐ด๐ด๐‘๐‘โˆ’1 NOUN american_scientific_journal-3454 42 22 = = SYM american_scientific_journal-3454 42 23 ๐ด๐ดโˆ’1(๐ผ๐ผ ๐ด๐ดโˆ’1(๐ผ๐ผ PROPN american_scientific_journal-3454 42 24 + + CCONJ american_scientific_journal-3454 42 25 ๐ต๐ต๐พ๐พ ๐ต๐ต๐พ๐พ ADJ american_scientific_journal-3454 42 26 ) ) PUNCT american_scientific_journal-3454 43 1 = = SYM american_scientific_journal-3454 43 2 ๐ด๐ดโˆ’1 ๐ด๐ดโˆ’1 NOUN american_scientific_journal-3454 43 3 + + CCONJ american_scientific_journal-3454 43 4 ๐ด๐ดโˆ’1๐ต๐ต๐พ๐พ ๐ด๐ดโˆ’1๐ต๐ต๐พ๐พ PROPN american_scientific_journal-3454 43 5 ( ( PUNCT american_scientific_journal-3454 43 6 9 9 X american_scientific_journal-3454 43 7 ) ) PUNCT american_scientific_journal-3454 43 8 comparing compare VERB american_scientific_journal-3454 43 9 both both DET american_scientific_journal-3454 43 10 sides side NOUN american_scientific_journal-3454 43 11 of of ADP american_scientific_journal-3454 43 12 equation equation NOUN american_scientific_journal-3454 43 13 ( ( PUNCT american_scientific_journal-3454 43 14 8) 8) NUM american_scientific_journal-3454 43 15 , , PUNCT american_scientific_journal-3454 43 16 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘๐‘โˆ’1 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘๐‘โˆ’1 PROPN american_scientific_journal-3454 43 17 + + CCONJ american_scientific_journal-3454 43 18 ๐ด๐ด๐‘๐‘โˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐ด๐ด๐‘๐‘โˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 43 19 + + NUM american_scientific_journal-3454 43 20 ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ PROPN american_scientific_journal-3454 44 1 + + CCONJ american_scientific_journal-3454 45 1 ๐‘„๐‘„ ๐‘„๐‘„ PROPN american_scientific_journal-3454 45 2 = = SYM american_scientific_journal-3454 45 3 0 0 NUM american_scientific_journal-3454 45 4 ( ( PUNCT american_scientific_journal-3454 45 5 10 10 NUM american_scientific_journal-3454 45 6 ) ) PUNCT american_scientific_journal-3454 45 7 where where SCONJ american_scientific_journal-3454 45 8 ๐ด๐ด๐‘๐‘โˆ’๐‘‡๐‘‡ ๐ด๐ด๐‘๐‘โˆ’๐‘‡๐‘‡ NOUN american_scientific_journal-3454 45 9 = = SYM american_scientific_journal-3454 45 10 ๐พ๐พ๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡ ๐พ๐พ๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡ PUNCT american_scientific_journal-3454 45 11 + + NUM american_scientific_journal-3454 45 12 ๐ด๐ดโˆ’๐‘‡๐‘‡ ๐ด๐ดโˆ’๐‘‡๐‘‡ NUM american_scientific_journal-3454 45 13 ( ( PUNCT american_scientific_journal-3454 45 14 11 11 NUM american_scientific_journal-3454 45 15 ) ) PUNCT american_scientific_journal-3454 45 16 substituting substitute VERB american_scientific_journal-3454 45 17 equation equation NOUN american_scientific_journal-3454 45 18 ( ( PUNCT american_scientific_journal-3454 45 19 9 9 NUM american_scientific_journal-3454 45 20 ) ) PUNCT american_scientific_journal-3454 45 21 and and CCONJ american_scientific_journal-3454 45 22 ( ( PUNCT american_scientific_journal-3454 45 23 11 11 NUM american_scientific_journal-3454 45 24 ) ) PUNCT american_scientific_journal-3454 45 25 in in ADP american_scientific_journal-3454 45 26 equation equation NOUN american_scientific_journal-3454 45 27 ( ( PUNCT american_scientific_journal-3454 45 28 10 10 NUM american_scientific_journal-3454 45 29 ) ) PUNCT american_scientific_journal-3454 45 30 , , PUNCT american_scientific_journal-3454 45 31 ๐‘ƒ๐‘ƒ(๐ด๐ดโˆ’1 ๐‘ƒ๐‘ƒ(๐ด๐ดโˆ’1 PROPN american_scientific_journal-3454 45 32 + + CCONJ american_scientific_journal-3454 45 33 ๐ด๐ดโˆ’1๐ต๐ต๐พ๐พ ๐ด๐ดโˆ’1๐ต๐ต๐พ๐พ PROPN american_scientific_journal-3454 45 34 ) ) PUNCT american_scientific_journal-3454 45 35 + + CCONJ american_scientific_journal-3454 46 1 ( ( PUNCT american_scientific_journal-3454 46 2 ๐พ๐พ๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡ ๐พ๐พ๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡ PUNCT american_scientific_journal-3454 46 3 + + CCONJ american_scientific_journal-3454 46 4 ๐ด๐ดโˆ’๐‘‡๐‘‡)๐‘ƒ๐‘ƒ ๐ด๐ดโˆ’๐‘‡๐‘‡)๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 46 5 + + CCONJ american_scientific_journal-3454 46 6 ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ PROPN american_scientific_journal-3454 46 7 + + CCONJ american_scientific_journal-3454 46 8 ๐‘„๐‘„ ๐‘„๐‘„ PROPN american_scientific_journal-3454 46 9 = = SYM american_scientific_journal-3454 46 10 0 0 NUM american_scientific_journal-3454 47 1 ( ( PUNCT american_scientific_journal-3454 47 2 12 12 NUM american_scientific_journal-3454 47 3 ) ) PUNCT american_scientific_journal-3454 47 4 then then ADV american_scientific_journal-3454 47 5 , , PUNCT american_scientific_journal-3454 47 6 equation equation NOUN american_scientific_journal-3454 47 7 ( ( PUNCT american_scientific_journal-3454 47 8 12 12 NUM american_scientific_journal-3454 47 9 ) ) PUNCT american_scientific_journal-3454 47 10 can can AUX american_scientific_journal-3454 47 11 be be AUX american_scientific_journal-3454 47 12 rewritten rewrite VERB american_scientific_journal-3454 47 13 as as ADP american_scientific_journal-3454 47 14 : : PUNCT american_scientific_journal-3454 47 15 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1 PROPN american_scientific_journal-3454 47 16 + + CCONJ american_scientific_journal-3454 47 17 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1๐ต๐ต๐พ๐พ ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1๐ต๐ต๐พ๐พ VERB american_scientific_journal-3454 47 18 + + CCONJ american_scientific_journal-3454 47 19 ๐พ๐พ๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐พ๐พ๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 47 20 + + CCONJ american_scientific_journal-3454 47 21 ๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ADJ american_scientific_journal-3454 47 22 + + CCONJ american_scientific_journal-3454 47 23 ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ ๐พ๐พ๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ PROPN american_scientific_journal-3454 47 24 + + CCONJ american_scientific_journal-3454 47 25 ๐‘„๐‘„ ๐‘„๐‘„ PROPN american_scientific_journal-3454 47 26 = = SYM american_scientific_journal-3454 47 27 0 0 NUM american_scientific_journal-3454 48 1 ( ( PUNCT american_scientific_journal-3454 48 2 13 13 NUM american_scientific_journal-3454 48 3 ) ) PUNCT american_scientific_journal-3454 48 4 since since SCONJ american_scientific_journal-3454 48 5 ๐‘…๐‘… ๐‘…๐‘… PROPN american_scientific_journal-3454 48 6 is be AUX american_scientific_journal-3454 48 7 positive positive ADJ american_scientific_journal-3454 48 8 - - PUNCT american_scientific_journal-3454 48 9 definite definite ADJ american_scientific_journal-3454 48 10 symmetric symmetric ADJ american_scientific_journal-3454 48 11 matrix matrix NOUN american_scientific_journal-3454 48 12 , , PUNCT american_scientific_journal-3454 48 13 then then ADV american_scientific_journal-3454 48 14 ๐‘…๐‘… ๐‘…๐‘… PROPN american_scientific_journal-3454 48 15 = = PUNCT american_scientific_journal-3454 48 16 ๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡ ๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡ PROPN american_scientific_journal-3454 48 17 ( ( PUNCT american_scientific_journal-3454 48 18 14 14 NUM american_scientific_journal-3454 48 19 ) ) PUNCT american_scientific_journal-3454 48 20 where where SCONJ american_scientific_journal-3454 48 21 ๐‘‡๐‘‡ ๐‘‡๐‘‡ PROPN american_scientific_journal-3454 48 22 is be AUX american_scientific_journal-3454 48 23 a a DET american_scientific_journal-3454 48 24 nonsingular nonsingular ADJ american_scientific_journal-3454 48 25 matrix matrix NOUN american_scientific_journal-3454 48 26 . . PUNCT american_scientific_journal-3454 49 1 substituting substitute VERB american_scientific_journal-3454 49 2 equation equation NOUN american_scientific_journal-3454 49 3 ( ( PUNCT american_scientific_journal-3454 49 4 14 14 NUM american_scientific_journal-3454 49 5 ) ) PUNCT american_scientific_journal-3454 49 6 in in ADP american_scientific_journal-3454 49 7 equation equation NOUN american_scientific_journal-3454 49 8 ( ( PUNCT american_scientific_journal-3454 49 9 13 13 NUM american_scientific_journal-3454 49 10 ) ) PUNCT american_scientific_journal-3454 49 11 , , PUNCT american_scientific_journal-3454 49 12 yields yield NOUN american_scientific_journal-3454 49 13 : : PUNCT american_scientific_journal-3454 49 14 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1 PROPN american_scientific_journal-3454 49 15 + + X american_scientific_journal-3454 49 16 ๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ+(๐‘‡๐‘‡๐พ๐พ ๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ+(๐‘‡๐‘‡๐พ๐พ PROPN american_scientific_journal-3454 49 17 + + CCONJ american_scientific_journal-3454 49 18 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ)๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ)๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ PROPN american_scientific_journal-3454 49 19 + + NUM american_scientific_journal-3454 49 20 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ NOUN american_scientific_journal-3454 49 21 ) ) PUNCT american_scientific_journal-3454 49 22 โˆ’ โˆ’ NOUN american_scientific_journal-3454 49 23 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1๐ต๐ต๐‘‡๐‘‡โˆ’1๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1๐ต๐ต๐‘‡๐‘‡โˆ’1๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 50 1 + + NUM american_scientific_journal-3454 50 2 ๐‘„๐‘„ ๐‘„๐‘„ PROPN american_scientific_journal-3454 50 3 = = SYM american_scientific_journal-3454 50 4 0 0 NUM american_scientific_journal-3454 50 5 ( ( PUNCT american_scientific_journal-3454 50 6 15 15 NUM american_scientific_journal-3454 50 7 ) ) PUNCT american_scientific_journal-3454 50 8 the the DET american_scientific_journal-3454 50 9 minimization minimization NOUN american_scientific_journal-3454 50 10 of of ADP american_scientific_journal-3454 50 11 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 50 12 requires require VERB american_scientific_journal-3454 50 13 the the DET american_scientific_journal-3454 50 14 minimization minimization NOUN american_scientific_journal-3454 50 15 of of ADP american_scientific_journal-3454 50 16 the the DET american_scientific_journal-3454 50 17 following following NOUN american_scientific_journal-3454 50 18 : : PUNCT american_scientific_journal-3454 50 19 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 50 20 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 50 21 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 50 22 ๐‘ฅ๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ ๐‘ฅ๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ PROPN american_scientific_journal-3454 50 23 + + CCONJ american_scientific_journal-3454 50 24 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ)๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ)๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ SYM american_scientific_journal-3454 50 25 + + CCONJ american_scientific_journal-3454 50 26 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ) ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ) PROPN american_scientific_journal-3454 50 27 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 50 28 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 50 29 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 50 30 ๐‘ฅ ๐‘ฅ PROPN american_scientific_journal-3454 50 31 ( ( PUNCT american_scientific_journal-3454 50 32 16 16 NUM american_scientific_journal-3454 50 33 ) ) PUNCT american_scientific_journal-3454 50 34 since since SCONJ american_scientific_journal-3454 50 35 the the DET american_scientific_journal-3454 50 36 last last ADJ american_scientific_journal-3454 50 37 expression expression NOUN american_scientific_journal-3454 50 38 is be AUX american_scientific_journal-3454 50 39 nonnegative nonnegative ADJ american_scientific_journal-3454 50 40 , , PUNCT american_scientific_journal-3454 50 41 the the DET american_scientific_journal-3454 50 42 minimum minimum NOUN american_scientific_journal-3454 50 43 occurs occur VERB american_scientific_journal-3454 50 44 when when SCONJ american_scientific_journal-3454 50 45 it it PRON american_scientific_journal-3454 50 46 is be AUX american_scientific_journal-3454 50 47 zero zero NUM american_scientific_journal-3454 50 48 , , PUNCT american_scientific_journal-3454 50 49 then then ADV american_scientific_journal-3454 50 50 american american PROPN american_scientific_journal-3454 50 51 scientific scientific ADJ american_scientific_journal-3454 50 52 research research PROPN american_scientific_journal-3454 50 53 journal journal NOUN american_scientific_journal-3454 50 54 for for ADP american_scientific_journal-3454 50 55 engineering engineering NOUN american_scientific_journal-3454 50 56 , , PUNCT american_scientific_journal-3454 50 57 technology technology NOUN american_scientific_journal-3454 50 58 , , PUNCT american_scientific_journal-3454 50 59 and and CCONJ american_scientific_journal-3454 50 60 sciences science NOUN american_scientific_journal-3454 50 61 ( ( PUNCT american_scientific_journal-3454 50 62 asrjets asrjet NOUN american_scientific_journal-3454 50 63 ) ) PUNCT american_scientific_journal-3454 50 64 ( ( PUNCT american_scientific_journal-3454 50 65 2017 2017 NUM american_scientific_journal-3454 50 66 ) ) PUNCT american_scientific_journal-3454 50 67 volume volume NOUN american_scientific_journal-3454 50 68 37 37 NUM american_scientific_journal-3454 50 69 , , PUNCT american_scientific_journal-3454 50 70 no no DET american_scientific_journal-3454 50 71 1 1 NUM american_scientific_journal-3454 50 72 , , PUNCT american_scientific_journal-3454 50 73 pp pp ADV american_scientific_journal-3454 50 74 118 118 NUM american_scientific_journal-3454 50 75 - - SYM american_scientific_journal-3454 50 76 128 128 NUM american_scientific_journal-3454 50 77 121 121 NUM american_scientific_journal-3454 50 78 ๐‘‡๐‘‡๐พ๐พ ๐‘‡๐‘‡๐พ๐พ PROPN american_scientific_journal-3454 50 79 = = SYM american_scientific_journal-3454 50 80 โˆ’๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ โˆ’๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 50 81 ( ( PUNCT american_scientific_journal-3454 50 82 17 17 NUM american_scientific_journal-3454 50 83 ) ) PUNCT american_scientific_journal-3454 50 84 the the DET american_scientific_journal-3454 50 85 optimal optimal ADJ american_scientific_journal-3454 50 86 gain gain NOUN american_scientific_journal-3454 50 87 matrix matrix NOUN american_scientific_journal-3454 50 88 ๐พ๐พ ๐พ๐พ NOUN american_scientific_journal-3454 50 89 is be AUX american_scientific_journal-3454 50 90 : : PUNCT american_scientific_journal-3454 50 91 ๐พ๐พ ๐พ๐พ PROPN american_scientific_journal-3454 50 92 = = SYM american_scientific_journal-3454 50 93 โˆ’๐‘…๐‘…โˆ’1๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ โˆ’๐‘…๐‘…โˆ’1๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ NUM american_scientific_journal-3454 50 94 ( ( PUNCT american_scientific_journal-3454 50 95 18 18 NUM american_scientific_journal-3454 50 96 ) ) PUNCT american_scientific_journal-3454 50 97 finally finally ADV american_scientific_journal-3454 50 98 , , PUNCT american_scientific_journal-3454 50 99 the the DET american_scientific_journal-3454 50 100 optimal optimal ADJ american_scientific_journal-3454 50 101 stabilizing stabilizing NOUN american_scientific_journal-3454 50 102 control control NOUN american_scientific_journal-3454 50 103 law law NOUN american_scientific_journal-3454 50 104 is be AUX american_scientific_journal-3454 50 105 given give VERB american_scientific_journal-3454 50 106 by by ADP american_scientific_journal-3454 50 107 : : PUNCT american_scientific_journal-3454 50 108 ๐ต๐ต(๐‘ก๐‘ก ๐ต๐ต(๐‘ก๐‘ก PROPN american_scientific_journal-3454 50 109 ) ) PUNCT american_scientific_journal-3454 51 1 = = PUNCT american_scientific_journal-3454 51 2 ๐‘…๐‘…โˆ’1๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘…๐‘…โˆ’1๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ VERB american_scientific_journal-3454 51 3 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 51 4 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 51 5 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 51 6 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 51 7 ) ) PUNCT american_scientific_journal-3454 51 8 ( ( PUNCT american_scientific_journal-3454 51 9 19 19 NUM american_scientific_journal-3454 51 10 ) ) PUNCT american_scientific_journal-3454 51 11 the the DET american_scientific_journal-3454 51 12 matrix matrix NOUN american_scientific_journal-3454 51 13 ๐‘ƒ๐‘ƒ ๐‘ƒ๐‘ƒ ADV american_scientific_journal-3454 51 14 in in ADP american_scientific_journal-3454 51 15 equation equation NOUN american_scientific_journal-3454 51 16 ( ( PUNCT american_scientific_journal-3454 51 17 19 19 NUM american_scientific_journal-3454 51 18 ) ) PUNCT american_scientific_journal-3454 51 19 must must AUX american_scientific_journal-3454 51 20 satisfy satisfy VERB american_scientific_journal-3454 51 21 equation equation NOUN american_scientific_journal-3454 51 22 ( ( PUNCT american_scientific_journal-3454 51 23 13 13 NUM american_scientific_journal-3454 51 24 ) ) PUNCT american_scientific_journal-3454 51 25 or or CCONJ american_scientific_journal-3454 51 26 the the DET american_scientific_journal-3454 51 27 following follow VERB american_scientific_journal-3454 51 28 algebraic algebraic ADJ american_scientific_journal-3454 51 29 riccati riccati PROPN american_scientific_journal-3454 51 30 equation equation NOUN american_scientific_journal-3454 51 31 ( ( PUNCT american_scientific_journal-3454 51 32 are be AUX american_scientific_journal-3454 51 33 ): ): PUNCT american_scientific_journal-3454 51 34 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1 PROPN american_scientific_journal-3454 51 35 + + CCONJ american_scientific_journal-3454 51 36 ๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ VERB american_scientific_journal-3454 51 37 โˆ’ โˆ’ NUM american_scientific_journal-3454 51 38 ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1๐ต๐ต๐‘…๐‘…โˆ’1๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘ƒ๐‘ƒ๐ด๐ดโˆ’1๐ต๐ต๐‘…๐‘…โˆ’1๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ NUM american_scientific_journal-3454 52 1 + + NUM american_scientific_journal-3454 52 2 ๐‘„๐‘„ ๐‘„๐‘„ PROPN american_scientific_journal-3454 52 3 = = SYM american_scientific_journal-3454 52 4 0 0 NUM american_scientific_journal-3454 52 5 ( ( PUNCT american_scientific_journal-3454 52 6 20 20 NUM american_scientific_journal-3454 52 7 ) ) PUNCT american_scientific_journal-3454 52 8 2.2 2.2 NUM american_scientific_journal-3454 52 9 . . PUNCT american_scientific_journal-3454 53 1 ๐‘ฏ๐‘ฏ๐Ÿ๐Ÿ ๐‘ฏ๐‘ฏ๐Ÿ๐Ÿ ADJ american_scientific_journal-3454 53 2 state state NOUN american_scientific_journal-3454 53 3 derivative derivative ADJ american_scientific_journal-3454 53 4 feedback feedback NOUN american_scientific_journal-3454 53 5 problem problem NOUN american_scientific_journal-3454 53 6 formulation formulation NOUN american_scientific_journal-3454 53 7 consider consider VERB american_scientific_journal-3454 53 8 a a DET american_scientific_journal-3454 53 9 linear linear ADJ american_scientific_journal-3454 53 10 time time NOUN american_scientific_journal-3454 53 11 invariant invariant ADJ american_scientific_journal-3454 53 12 system system NOUN american_scientific_journal-3454 53 13 expressed express VERB american_scientific_journal-3454 53 14 by by ADP american_scientific_journal-3454 53 15 : : PUNCT american_scientific_journal-3454 53 16 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 53 17 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 53 18 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 53 19 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 53 20 ) ) PUNCT american_scientific_journal-3454 53 21 = = SYM american_scientific_journal-3454 54 1 ๐ด๐ด๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐ด๐ด๐‘ฅ๐‘ฅ(๐‘ก๐‘ก X american_scientific_journal-3454 54 2 ) ) PUNCT american_scientific_journal-3454 55 1 + + NUM american_scientific_journal-3454 55 2 ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก NOUN american_scientific_journal-3454 55 3 ) ) PUNCT american_scientific_journal-3454 55 4 + + NUM american_scientific_journal-3454 55 5 ๐ต๐ต2๐ต๐ต(๐‘ก๐‘ก ๐ต๐ต2๐ต๐ต(๐‘ก๐‘ก NOUN american_scientific_journal-3454 55 6 ) ) PUNCT american_scientific_journal-3454 55 7 ( ( PUNCT american_scientific_journal-3454 55 8 21 21 NUM american_scientific_journal-3454 55 9 ) ) PUNCT american_scientific_journal-3454 55 10 ๐‘’๐‘’(๐‘ก๐‘ก ๐‘’๐‘’(๐‘ก๐‘ก NOUN american_scientific_journal-3454 55 11 ) ) PUNCT american_scientific_journal-3454 55 12 = = SYM american_scientific_journal-3454 55 13 ๐ถ๐ถ1 ๐ถ๐ถ1 PROPN american_scientific_journal-3454 55 14 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 55 15 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 55 16 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 55 17 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 55 18 ) ) PUNCT american_scientific_journal-3454 56 1 + + NUM american_scientific_journal-3454 56 2 ๐ท๐ท12๐ต๐ต(๐‘ก๐‘ก ๐ท๐ท12๐ต๐ต(๐‘ก๐‘ก NOUN american_scientific_journal-3454 56 3 ) ) PUNCT american_scientific_journal-3454 56 4 ( ( PUNCT american_scientific_journal-3454 56 5 22 22 NUM american_scientific_journal-3454 56 6 ) ) PUNCT american_scientific_journal-3454 56 7 ๐‘๐‘(๐‘ก๐‘ก ๐‘๐‘(๐‘ก๐‘ก NUM american_scientific_journal-3454 56 8 ) ) PUNCT american_scientific_journal-3454 56 9 = = SYM american_scientific_journal-3454 56 10 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 56 11 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 56 12 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 56 13 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 56 14 ) ) PUNCT american_scientific_journal-3454 56 15 ( ( PUNCT american_scientific_journal-3454 56 16 23 23 NUM american_scientific_journal-3454 56 17 ) ) PUNCT american_scientific_journal-3454 56 18 the the DET american_scientific_journal-3454 56 19 following follow VERB american_scientific_journal-3454 56 20 assumptions assumption NOUN american_scientific_journal-3454 56 21 are be AUX american_scientific_journal-3454 56 22 made make VERB american_scientific_journal-3454 56 23 : : PUNCT american_scientific_journal-3454 57 1 1 1 X american_scientific_journal-3454 57 2 . . X american_scientific_journal-3454 57 3 the the DET american_scientific_journal-3454 57 4 system system NOUN american_scientific_journal-3454 57 5 matrix matrix NOUN american_scientific_journal-3454 57 6 ๐ด๐ด ๐ด๐ด PROPN american_scientific_journal-3454 57 7 is be AUX american_scientific_journal-3454 57 8 of of ADP american_scientific_journal-3454 57 9 full full ADJ american_scientific_journal-3454 57 10 rank rank NOUN american_scientific_journal-3454 57 11 . . PUNCT american_scientific_journal-3454 58 1 2 2 X american_scientific_journal-3454 58 2 . . X american_scientific_journal-3454 58 3 ( ( PUNCT american_scientific_journal-3454 58 4 ๐ด๐ด ๐ด๐ด PROPN american_scientific_journal-3454 58 5 , , PUNCT american_scientific_journal-3454 58 6 ๐ต๐ต1 ๐ต๐ต1 PROPN american_scientific_journal-3454 58 7 ) ) PUNCT american_scientific_journal-3454 58 8 and and CCONJ american_scientific_journal-3454 58 9 ( ( PUNCT american_scientific_journal-3454 58 10 ๐ด๐ด ๐ด๐ด PROPN american_scientific_journal-3454 58 11 , , PUNCT american_scientific_journal-3454 58 12 ๐ต๐ต2 ๐ต๐ต2 PROPN american_scientific_journal-3454 58 13 ) ) PUNCT american_scientific_journal-3454 58 14 are be AUX american_scientific_journal-3454 58 15 stabilizable stabilizable ADJ american_scientific_journal-3454 58 16 . . PUNCT american_scientific_journal-3454 59 1 3 3 X american_scientific_journal-3454 59 2 . . X american_scientific_journal-3454 59 3 ( ( PUNCT american_scientific_journal-3454 59 4 ๐ถ๐ถ1 ๐ถ๐ถ1 PROPN american_scientific_journal-3454 59 5 , , PUNCT american_scientific_journal-3454 59 6 ๐ด๐ด ๐ด๐ด PROPN american_scientific_journal-3454 59 7 ) ) PUNCT american_scientific_journal-3454 59 8 is be AUX american_scientific_journal-3454 59 9 detectable detectable ADJ american_scientific_journal-3454 59 10 . . PUNCT american_scientific_journal-3454 60 1 4 4 X american_scientific_journal-3454 60 2 . . X american_scientific_journal-3454 60 3 all all DET american_scientific_journal-3454 60 4 state state NOUN american_scientific_journal-3454 60 5 derivative derivative ADJ american_scientific_journal-3454 60 6 measurements measurement NOUN american_scientific_journal-3454 60 7 are be AUX american_scientific_journal-3454 60 8 possible possible ADJ american_scientific_journal-3454 60 9 . . PUNCT american_scientific_journal-3454 61 1 the the DET american_scientific_journal-3454 61 2 objective objective NOUN american_scientific_journal-3454 61 3 of of ADP american_scientific_journal-3454 61 4 this this DET american_scientific_journal-3454 61 5 work work NOUN american_scientific_journal-3454 61 6 is be AUX american_scientific_journal-3454 61 7 to to PART american_scientific_journal-3454 61 8 obtain obtain VERB american_scientific_journal-3454 61 9 a a DET american_scientific_journal-3454 61 10 scalar scalar ADJ american_scientific_journal-3454 61 11 state state NOUN american_scientific_journal-3454 61 12 derivative derivative ADJ american_scientific_journal-3454 61 13 feedback feedback NOUN american_scientific_journal-3454 61 14 control control NOUN american_scientific_journal-3454 61 15 law law NOUN american_scientific_journal-3454 61 16 described describe VERB american_scientific_journal-3454 61 17 by by ADP american_scientific_journal-3454 61 18 : : PUNCT american_scientific_journal-3454 61 19 ๐ต๐ต(๐‘ก๐‘ก ๐ต๐ต(๐‘ก๐‘ก PROPN american_scientific_journal-3454 61 20 ) ) PUNCT american_scientific_journal-3454 61 21 = = SYM american_scientific_journal-3454 61 22 โˆ’๐พ๐พ โˆ’๐พ๐พ NUM american_scientific_journal-3454 61 23 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 61 24 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 61 25 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 61 26 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 61 27 ) ) PUNCT american_scientific_journal-3454 61 28 ( ( PUNCT american_scientific_journal-3454 61 29 24 24 NUM american_scientific_journal-3454 61 30 ) ) PUNCT american_scientific_journal-3454 61 31 assuming assume VERB american_scientific_journal-3454 61 32 that that SCONJ american_scientific_journal-3454 61 33 ๐‘‘๐‘‘(๐‘ก๐‘ก ๐‘‘๐‘‘(๐‘ก๐‘ก NOUN american_scientific_journal-3454 61 34 ) ) PUNCT american_scientific_journal-3454 61 35 is be AUX american_scientific_journal-3454 61 36 the the DET american_scientific_journal-3454 61 37 white white ADJ american_scientific_journal-3454 61 38 noise noise PROPN american_scientific_journal-3454 61 39 vector vector NOUN american_scientific_journal-3454 61 40 with with ADP american_scientific_journal-3454 61 41 unit unit NOUN american_scientific_journal-3454 61 42 intensity intensity NOUN american_scientific_journal-3454 61 43 , , PUNCT american_scientific_journal-3454 61 44 then then ADV american_scientific_journal-3454 61 45 [ [ X american_scientific_journal-3454 61 46 11 11 NUM american_scientific_journal-3454 61 47 ] ] SYM american_scientific_journal-3454 61 48 : : PUNCT american_scientific_journal-3454 61 49 โ€–๐‘‡๐‘‡๐‘’๐‘’๐‘‘๐‘‘โ€–๐ป๐ป2 โ€–๐‘‡๐‘‡๐‘’๐‘’๐‘‘๐‘‘โ€–๐ป๐ป2 ADV american_scientific_journal-3454 61 50 2 2 NUM american_scientific_journal-3454 61 51 = = SYM american_scientific_journal-3454 61 52 ๐ธ๐ธ(๐‘’๐‘’๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘’๐‘’(๐‘ก๐‘ก ๐ธ๐ธ(๐‘’๐‘’๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘’๐‘’(๐‘ก๐‘ก PROPN american_scientific_journal-3454 61 53 ) ) PUNCT american_scientific_journal-3454 61 54 ) ) PUNCT american_scientific_journal-3454 61 55 ( ( PUNCT american_scientific_journal-3454 61 56 25 25 NUM american_scientific_journal-3454 61 57 ) ) PUNCT american_scientific_journal-3454 61 58 where where SCONJ american_scientific_journal-3454 61 59 ๐‘‡๐‘‡๐‘’๐‘’๐‘‘๐‘‘ ๐‘‡๐‘‡๐‘’๐‘’๐‘‘๐‘‘ PROPN american_scientific_journal-3454 61 60 represents represent VERB american_scientific_journal-3454 61 61 the the DET american_scientific_journal-3454 61 62 overall overall ADJ american_scientific_journal-3454 61 63 transfer transfer NOUN american_scientific_journal-3454 61 64 function function NOUN american_scientific_journal-3454 61 65 ๐‘‘๐‘‘(๐‘ก๐‘ก ๐‘‘๐‘‘(๐‘ก๐‘ก NOUN american_scientific_journal-3454 61 66 ) ) PUNCT american_scientific_journal-3454 61 67 to to ADP american_scientific_journal-3454 61 68 ๐‘’๐‘’(๐‘ก๐‘ก ๐‘’๐‘’(๐‘ก๐‘ก NOUN american_scientific_journal-3454 61 69 ) ) PUNCT american_scientific_journal-3454 61 70 , , PUNCT american_scientific_journal-3454 61 71 then then ADV american_scientific_journal-3454 61 72 american american PROPN american_scientific_journal-3454 61 73 scientific scientific ADJ american_scientific_journal-3454 61 74 research research PROPN american_scientific_journal-3454 61 75 journal journal NOUN american_scientific_journal-3454 61 76 for for ADP american_scientific_journal-3454 61 77 engineering engineering NOUN american_scientific_journal-3454 61 78 , , PUNCT american_scientific_journal-3454 61 79 technology technology NOUN american_scientific_journal-3454 61 80 , , PUNCT american_scientific_journal-3454 61 81 and and CCONJ american_scientific_journal-3454 61 82 sciences science NOUN american_scientific_journal-3454 61 83 ( ( PUNCT american_scientific_journal-3454 61 84 asrjets asrjet NOUN american_scientific_journal-3454 61 85 ) ) PUNCT american_scientific_journal-3454 61 86 ( ( PUNCT american_scientific_journal-3454 61 87 2017 2017 NUM american_scientific_journal-3454 61 88 ) ) PUNCT american_scientific_journal-3454 61 89 volume volume NOUN american_scientific_journal-3454 61 90 37 37 NUM american_scientific_journal-3454 61 91 , , PUNCT american_scientific_journal-3454 61 92 no no DET american_scientific_journal-3454 61 93 1 1 NUM american_scientific_journal-3454 61 94 , , PUNCT american_scientific_journal-3454 61 95 pp pp ADV american_scientific_journal-3454 61 96 118 118 NUM american_scientific_journal-3454 61 97 - - SYM american_scientific_journal-3454 61 98 128 128 NUM american_scientific_journal-3454 61 99 122 122 NUM american_scientific_journal-3454 61 100 ๐‘’๐‘’๐‘‡๐‘‡๐‘’๐‘’ ๐‘’๐‘’๐‘‡๐‘‡๐‘’๐‘’ PROPN american_scientific_journal-3454 61 101 = = SYM american_scientific_journal-3454 61 102 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 61 103 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 61 104 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 61 105 ๐‘ฅ๐‘‡๐‘‡๐ถ๐ถ1๐‘‡๐‘‡๐ถ๐ถ1 ๐‘ฅ๐‘‡๐‘‡๐ถ๐ถ1๐‘‡๐‘‡๐ถ๐ถ1 PROPN american_scientific_journal-3454 61 106 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 61 107 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 61 108 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 61 109 ๐‘ฅ ๐‘ฅ PROPN american_scientific_journal-3454 61 110 + + PROPN american_scientific_journal-3454 61 111 2 2 NUM american_scientific_journal-3454 61 112 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 61 113 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 61 114 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 62 1 ๐‘ฅ๐‘‡๐‘‡๐ถ๐ถ1๐‘‡๐‘‡๐ท๐ท12๐ต๐ต ๐‘ฅ๐‘‡๐‘‡๐ถ๐ถ1๐‘‡๐‘‡๐ท๐ท12๐ต๐ต PROPN american_scientific_journal-3454 62 2 + + X american_scientific_journal-3454 62 3 ๐ต๐ต๐‘‡๐‘‡๐ท๐ท12๐‘‡๐‘‡๐ท๐ท12๐ต๐ต ๐ต๐ต๐‘‡๐‘‡๐ท๐ท12๐‘‡๐‘‡๐ท๐ท12๐ต๐ต PROPN american_scientific_journal-3454 62 4 ( ( PUNCT american_scientific_journal-3454 62 5 26 26 NUM american_scientific_journal-3454 62 6 ) ) PUNCT american_scientific_journal-3454 62 7 the the DET american_scientific_journal-3454 62 8 minimization minimization NOUN american_scientific_journal-3454 62 9 of of ADP american_scientific_journal-3454 62 10 โ€–๐‘‡๐‘‡๐‘’๐‘’๐‘‘๐‘‘โ€–๐ป๐ป2 โ€–๐‘‡๐‘‡๐‘’๐‘’๐‘‘๐‘‘โ€–๐ป๐ป2 ADV american_scientific_journal-3454 62 11 2 2 NUM american_scientific_journal-3454 62 12 is be AUX american_scientific_journal-3454 62 13 equivalent equivalent ADJ american_scientific_journal-3454 62 14 to to ADP american_scientific_journal-3454 62 15 the the DET american_scientific_journal-3454 62 16 solution solution NOUN american_scientific_journal-3454 62 17 of of ADP american_scientific_journal-3454 62 18 the the DET american_scientific_journal-3454 62 19 stochastic stochastic ADJ american_scientific_journal-3454 62 20 regulator regulator NOUN american_scientific_journal-3454 62 21 problem problem NOUN american_scientific_journal-3454 62 22 by by ADP american_scientific_journal-3454 62 23 setting set VERB american_scientific_journal-3454 62 24 : : PUNCT american_scientific_journal-3454 62 25 ๐‘„๐‘„ ๐‘„๐‘„ PROPN american_scientific_journal-3454 62 26 = = SYM american_scientific_journal-3454 62 27 ๐ถ๐ถ1๐‘‡๐‘‡๐ถ๐ถ1 ๐ถ๐ถ1๐‘‡๐‘‡๐ถ๐ถ1 ADJ american_scientific_journal-3454 62 28 , , PUNCT american_scientific_journal-3454 62 29 ๐‘๐‘ ๐‘๐‘ PROPN american_scientific_journal-3454 62 30 = = SYM american_scientific_journal-3454 62 31 ๐ถ๐ถ1๐‘‡๐‘‡๐ท๐ท12 ๐ถ๐ถ1๐‘‡๐‘‡๐ท๐ท12 NOUN american_scientific_journal-3454 62 32 , , PUNCT american_scientific_journal-3454 62 33 ๐‘…๐‘… ๐‘…๐‘… PROPN american_scientific_journal-3454 62 34 = = PUNCT american_scientific_journal-3454 62 35 ๐ท๐ท12๐‘‡๐‘‡๐ท๐ท12 ๐ท๐ท12๐‘‡๐‘‡๐ท๐ท12 PROPN american_scientific_journal-3454 62 36 then then ADV american_scientific_journal-3454 62 37 ๐ธ๐ธ ๐ธ๐ธ PROPN american_scientific_journal-3454 62 38 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 62 39 ๐‘’๐‘’๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘’๐‘’(๐‘ก๐‘ก ๐‘’๐‘’๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘’๐‘’(๐‘ก๐‘ก PROPN american_scientific_journal-3454 62 40 ) ) PUNCT american_scientific_journal-3454 62 41 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 62 42 = = SYM american_scientific_journal-3454 62 43 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 62 44 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 62 45 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 62 46 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 62 47 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 62 48 ๐‘ฅ(๐‘ก๐‘ก),๐ต๐ต(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก),๐ต๐ต(๐‘ก๐‘ก PROPN american_scientific_journal-3454 62 49 ) ) PUNCT american_scientific_journal-3454 62 50 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 62 51 = = SYM american_scientific_journal-3454 62 52 โˆซ โˆซ PROPN american_scientific_journal-3454 62 53 ( ( PUNCT american_scientific_journal-3454 62 54 โˆž โˆž PROPN american_scientific_journal-3454 62 55 0 0 NUM american_scientific_journal-3454 62 56 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 62 57 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 62 58 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 62 59 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘„๐‘„๐‘ฅ๐‘ฅ(t ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘„๐‘„๐‘ฅ๐‘ฅ(t NOUN american_scientific_journal-3454 62 60 ) ) PUNCT american_scientific_journal-3454 62 61 + + CCONJ american_scientific_journal-3454 62 62 2 2 NUM american_scientific_journal-3454 62 63 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 62 64 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 62 65 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 62 66 ๐‘ฅ๐‘‡๐‘‡(t)๐‘๐‘๐ต๐ต(t ๐‘ฅ๐‘‡๐‘‡(t)๐‘๐‘๐ต๐ต(t NOUN american_scientific_journal-3454 62 67 ) ) PUNCT american_scientific_journal-3454 63 1 + + CCONJ american_scientific_journal-3454 63 2 ๐ต๐ต๐‘‡๐‘‡(t)๐‘…๐‘…๐ต๐ต(t))๐‘‘๐‘‘๐‘ก๐‘ก ๐ต๐ต๐‘‡๐‘‡(t)๐‘…๐‘…๐ต๐ต(t))๐‘‘๐‘‘๐‘ก๐‘ก PROPN american_scientific_journal-3454 63 3 ( ( PUNCT american_scientific_journal-3454 63 4 27 27 NUM american_scientific_journal-3454 63 5 ) ) PUNCT american_scientific_journal-3454 63 6 and and CCONJ american_scientific_journal-3454 63 7 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 63 8 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 63 9 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 63 10 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 63 11 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 63 12 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 63 13 ) ) PUNCT american_scientific_journal-3454 63 14 , , PUNCT american_scientific_journal-3454 63 15 ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 63 16 ) ) PUNCT american_scientific_journal-3454 63 17 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 63 18 = = SYM american_scientific_journal-3454 63 19 โˆซ โˆซ PROPN american_scientific_journal-3454 63 20 ( ( PUNCT american_scientific_journal-3454 63 21 โˆž โˆž PROPN american_scientific_journal-3454 63 22 0 0 NUM american_scientific_journal-3454 63 23 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 63 24 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 63 25 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 63 26 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘„๐‘„๐‘š๐‘š ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘„๐‘„๐‘š๐‘š PROPN american_scientific_journal-3454 63 27 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 63 28 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 63 29 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 63 30 ๐‘ฅ(t ๐‘ฅ(t PROPN american_scientific_journal-3454 63 31 ) ) PUNCT american_scientific_journal-3454 64 1 + + CCONJ american_scientific_journal-3454 64 2 ๐‘ฃ๐‘ฃ๐‘‡๐‘‡(t)๐‘…๐‘…๐‘ฃ๐‘ฃ(t))๐‘‘๐‘‘๐‘ก๐‘ก ๐‘ฃ๐‘ฃ๐‘‡๐‘‡(t)๐‘…๐‘…๐‘ฃ๐‘ฃ(t))๐‘‘๐‘‘๐‘ก๐‘ก NUM american_scientific_journal-3454 64 3 ( ( PUNCT american_scientific_journal-3454 64 4 28 28 NUM american_scientific_journal-3454 64 5 ) ) PUNCT american_scientific_journal-3454 64 6 where where SCONJ american_scientific_journal-3454 64 7 ๐‘„๐‘„๐‘š๐‘š ๐‘„๐‘„๐‘š๐‘š PROPN american_scientific_journal-3454 64 8 = = PUNCT american_scientific_journal-3454 65 1 ๐‘„๐‘„ ๐‘„๐‘„ PROPN american_scientific_journal-3454 65 2 โˆ’ โˆ’ PROPN american_scientific_journal-3454 65 3 ๐‘๐‘๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ ๐‘๐‘๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ NOUN american_scientific_journal-3454 65 4 ( ( PUNCT american_scientific_journal-3454 65 5 29 29 NUM american_scientific_journal-3454 65 6 ) ) PUNCT american_scientific_journal-3454 65 7 ๐‘ฃ๐‘ฃ(t ๐‘ฃ๐‘ฃ(t NOUN american_scientific_journal-3454 65 8 ) ) PUNCT american_scientific_journal-3454 65 9 = = SYM american_scientific_journal-3454 65 10 ๐ต๐ต(t ๐ต๐ต(t NOUN american_scientific_journal-3454 65 11 ) ) PUNCT american_scientific_journal-3454 65 12 + + CCONJ american_scientific_journal-3454 65 13 ๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ ๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ SYM american_scientific_journal-3454 65 14 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 65 15 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 65 16 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 65 17 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 65 18 ) ) PUNCT american_scientific_journal-3454 65 19 ( ( PUNCT american_scientific_journal-3454 65 20 30 30 NUM american_scientific_journal-3454 65 21 ) ) PUNCT american_scientific_journal-3454 65 22 consequently consequently ADV american_scientific_journal-3454 65 23 , , PUNCT american_scientific_journal-3454 65 24 the the DET american_scientific_journal-3454 65 25 system system NOUN american_scientific_journal-3454 65 26 in in ADP american_scientific_journal-3454 65 27 equation equation NOUN american_scientific_journal-3454 65 28 ( ( PUNCT american_scientific_journal-3454 65 29 21 21 NUM american_scientific_journal-3454 65 30 ) ) PUNCT american_scientific_journal-3454 65 31 will will AUX american_scientific_journal-3454 65 32 be be AUX american_scientific_journal-3454 65 33 rewritten rewrite VERB american_scientific_journal-3454 65 34 as as ADP american_scientific_journal-3454 65 35 : : PUNCT american_scientific_journal-3454 65 36 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 65 37 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 65 38 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 65 39 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 65 40 ) ) PUNCT american_scientific_journal-3454 65 41 = = SYM american_scientific_journal-3454 65 42 ๐ด๐ด๐‘š๐‘š๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐ด๐ด๐‘š๐‘š๐‘ฅ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 65 43 ) ) PUNCT american_scientific_journal-3454 66 1 + + CCONJ american_scientific_journal-3454 66 2 ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก NOUN american_scientific_journal-3454 66 3 ) ) PUNCT american_scientific_journal-3454 67 1 + + CCONJ american_scientific_journal-3454 67 2 ๐ต๐ต2๐‘ฃ๐‘ฃ(๐‘ก๐‘ก ๐ต๐ต2๐‘ฃ๐‘ฃ(๐‘ก๐‘ก X american_scientific_journal-3454 67 3 ) ) PUNCT american_scientific_journal-3454 67 4 ( ( PUNCT american_scientific_journal-3454 67 5 31 31 NUM american_scientific_journal-3454 67 6 ) ) PUNCT american_scientific_journal-3454 67 7 where where SCONJ american_scientific_journal-3454 67 8 ๐ด๐ด๐‘š๐‘š ๐ด๐ด๐‘š๐‘š PROPN american_scientific_journal-3454 67 9 = = SYM american_scientific_journal-3454 67 10 ๐ด๐ด ๐ด๐ด PROPN american_scientific_journal-3454 67 11 โˆ’ โˆ’ PROPN american_scientific_journal-3454 67 12 ๐ต๐ต2๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ ๐ต๐ต2๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ NOUN american_scientific_journal-3454 67 13 ( ( PUNCT american_scientific_journal-3454 67 14 32 32 NUM american_scientific_journal-3454 67 15 ) ) PUNCT american_scientific_journal-3454 67 16 in in ADP american_scientific_journal-3454 67 17 term term NOUN american_scientific_journal-3454 67 18 of of ADP american_scientific_journal-3454 67 19 ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 67 20 ) ) PUNCT american_scientific_journal-3454 67 21 and and CCONJ american_scientific_journal-3454 67 22 from from ADP american_scientific_journal-3454 67 23 equation equation NOUN american_scientific_journal-3454 67 24 ( ( PUNCT american_scientific_journal-3454 67 25 30 30 NUM american_scientific_journal-3454 67 26 ) ) PUNCT american_scientific_journal-3454 67 27 , , PUNCT american_scientific_journal-3454 67 28 the the DET american_scientific_journal-3454 67 29 optimal optimal ADJ american_scientific_journal-3454 67 30 state state NOUN american_scientific_journal-3454 67 31 derivative derivative ADJ american_scientific_journal-3454 67 32 feedback feedback NOUN american_scientific_journal-3454 67 33 is be AUX american_scientific_journal-3454 67 34 : : PUNCT american_scientific_journal-3454 67 35 ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 67 36 ) ) PUNCT american_scientific_journal-3454 67 37 = = SYM american_scientific_journal-3454 67 38 โˆ’๐พ๐พ๐‘š๐‘š โˆ’๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 67 39 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 67 40 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 67 41 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 67 42 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 67 43 ) ) PUNCT american_scientific_journal-3454 67 44 ( ( PUNCT american_scientific_journal-3454 67 45 33 33 NUM american_scientific_journal-3454 67 46 ) ) PUNCT american_scientific_journal-3454 67 47 where where SCONJ american_scientific_journal-3454 67 48 ๐พ๐พ๐‘š๐‘š ๐พ๐พ๐‘š๐‘š VERB american_scientific_journal-3454 67 49 = = PUNCT american_scientific_journal-3454 67 50 ๐พ๐พ ๐พ๐พ PROPN american_scientific_journal-3454 67 51 โˆ’ โˆ’ NOUN american_scientific_journal-3454 67 52 ๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ ๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ NUM american_scientific_journal-3454 67 53 ( ( PUNCT american_scientific_journal-3454 67 54 34 34 NUM american_scientific_journal-3454 67 55 ) ) PUNCT american_scientific_journal-3454 67 56 substitute substitute NOUN american_scientific_journal-3454 67 57 equation equation NOUN american_scientific_journal-3454 67 58 ( ( PUNCT american_scientific_journal-3454 67 59 33 33 NUM american_scientific_journal-3454 67 60 ) ) PUNCT american_scientific_journal-3454 67 61 in in ADP american_scientific_journal-3454 67 62 equation equation NOUN american_scientific_journal-3454 67 63 ( ( PUNCT american_scientific_journal-3454 67 64 31 31 NUM american_scientific_journal-3454 67 65 ) ) PUNCT american_scientific_journal-3454 67 66 , , PUNCT american_scientific_journal-3454 67 67 the the DET american_scientific_journal-3454 67 68 system system NOUN american_scientific_journal-3454 67 69 equation equation NOUN american_scientific_journal-3454 67 70 will will AUX american_scientific_journal-3454 67 71 be be AUX american_scientific_journal-3454 67 72 : : PUNCT american_scientific_journal-3454 67 73 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 67 74 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 67 75 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 67 76 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 67 77 ) ) PUNCT american_scientific_journal-3454 67 78 = = SYM american_scientific_journal-3454 67 79 ๐ด๐ด๐‘š๐‘š๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐ด๐ด๐‘š๐‘š๐‘ฅ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 67 80 ) ) PUNCT american_scientific_journal-3454 68 1 + + CCONJ american_scientific_journal-3454 69 1 ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก NOUN american_scientific_journal-3454 69 2 ) ) PUNCT american_scientific_journal-3454 69 3 โˆ’ โˆ’ PROPN american_scientific_journal-3454 69 4 ๐ต๐ต2k๐‘š๐‘š ๐ต๐ต2k๐‘š๐‘š PROPN american_scientific_journal-3454 69 5 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 69 6 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 69 7 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 69 8 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 69 9 ) ) PUNCT american_scientific_journal-3454 69 10 = = SYM american_scientific_journal-3454 69 11 ๐ด๐ด๐‘›๐‘›๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐ด๐ด๐‘›๐‘›๐‘ฅ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 69 12 ) ) PUNCT american_scientific_journal-3454 70 1 + + CCONJ american_scientific_journal-3454 70 2 ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก NOUN american_scientific_journal-3454 70 3 ) ) PUNCT american_scientific_journal-3454 70 4 ( ( PUNCT american_scientific_journal-3454 70 5 35 35 NUM american_scientific_journal-3454 70 6 ) ) PUNCT american_scientific_journal-3454 70 7 where where SCONJ american_scientific_journal-3454 70 8 ๐ด๐ด๐‘›๐‘› ๐ด๐ด๐‘›๐‘› NOUN american_scientific_journal-3454 70 9 = = PUNCT american_scientific_journal-3454 70 10 ( ( PUNCT american_scientific_journal-3454 70 11 ๐ผ๐ผ ๐ผ๐ผ PROPN american_scientific_journal-3454 70 12 + + NUM american_scientific_journal-3454 70 13 ๐ต๐ต2k๐‘š๐‘š)โˆ’1๐ด๐ด๐‘š๐‘š ๐ต๐ต2k๐‘š๐‘š)โˆ’1๐ด๐ด๐‘š๐‘š NUM american_scientific_journal-3454 70 14 ( ( PUNCT american_scientific_journal-3454 70 15 36 36 NUM american_scientific_journal-3454 70 16 ) ) PUNCT american_scientific_journal-3454 70 17 american american ADJ american_scientific_journal-3454 70 18 scientific scientific ADJ american_scientific_journal-3454 70 19 research research NOUN american_scientific_journal-3454 70 20 journal journal NOUN american_scientific_journal-3454 70 21 for for ADP american_scientific_journal-3454 70 22 engineering engineering NOUN american_scientific_journal-3454 70 23 , , PUNCT american_scientific_journal-3454 70 24 technology technology NOUN american_scientific_journal-3454 70 25 , , PUNCT american_scientific_journal-3454 70 26 and and CCONJ american_scientific_journal-3454 70 27 sciences science NOUN american_scientific_journal-3454 70 28 ( ( PUNCT american_scientific_journal-3454 70 29 asrjets asrjet NOUN american_scientific_journal-3454 70 30 ) ) PUNCT american_scientific_journal-3454 70 31 ( ( PUNCT american_scientific_journal-3454 70 32 2017 2017 NUM american_scientific_journal-3454 70 33 ) ) PUNCT american_scientific_journal-3454 70 34 volume volume NOUN american_scientific_journal-3454 70 35 37 37 NUM american_scientific_journal-3454 70 36 , , PUNCT american_scientific_journal-3454 70 37 no no DET american_scientific_journal-3454 70 38 1 1 NUM american_scientific_journal-3454 70 39 , , PUNCT american_scientific_journal-3454 70 40 pp pp ADV american_scientific_journal-3454 70 41 118 118 NUM american_scientific_journal-3454 70 42 - - SYM american_scientific_journal-3454 70 43 128 128 NUM american_scientific_journal-3454 70 44 123 123 NUM american_scientific_journal-3454 70 45 substitute substitute NOUN american_scientific_journal-3454 70 46 equation equation NOUN american_scientific_journal-3454 70 47 ( ( PUNCT american_scientific_journal-3454 70 48 33 33 NUM american_scientific_journal-3454 70 49 ) ) PUNCT american_scientific_journal-3454 70 50 in in ADP american_scientific_journal-3454 70 51 equation equation NOUN american_scientific_journal-3454 70 52 ( ( PUNCT american_scientific_journal-3454 70 53 28 28 NUM american_scientific_journal-3454 70 54 ) ) PUNCT american_scientific_journal-3454 70 55 , , PUNCT american_scientific_journal-3454 70 56 the the DET american_scientific_journal-3454 70 57 objective objective ADJ american_scientific_journal-3454 70 58 function function NOUN american_scientific_journal-3454 70 59 will will AUX american_scientific_journal-3454 70 60 be be AUX american_scientific_journal-3454 70 61 : : PUNCT american_scientific_journal-3454 70 62 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 70 63 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 64 x(๐‘ก๐‘ก x(๐‘ก๐‘ก NOUN american_scientific_journal-3454 70 65 ) ) PUNCT american_scientific_journal-3454 70 66 , , PUNCT american_scientific_journal-3454 70 67 ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 70 68 ) ) PUNCT american_scientific_journal-3454 70 69 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 70 = = SYM american_scientific_journal-3454 70 71 โˆซ โˆซ PROPN american_scientific_journal-3454 70 72 ( ( PUNCT american_scientific_journal-3454 70 73 โˆž โˆž PROPN american_scientific_journal-3454 70 74 0 0 NUM american_scientific_journal-3454 70 75 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 76 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 70 77 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 78 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)(๐‘„๐‘„๐‘š๐‘š ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)(๐‘„๐‘„๐‘š๐‘š PROPN american_scientific_journal-3454 70 79 + + X american_scientific_journal-3454 70 80 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š)๐‘ฅ๐‘ฅ(t))๐‘‘๐‘‘๐‘ก๐‘ก ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š)๐‘ฅ๐‘ฅ(t))๐‘‘๐‘‘๐‘ก๐‘ก NUM american_scientific_journal-3454 70 81 ( ( PUNCT american_scientific_journal-3454 70 82 37 37 NUM american_scientific_journal-3454 70 83 ) ) PUNCT american_scientific_journal-3454 70 84 suppose suppose VERB american_scientific_journal-3454 70 85 that that SCONJ american_scientific_journal-3454 70 86 , , PUNCT american_scientific_journal-3454 70 87 it it PRON american_scientific_journal-3454 70 88 can can AUX american_scientific_journal-3454 70 89 be be AUX american_scientific_journal-3454 70 90 found find VERB american_scientific_journal-3454 70 91 a a DET american_scientific_journal-3454 70 92 constant constant ADJ american_scientific_journal-3454 70 93 positive positive ADJ american_scientific_journal-3454 70 94 simidefinite simidefinite NOUN american_scientific_journal-3454 70 95 symmetric symmetric ADJ american_scientific_journal-3454 70 96 ๐‘ƒ๐‘ƒ ๐‘ƒ๐‘ƒ NOUN american_scientific_journal-3454 70 97 that that PRON american_scientific_journal-3454 70 98 satisfy satisfy VERB american_scientific_journal-3454 70 99 equation equation NOUN american_scientific_journal-3454 70 100 ( ( PUNCT american_scientific_journal-3454 70 101 37 37 NUM american_scientific_journal-3454 70 102 ) ) PUNCT american_scientific_journal-3454 70 103 , , PUNCT american_scientific_journal-3454 70 104 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 105 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 70 106 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 107 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)(๐‘„๐‘„๐‘š๐‘š ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)(๐‘„๐‘„๐‘š๐‘š PROPN american_scientific_journal-3454 70 108 + + NOUN american_scientific_journal-3454 70 109 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…k๐‘š๐‘š) ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…k๐‘š๐‘š) PROPN american_scientific_journal-3454 70 110 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 111 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 70 112 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 113 ๐‘ฅ(t ๐‘ฅ(t PROPN american_scientific_journal-3454 70 114 ) ) PUNCT american_scientific_journal-3454 70 115 = = SYM american_scientific_journal-3454 70 116 โˆ’ โˆ’ PROPN american_scientific_journal-3454 70 117 ๐‘‘๐‘‘ ๐‘‘๐‘‘ PROPN american_scientific_journal-3454 70 118 ๐‘‘๐‘‘๐‘‘๐‘‘ ๐‘‘๐‘‘๐‘‘๐‘‘ PROPN american_scientific_journal-3454 70 119 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 120 ๐‘ฅ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 70 121 ) ) PUNCT american_scientific_journal-3454 70 122 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 123 = = SYM american_scientific_journal-3454 70 124 โˆ’ โˆ’ PROPN american_scientific_journal-3454 70 125 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 126 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 70 127 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 128 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 70 129 ) ) PUNCT american_scientific_journal-3454 70 130 โˆ’ โˆ’ ADP american_scientific_journal-3454 70 131 ๐‘ฅ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘ƒ๐‘ƒ ๐‘ฅ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 70 132 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 133 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 70 134 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 70 135 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 70 136 ) ) PUNCT american_scientific_journal-3454 70 137 ( ( PUNCT american_scientific_journal-3454 70 138 38 38 NUM american_scientific_journal-3454 70 139 ) ) PUNCT american_scientific_journal-3454 70 140 therefore therefore ADV american_scientific_journal-3454 70 141 , , PUNCT american_scientific_journal-3454 70 142 the the DET american_scientific_journal-3454 70 143 performance performance NOUN american_scientific_journal-3454 70 144 index index NOUN american_scientific_journal-3454 70 145 can can AUX american_scientific_journal-3454 70 146 be be AUX american_scientific_journal-3454 70 147 obtained obtain VERB american_scientific_journal-3454 70 148 as as ADP american_scientific_journal-3454 70 149 : : PUNCT american_scientific_journal-3454 70 150 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 70 151 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 152 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 153 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 70 154 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 70 155 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 70 156 ) ) PUNCT american_scientific_journal-3454 70 157 , , PUNCT american_scientific_journal-3454 70 158 ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 70 159 ) ) PUNCT american_scientific_journal-3454 70 160 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 161 = = SYM american_scientific_journal-3454 70 162 โˆซ โˆซ PROPN american_scientific_journal-3454 70 163 ( ( PUNCT american_scientific_journal-3454 70 164 โˆž โˆž PROPN american_scientific_journal-3454 70 165 0 0 NUM american_scientific_journal-3454 70 166 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 167 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 70 168 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 169 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘„๐‘„๐‘š๐‘š ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘„๐‘„๐‘š๐‘š PROPN american_scientific_journal-3454 70 170 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 171 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 70 172 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 70 173 ๐‘ฅ(t ๐‘ฅ(t NUM american_scientific_journal-3454 70 174 ) ) PUNCT american_scientific_journal-3454 71 1 + + CCONJ american_scientific_journal-3454 71 2 ( ( PUNCT american_scientific_journal-3454 71 3 ๐พ๐พ๐‘š๐‘š ๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 71 4 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 71 5 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 71 6 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 71 7 ๐‘ฅ(t))๐‘‡๐‘‡๐‘…๐‘…(๐พ๐พ๐‘š๐‘š ๐‘ฅ(t))๐‘‡๐‘‡๐‘…๐‘…(๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 71 8 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 71 9 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 71 10 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 71 11 ๐‘ฅ(t)))๐‘‘๐‘‘๐‘ก๐‘ก ๐‘ฅ(t)))๐‘‘๐‘‘๐‘ก๐‘ก PROPN american_scientific_journal-3454 71 12 = = SYM american_scientific_journal-3454 71 13 โˆ’๐‘ฅ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก)|0โˆž โˆ’๐‘ฅ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก)|0โˆž PROPN american_scientific_journal-3454 71 14 = = PUNCT american_scientific_journal-3454 71 15 โˆ’๐‘ฅ๐‘ฅ๐‘‡๐‘‡(โˆž)๐‘ƒ๐‘ƒ๐‘ƒ๐‘ƒ(โˆž โˆ’๐‘ฅ๐‘ฅ๐‘‡๐‘‡(โˆž)๐‘ƒ๐‘ƒ๐‘ƒ๐‘ƒ(โˆž X american_scientific_journal-3454 71 16 ) ) PUNCT american_scientific_journal-3454 71 17 + + ADJ american_scientific_journal-3454 71 18 ๐‘ฅ๐‘ฅ๐‘‡๐‘‡(0)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(0 ๐‘ฅ๐‘ฅ๐‘‡๐‘‡(0)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(0 NUM american_scientific_journal-3454 71 19 ) ) PUNCT american_scientific_journal-3454 71 20 ( ( PUNCT american_scientific_journal-3454 71 21 39 39 NUM american_scientific_journal-3454 71 22 ) ) PUNCT american_scientific_journal-3454 71 23 assume assume VERB american_scientific_journal-3454 71 24 that that SCONJ american_scientific_journal-3454 71 25 the the DET american_scientific_journal-3454 71 26 closed closed ADJ american_scientific_journal-3454 71 27 loop loop NOUN american_scientific_journal-3454 71 28 system system NOUN american_scientific_journal-3454 71 29 is be AUX american_scientific_journal-3454 71 30 asymptotically asymptotically ADV american_scientific_journal-3454 71 31 stable stable ADJ american_scientific_journal-3454 71 32 , , PUNCT american_scientific_journal-3454 71 33 then then ADV american_scientific_journal-3454 71 34 ๐‘ฅ๐‘ฅ(โˆž ๐‘ฅ๐‘ฅ(โˆž NUM american_scientific_journal-3454 71 35 ) ) PUNCT american_scientific_journal-3454 71 36 โ†’ โ†’ SYM american_scientific_journal-3454 72 1 0 0 X american_scientific_journal-3454 72 2 . . PUNCT american_scientific_journal-3454 73 1 therefore therefore ADV american_scientific_journal-3454 73 2 the the DET american_scientific_journal-3454 73 3 performance performance NOUN american_scientific_journal-3454 73 4 index index NOUN american_scientific_journal-3454 73 5 can can AUX american_scientific_journal-3454 73 6 be be AUX american_scientific_journal-3454 73 7 obtained obtain VERB american_scientific_journal-3454 73 8 in in ADP american_scientific_journal-3454 73 9 terms term NOUN american_scientific_journal-3454 73 10 of of ADP american_scientific_journal-3454 73 11 initial initial ADJ american_scientific_journal-3454 73 12 conditions condition NOUN american_scientific_journal-3454 73 13 and and CCONJ american_scientific_journal-3454 73 14 matrix matrix NOUN american_scientific_journal-3454 73 15 ๐‘ƒ๐‘ƒ ๐‘ƒ๐‘ƒ ADV american_scientific_journal-3454 73 16 as as ADP american_scientific_journal-3454 73 17 : : PUNCT american_scientific_journal-3454 73 18 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 73 19 = = SYM american_scientific_journal-3454 73 20 ๐‘ฅ๐‘ฅ๐‘‡๐‘‡(0)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(0 ๐‘ฅ๐‘ฅ๐‘‡๐‘‡(0)๐‘ƒ๐‘ƒ๐‘ฅ๐‘ฅ(0 PROPN american_scientific_journal-3454 73 21 ) ) PUNCT american_scientific_journal-3454 73 22 ( ( PUNCT american_scientific_journal-3454 73 23 40 40 NUM american_scientific_journal-3454 73 24 ) ) PUNCT american_scientific_journal-3454 73 25 from from ADP american_scientific_journal-3454 73 26 equation equation NOUN american_scientific_journal-3454 73 27 ( ( PUNCT american_scientific_journal-3454 73 28 35 35 NUM american_scientific_journal-3454 73 29 ) ) PUNCT american_scientific_journal-3454 73 30 , , PUNCT american_scientific_journal-3454 73 31 the the DET american_scientific_journal-3454 73 32 following follow VERB american_scientific_journal-3454 73 33 relationship relationship NOUN american_scientific_journal-3454 73 34 can can AUX american_scientific_journal-3454 73 35 be be AUX american_scientific_journal-3454 73 36 obtained obtain VERB american_scientific_journal-3454 73 37 : : PUNCT american_scientific_journal-3454 73 38 ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 73 39 ) ) PUNCT american_scientific_journal-3454 74 1 = = PUNCT american_scientific_journal-3454 74 2 ๐ด๐ด๐‘›๐‘›โˆ’1 ๐ด๐ด๐‘›๐‘›โˆ’1 PROPN american_scientific_journal-3454 74 3 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 74 4 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 74 5 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 74 6 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 74 7 ) ) PUNCT american_scientific_journal-3454 75 1 + + NUM american_scientific_journal-3454 75 2 ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก NOUN american_scientific_journal-3454 75 3 ) ) PUNCT american_scientific_journal-3454 75 4 ( ( PUNCT american_scientific_journal-3454 75 5 41 41 NUM american_scientific_journal-3454 75 6 ) ) PUNCT american_scientific_journal-3454 75 7 where where SCONJ american_scientific_journal-3454 75 8 ๐ด๐ด๐‘›๐‘›โˆ’1 ๐ด๐ด๐‘›๐‘›โˆ’1 PROPN american_scientific_journal-3454 75 9 = = PUNCT american_scientific_journal-3454 76 1 ๐ด๐ด๐‘š๐‘šโˆ’1(๐ผ๐ผ ๐ด๐ด๐‘š๐‘šโˆ’1(๐ผ๐ผ PROPN american_scientific_journal-3454 76 2 + + NUM american_scientific_journal-3454 76 3 ๐ต๐ต2๐พ๐พ๐‘š๐‘š ๐ต๐ต2๐พ๐พ๐‘š๐‘š NOUN american_scientific_journal-3454 76 4 ) ) PUNCT american_scientific_journal-3454 76 5 ( ( PUNCT american_scientific_journal-3454 76 6 42 42 NUM american_scientific_journal-3454 76 7 ) ) PUNCT american_scientific_journal-3454 76 8 then then ADV american_scientific_journal-3454 76 9 equation equation NOUN american_scientific_journal-3454 76 10 ( ( PUNCT american_scientific_journal-3454 76 11 38 38 NUM american_scientific_journal-3454 76 12 ) ) PUNCT american_scientific_journal-3454 76 13 can can AUX american_scientific_journal-3454 76 14 be be AUX american_scientific_journal-3454 76 15 rewritten rewrite VERB american_scientific_journal-3454 76 16 as as ADP american_scientific_journal-3454 76 17 : : PUNCT american_scientific_journal-3454 76 18 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 76 19 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 76 20 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 76 21 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)(๐‘„๐‘„๐‘š๐‘š ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)(๐‘„๐‘„๐‘š๐‘š PROPN american_scientific_journal-3454 76 22 + + CCONJ american_scientific_journal-3454 76 23 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š) ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š) PROPN american_scientific_journal-3454 76 24 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 76 25 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 76 26 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 76 27 ๐‘ฅ(t ๐‘ฅ(t PROPN american_scientific_journal-3454 76 28 ) ) PUNCT american_scientific_journal-3454 77 1 = = PUNCT american_scientific_journal-3454 77 2 โˆ’ โˆ’ PROPN american_scientific_journal-3454 77 3 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 77 4 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 77 5 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 77 6 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)(๐‘ƒ๐‘ƒ๐ด๐ด๐‘›๐‘›โˆ’1 ๐‘ฅ๐‘‡๐‘‡(๐‘ก๐‘ก)(๐‘ƒ๐‘ƒ๐ด๐ด๐‘›๐‘›โˆ’1 PUNCT american_scientific_journal-3454 77 7 + + ADJ american_scientific_journal-3454 77 8 ๐ด๐ด๐‘›๐‘›โˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ) ๐ด๐ด๐‘›๐‘›โˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ) PROPN american_scientific_journal-3454 77 9 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 77 10 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 77 11 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 77 12 ๐‘ฅ(t ๐‘ฅ(t PROPN american_scientific_journal-3454 77 13 ) ) PUNCT american_scientific_journal-3454 77 14 ( ( PUNCT american_scientific_journal-3454 77 15 43 43 NUM american_scientific_journal-3454 77 16 ) ) PUNCT american_scientific_journal-3454 77 17 by by ADP american_scientific_journal-3454 77 18 comparing compare VERB american_scientific_journal-3454 77 19 the the DET american_scientific_journal-3454 77 20 two two NUM american_scientific_journal-3454 77 21 sides side NOUN american_scientific_journal-3454 77 22 of of ADP american_scientific_journal-3454 77 23 equation equation NOUN american_scientific_journal-3454 77 24 ( ( PUNCT american_scientific_journal-3454 77 25 43 43 NUM american_scientific_journal-3454 77 26 ) ) PUNCT american_scientific_journal-3454 77 27 , , PUNCT american_scientific_journal-3454 77 28 we we PRON american_scientific_journal-3454 77 29 obtain obtain VERB american_scientific_journal-3454 77 30 : : PUNCT american_scientific_journal-3454 77 31 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘›๐‘›โˆ’1 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘›๐‘›โˆ’1 NOUN american_scientific_journal-3454 77 32 + + CCONJ american_scientific_journal-3454 77 33 ๐ด๐ด๐‘›๐‘›โˆ’1๐‘ƒ๐‘ƒ ๐ด๐ด๐‘›๐‘›โˆ’1๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 77 34 + + CCONJ american_scientific_journal-3454 77 35 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 77 36 + + NUM american_scientific_journal-3454 77 37 ๐‘„๐‘„๐‘š๐‘š ๐‘„๐‘„๐‘š๐‘š NOUN american_scientific_journal-3454 77 38 = = SYM american_scientific_journal-3454 77 39 0 0 PUNCT american_scientific_journal-3454 78 1 ( ( PUNCT american_scientific_journal-3454 78 2 44 44 NUM american_scientific_journal-3454 78 3 ) ) PUNCT american_scientific_journal-3454 78 4 substituting substitute VERB american_scientific_journal-3454 78 5 equation equation NOUN american_scientific_journal-3454 78 6 ( ( PUNCT american_scientific_journal-3454 78 7 42 42 NUM american_scientific_journal-3454 78 8 ) ) PUNCT american_scientific_journal-3454 78 9 in in ADP american_scientific_journal-3454 78 10 equation equation NOUN american_scientific_journal-3454 78 11 ( ( PUNCT american_scientific_journal-3454 78 12 44 44 NUM american_scientific_journal-3454 78 13 ) ) PUNCT american_scientific_journal-3454 78 14 , , PUNCT american_scientific_journal-3454 78 15 one one PRON american_scientific_journal-3454 78 16 can can AUX american_scientific_journal-3454 78 17 obtain obtain VERB american_scientific_journal-3454 78 18 : : PUNCT american_scientific_journal-3454 78 19 ๐‘ƒ๐‘ƒ(๐ด๐ด๐‘š๐‘šโˆ’1(๐ผ๐ผ ๐‘ƒ๐‘ƒ(๐ด๐ด๐‘š๐‘šโˆ’1(๐ผ๐ผ NOUN american_scientific_journal-3454 78 20 + + CCONJ american_scientific_journal-3454 78 21 ๐ต๐ต2๐พ๐พ๐‘š๐‘š ๐ต๐ต2๐พ๐พ๐‘š๐‘š NOUN american_scientific_journal-3454 78 22 ) ) PUNCT american_scientific_journal-3454 78 23 ) ) PUNCT american_scientific_journal-3454 79 1 + + CCONJ american_scientific_journal-3454 79 2 ( ( PUNCT american_scientific_journal-3454 79 3 ๐ด๐ด๐‘š๐‘šโˆ’1(๐ผ๐ผ ๐ด๐ด๐‘š๐‘šโˆ’1(๐ผ๐ผ X american_scientific_journal-3454 79 4 + + CCONJ american_scientific_journal-3454 79 5 ๐ต๐ต2๐พ๐พ๐‘š๐‘š))๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐ต๐ต2๐พ๐พ๐‘š๐‘š))๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 79 6 + + CCONJ american_scientific_journal-3454 79 7 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 79 8 + + NUM american_scientific_journal-3454 79 9 ๐‘„๐‘„๐‘š๐‘š ๐‘„๐‘„๐‘š๐‘š NOUN american_scientific_journal-3454 79 10 = = SYM american_scientific_journal-3454 79 11 0 0 PUNCT american_scientific_journal-3454 80 1 ( ( PUNCT american_scientific_journal-3454 80 2 45 45 NUM american_scientific_journal-3454 80 3 ) ) PUNCT american_scientific_journal-3454 80 4 then then ADV american_scientific_journal-3454 80 5 , , PUNCT american_scientific_journal-3454 80 6 equation equation NOUN american_scientific_journal-3454 80 7 ( ( PUNCT american_scientific_journal-3454 80 8 45 45 NUM american_scientific_journal-3454 80 9 ) ) PUNCT american_scientific_journal-3454 80 10 can can AUX american_scientific_journal-3454 80 11 be be AUX american_scientific_journal-3454 80 12 rewritten rewrite VERB american_scientific_journal-3454 80 13 as as ADP american_scientific_journal-3454 80 14 : : PUNCT american_scientific_journal-3454 80 15 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1 PROPN american_scientific_journal-3454 80 16 + + PUNCT american_scientific_journal-3454 80 17 ๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 80 18 + + CCONJ american_scientific_journal-3454 80 19 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐ต๐ต2๐พ๐พ๐‘š๐‘š ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐ต๐ต2๐พ๐พ๐‘š๐‘š ADJ american_scientific_journal-3454 80 20 + + CCONJ american_scientific_journal-3454 80 21 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PUNCT american_scientific_journal-3454 80 22 + + CCONJ american_scientific_journal-3454 80 23 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘…๐‘…๐พ๐พ๐‘š๐‘š ADJ american_scientific_journal-3454 80 24 + + NUM american_scientific_journal-3454 80 25 ๐‘„๐‘„๐‘š๐‘š ๐‘„๐‘„๐‘š๐‘š NOUN american_scientific_journal-3454 80 26 = = SYM american_scientific_journal-3454 80 27 0 0 PUNCT american_scientific_journal-3454 80 28 ( ( PUNCT american_scientific_journal-3454 80 29 46 46 NUM american_scientific_journal-3454 80 30 ) ) PUNCT american_scientific_journal-3454 80 31 since since SCONJ american_scientific_journal-3454 80 32 ๐‘…๐‘… ๐‘…๐‘… PROPN american_scientific_journal-3454 80 33 is be AUX american_scientific_journal-3454 80 34 positive positive ADJ american_scientific_journal-3454 80 35 definite definite ADJ american_scientific_journal-3454 80 36 symmetric symmetric ADJ american_scientific_journal-3454 80 37 matrix matrix NOUN american_scientific_journal-3454 80 38 , , PUNCT american_scientific_journal-3454 80 39 then then ADV american_scientific_journal-3454 80 40 ๐‘…๐‘… ๐‘…๐‘… PROPN american_scientific_journal-3454 80 41 = = PUNCT american_scientific_journal-3454 80 42 ๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡ ๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡ PROPN american_scientific_journal-3454 80 43 , , PUNCT american_scientific_journal-3454 80 44 where where SCONJ american_scientific_journal-3454 80 45 ๐‘‡๐‘‡ ๐‘‡๐‘‡ PROPN american_scientific_journal-3454 80 46 is be AUX american_scientific_journal-3454 80 47 nonsingular nonsingular ADJ american_scientific_journal-3454 80 48 matrix matrix NOUN american_scientific_journal-3454 80 49 . . PUNCT american_scientific_journal-3454 81 1 equation equation NOUN american_scientific_journal-3454 81 2 ( ( PUNCT american_scientific_journal-3454 81 3 46 46 NUM american_scientific_journal-3454 81 4 ) ) PUNCT american_scientific_journal-3454 81 5 can can AUX american_scientific_journal-3454 81 6 american american VERB american_scientific_journal-3454 81 7 scientific scientific ADJ american_scientific_journal-3454 81 8 research research NOUN american_scientific_journal-3454 81 9 journal journal NOUN american_scientific_journal-3454 81 10 for for ADP american_scientific_journal-3454 81 11 engineering engineering NOUN american_scientific_journal-3454 81 12 , , PUNCT american_scientific_journal-3454 81 13 technology technology NOUN american_scientific_journal-3454 81 14 , , PUNCT american_scientific_journal-3454 81 15 and and CCONJ american_scientific_journal-3454 81 16 sciences science NOUN american_scientific_journal-3454 81 17 ( ( PUNCT american_scientific_journal-3454 81 18 asrjets asrjet NOUN american_scientific_journal-3454 81 19 ) ) PUNCT american_scientific_journal-3454 81 20 ( ( PUNCT american_scientific_journal-3454 81 21 2017 2017 NUM american_scientific_journal-3454 81 22 ) ) PUNCT american_scientific_journal-3454 81 23 volume volume NOUN american_scientific_journal-3454 81 24 37 37 NUM american_scientific_journal-3454 81 25 , , PUNCT american_scientific_journal-3454 81 26 no no DET american_scientific_journal-3454 81 27 1 1 NUM american_scientific_journal-3454 81 28 , , PUNCT american_scientific_journal-3454 81 29 pp pp ADV american_scientific_journal-3454 81 30 118 118 NUM american_scientific_journal-3454 81 31 - - SYM american_scientific_journal-3454 81 32 128 128 NUM american_scientific_journal-3454 81 33 124 124 NUM american_scientific_journal-3454 81 34 be be AUX american_scientific_journal-3454 81 35 rewritten rewrite VERB american_scientific_journal-3454 81 36 as as ADP american_scientific_journal-3454 81 37 : : PUNCT american_scientific_journal-3454 81 38 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1 PROPN american_scientific_journal-3454 81 39 + + PUNCT american_scientific_journal-3454 81 40 ๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 81 41 + + CCONJ american_scientific_journal-3454 81 42 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1๐ต๐ต2๐พ๐พ๐‘š๐‘š ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1๐ต๐ต2๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 81 43 + + CCONJ american_scientific_journal-3454 81 44 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PUNCT american_scientific_journal-3454 82 1 + + CCONJ american_scientific_journal-3454 82 2 ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐พ๐พ๐‘š๐‘š ๐พ๐พ๐‘š๐‘š๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐‘‡๐พ๐พ๐‘š๐‘š ADJ american_scientific_journal-3454 82 3 + + CCONJ american_scientific_journal-3454 82 4 ๐‘„๐‘„๐‘š๐‘š ๐‘„๐‘„๐‘š๐‘š PROPN american_scientific_journal-3454 82 5 = = SYM american_scientific_journal-3454 82 6 0 0 PUNCT american_scientific_journal-3454 82 7 ( ( PUNCT american_scientific_journal-3454 82 8 47 47 NUM american_scientific_journal-3454 82 9 ) ) PUNCT american_scientific_journal-3454 82 10 by by ADP american_scientific_journal-3454 82 11 reformulating reformulate VERB american_scientific_journal-3454 82 12 equation equation NOUN american_scientific_journal-3454 82 13 ( ( PUNCT american_scientific_journal-3454 82 14 47 47 NUM american_scientific_journal-3454 82 15 ) ) PUNCT american_scientific_journal-3454 82 16 , , PUNCT american_scientific_journal-3454 82 17 the the DET american_scientific_journal-3454 82 18 following follow VERB american_scientific_journal-3454 82 19 equation equation NOUN american_scientific_journal-3454 82 20 can can AUX american_scientific_journal-3454 82 21 be be AUX american_scientific_journal-3454 82 22 obtained obtain VERB american_scientific_journal-3454 82 23 : : PUNCT american_scientific_journal-3454 82 24 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1 PROPN american_scientific_journal-3454 82 25 + + PUNCT american_scientific_journal-3454 82 26 ๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 82 27 ( ( PUNCT american_scientific_journal-3454 82 28 ๐‘‡๐‘‡๐พ๐พ๐‘š๐‘š ๐‘‡๐‘‡๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 82 29 + + NUM american_scientific_journal-3454 82 30 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ)๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ๐‘š๐‘š ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ)๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 82 31 + + CCONJ american_scientific_journal-3454 82 32 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ NOUN american_scientific_journal-3454 82 33 ) ) PUNCT american_scientific_journal-3454 82 34 โˆ’ โˆ’ PROPN american_scientific_journal-3454 83 1 ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1๐ต๐ต2๐‘…๐‘…โˆ’1๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘ƒ๐‘ƒ๐ด๐ด๐‘š๐‘šโˆ’1๐ต๐ต2๐‘…๐‘…โˆ’1๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 83 2 + + NUM american_scientific_journal-3454 83 3 ๐‘„๐‘„๐‘š๐‘š ๐‘„๐‘„๐‘š๐‘š PROPN american_scientific_journal-3454 83 4 = = SYM american_scientific_journal-3454 83 5 0 0 PUNCT american_scientific_journal-3454 83 6 ( ( PUNCT american_scientific_journal-3454 83 7 48 48 NUM american_scientific_journal-3454 83 8 ) ) PUNCT american_scientific_journal-3454 83 9 the the DET american_scientific_journal-3454 83 10 minimization minimization NOUN american_scientific_journal-3454 83 11 of of ADP american_scientific_journal-3454 83 12 ๐ฝ๐ฝ ๐ฝ๐ฝ PROPN american_scientific_journal-3454 83 13 requires require VERB american_scientific_journal-3454 83 14 the the DET american_scientific_journal-3454 83 15 minimization minimization NOUN american_scientific_journal-3454 83 16 of of ADP american_scientific_journal-3454 83 17 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 83 18 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 83 19 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 83 20 ๐‘ฅ๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ ๐‘ฅ๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ PROPN american_scientific_journal-3454 83 21 + + CCONJ american_scientific_journal-3454 83 22 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ)๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ)๐‘‡๐‘‡(๐‘‡๐‘‡๐พ๐พ SYM american_scientific_journal-3454 83 23 + + CCONJ american_scientific_journal-3454 83 24 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ) ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต๐‘‡๐‘‡๐ด๐ดโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ) PROPN american_scientific_journal-3454 83 25 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 83 26 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 83 27 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 83 28 ๐‘ฅ ๐‘ฅ PROPN american_scientific_journal-3454 83 29 ( ( PUNCT american_scientific_journal-3454 83 30 49 49 NUM american_scientific_journal-3454 83 31 ) ) PUNCT american_scientific_journal-3454 83 32 since since SCONJ american_scientific_journal-3454 83 33 the the DET american_scientific_journal-3454 83 34 last last ADJ american_scientific_journal-3454 83 35 expression expression NOUN american_scientific_journal-3454 83 36 is be AUX american_scientific_journal-3454 83 37 nonnegative nonnegative ADJ american_scientific_journal-3454 83 38 , , PUNCT american_scientific_journal-3454 83 39 the the DET american_scientific_journal-3454 83 40 minimum minimum NOUN american_scientific_journal-3454 83 41 occurs occur VERB american_scientific_journal-3454 83 42 when when SCONJ american_scientific_journal-3454 83 43 it it PRON american_scientific_journal-3454 83 44 is be AUX american_scientific_journal-3454 83 45 zero zero NUM american_scientific_journal-3454 83 46 ๐‘‡๐‘‡๐พ๐พ๐‘š๐‘š ๐‘‡๐‘‡๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 83 47 + + CCONJ american_scientific_journal-3454 83 48 ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ NOUN american_scientific_journal-3454 83 49 = = SYM american_scientific_journal-3454 83 50 0 0 NUM american_scientific_journal-3454 83 51 ( ( PUNCT american_scientific_journal-3454 83 52 50 50 NUM american_scientific_journal-3454 83 53 ) ) PUNCT american_scientific_journal-3454 83 54 the the DET american_scientific_journal-3454 83 55 optimal optimal ADJ american_scientific_journal-3454 83 56 gain gain NOUN american_scientific_journal-3454 83 57 matrix matrix NOUN american_scientific_journal-3454 83 58 ๐พ๐พ๐‘š๐‘š ๐พ๐พ๐‘š๐‘š NOUN american_scientific_journal-3454 83 59 is be AUX american_scientific_journal-3454 83 60 : : PUNCT american_scientific_journal-3454 84 1 ๐พ๐พ๐‘š๐‘š ๐พ๐พ๐‘š๐‘š NOUN american_scientific_journal-3454 84 2 = = PUNCT american_scientific_journal-3454 85 1 โˆ’๐‘‡๐‘‡โˆ’1๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ โˆ’๐‘‡๐‘‡โˆ’1๐‘‡๐‘‡โˆ’๐‘‡๐‘‡๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PUNCT american_scientific_journal-3454 85 2 = = PUNCT american_scientific_journal-3454 85 3 โˆ’๐‘…๐‘…โˆ’1๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ โˆ’๐‘…๐‘…โˆ’1๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ PROPN american_scientific_journal-3454 85 4 ( ( PUNCT american_scientific_journal-3454 85 5 51 51 NUM american_scientific_journal-3454 85 6 ) ) PUNCT american_scientific_journal-3454 85 7 finally finally ADV american_scientific_journal-3454 85 8 , , PUNCT american_scientific_journal-3454 85 9 the the DET american_scientific_journal-3454 85 10 optimal optimal ADJ american_scientific_journal-3454 85 11 stabilizing stabilizing NOUN american_scientific_journal-3454 85 12 control control NOUN american_scientific_journal-3454 85 13 is be AUX american_scientific_journal-3454 85 14 : : PUNCT american_scientific_journal-3454 85 15 ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก ๐‘ฃ๐‘ฃ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 85 16 ) ) PUNCT american_scientific_journal-3454 86 1 = = SYM american_scientific_journal-3454 86 2 โˆ’๐พ๐พ๐‘š๐‘š โˆ’๐พ๐พ๐‘š๐‘š PROPN american_scientific_journal-3454 86 3 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 86 4 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 86 5 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 86 6 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 86 7 ) ) PUNCT american_scientific_journal-3454 86 8 = = PUNCT american_scientific_journal-3454 86 9 ๐‘…๐‘…โˆ’1๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘…๐‘…โˆ’1๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ VERB american_scientific_journal-3454 86 10 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 86 11 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 86 12 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 86 13 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 86 14 ) ) PUNCT american_scientific_journal-3454 86 15 ( ( PUNCT american_scientific_journal-3454 86 16 52 52 NUM american_scientific_journal-3454 86 17 ) ) PUNCT american_scientific_journal-3454 86 18 substituting substitute VERB american_scientific_journal-3454 86 19 equation equation NOUN american_scientific_journal-3454 86 20 ( ( PUNCT american_scientific_journal-3454 86 21 52 52 NUM american_scientific_journal-3454 86 22 ) ) PUNCT american_scientific_journal-3454 86 23 in in ADP american_scientific_journal-3454 86 24 equation equation NOUN american_scientific_journal-3454 86 25 ( ( PUNCT american_scientific_journal-3454 86 26 30 30 NUM american_scientific_journal-3454 86 27 ) ) PUNCT american_scientific_journal-3454 86 28 yields yield NOUN american_scientific_journal-3454 86 29 : : PUNCT american_scientific_journal-3454 86 30 ๐ต๐ต(๐‘ก๐‘ก ๐ต๐ต(๐‘ก๐‘ก X american_scientific_journal-3454 86 31 ) ) PUNCT american_scientific_journal-3454 86 32 = = PUNCT american_scientific_journal-3454 86 33 ๐‘…๐‘…โˆ’1๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐‘…๐‘…โˆ’1๐ต๐ต2๐‘‡๐‘‡๐ด๐ด๐‘š๐‘šโˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ VERB american_scientific_journal-3454 86 34 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 86 35 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 86 36 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 86 37 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 86 38 ) ) PUNCT american_scientific_journal-3454 86 39 โˆ’ โˆ’ PROPN american_scientific_journal-3454 86 40 ๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ ๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡ SYM american_scientific_journal-3454 86 41 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 86 42 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 86 43 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 86 44 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 86 45 ) ) PUNCT american_scientific_journal-3454 86 46 ( ( PUNCT american_scientific_journal-3454 86 47 53 53 NUM american_scientific_journal-3454 86 48 ) ) PUNCT american_scientific_journal-3454 86 49 then then ADV american_scientific_journal-3454 86 50 ๐พ๐พ ๐พ๐พ PROPN american_scientific_journal-3454 86 51 = = PUNCT american_scientific_journal-3454 86 52 โˆ’๐‘…๐‘…โˆ’1[๐ต๐ต2๐‘‡๐‘‡(๐ด๐ด โˆ’๐‘…๐‘…โˆ’1[๐ต๐ต2๐‘‡๐‘‡(๐ด๐ด NUM american_scientific_journal-3454 86 53 โˆ’ โˆ’ PROPN american_scientific_journal-3454 86 54 ๐ต๐ต2๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡)โˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ ๐ต๐ต2๐‘…๐‘…โˆ’1๐‘๐‘๐‘‡๐‘‡)โˆ’๐‘‡๐‘‡๐‘ƒ๐‘ƒ NOUN american_scientific_journal-3454 86 55 โˆ’ โˆ’ PROPN american_scientific_journal-3454 86 56 ๐‘๐‘๐‘‡๐‘‡ ๐‘๐‘๐‘‡๐‘‡ PROPN american_scientific_journal-3454 86 57 ] ] X american_scientific_journal-3454 86 58 ( ( PUNCT american_scientific_journal-3454 86 59 54 54 NUM american_scientific_journal-3454 86 60 ) ) PUNCT american_scientific_journal-3454 86 61 the the DET american_scientific_journal-3454 86 62 equations equation NOUN american_scientific_journal-3454 86 63 of of ADP american_scientific_journal-3454 86 64 the the DET american_scientific_journal-3454 86 65 closed closed ADJ american_scientific_journal-3454 86 66 loop loop NOUN american_scientific_journal-3454 86 67 system system NOUN american_scientific_journal-3454 86 68 using use VERB american_scientific_journal-3454 86 69 state state NOUN american_scientific_journal-3454 86 70 derivative derivative ADJ american_scientific_journal-3454 86 71 feedback feedback NOUN american_scientific_journal-3454 86 72 h2 h2 NOUN american_scientific_journal-3454 86 73 control control NOUN american_scientific_journal-3454 86 74 are be AUX american_scientific_journal-3454 86 75 : : PUNCT american_scientific_journal-3454 86 76 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 86 77 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 86 78 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 86 79 ๐‘ฅ(๐‘ก๐‘ก ๐‘ฅ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 86 80 ) ) PUNCT american_scientific_journal-3454 86 81 = = SYM american_scientific_journal-3454 86 82 ๐ด๐ด๐‘๐‘๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐ด๐ด๐‘๐‘๐‘ฅ๐‘ฅ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 86 83 ) ) PUNCT american_scientific_journal-3454 87 1 + + CCONJ american_scientific_journal-3454 87 2 ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก ๐ต๐ต1๐‘‘๐‘‘(๐‘ก๐‘ก X american_scientific_journal-3454 87 3 ) ) PUNCT american_scientific_journal-3454 88 1 + + CCONJ american_scientific_journal-3454 88 2 ๐ต๐ต๐‘๐‘๐‘Ÿ๐‘Ÿ(๐‘ก๐‘ก ๐ต๐ต๐‘๐‘๐‘Ÿ๐‘Ÿ(๐‘ก๐‘ก NOUN american_scientific_journal-3454 88 3 ) ) PUNCT american_scientific_journal-3454 88 4 ( ( PUNCT american_scientific_journal-3454 88 5 55 55 NUM american_scientific_journal-3454 88 6 ) ) PUNCT american_scientific_journal-3454 88 7 ๐‘ฆ๐‘ฆ(๐‘ก๐‘ก ๐‘ฆ๐‘ฆ(๐‘ก๐‘ก PROPN american_scientific_journal-3454 88 8 ) ) PUNCT american_scientific_journal-3454 89 1 = = PUNCT american_scientific_journal-3454 89 2 ๐ถ๐ถ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก ๐ถ๐ถ๐‘ฅ๐‘ฅ(๐‘ก๐‘ก X american_scientific_journal-3454 89 3 ) ) PUNCT american_scientific_journal-3454 89 4 ( ( PUNCT american_scientific_journal-3454 89 5 56 56 NUM american_scientific_journal-3454 89 6 ) ) PUNCT american_scientific_journal-3454 89 7 where where SCONJ american_scientific_journal-3454 89 8 ๐ด๐ด๐‘๐‘ ๐ด๐ด๐‘๐‘ VERB american_scientific_journal-3454 89 9 = = PUNCT american_scientific_journal-3454 89 10 ( ( PUNCT american_scientific_journal-3454 89 11 ๐ผ๐ผ ๐ผ๐ผ PROPN american_scientific_journal-3454 89 12 + + CCONJ american_scientific_journal-3454 89 13 ๐ต๐ต2๐พ๐พ)โˆ’1(๐ด๐ด ๐ต๐ต2๐พ๐พ)โˆ’1(๐ด๐ด PROPN american_scientific_journal-3454 89 14 โˆ’ โˆ’ PROPN american_scientific_journal-3454 89 15 ๐ต๐ต2๐ถ๐ถ ๐ต๐ต2๐ถ๐ถ PROPN american_scientific_journal-3454 89 16 ) ) PUNCT american_scientific_journal-3454 89 17 ( ( PUNCT american_scientific_journal-3454 89 18 57 57 NUM american_scientific_journal-3454 89 19 ) ) PUNCT american_scientific_journal-3454 89 20 ๐ต๐ต๐‘๐‘ ๐ต๐ต๐‘๐‘ PROPN american_scientific_journal-3454 89 21 = = PUNCT american_scientific_journal-3454 89 22 ( ( PUNCT american_scientific_journal-3454 89 23 ๐ผ๐ผ ๐ผ๐ผ PROPN american_scientific_journal-3454 89 24 + + CCONJ american_scientific_journal-3454 89 25 ๐ต๐ต2๐พ๐พ)โˆ’1๐ต๐ต2 ๐ต๐ต2๐พ๐พ)โˆ’1๐ต๐ต2 PROPN american_scientific_journal-3454 89 26 ( ( PUNCT american_scientific_journal-3454 89 27 58 58 NUM american_scientific_journal-3454 89 28 ) ) PUNCT american_scientific_journal-3454 89 29 american american ADJ american_scientific_journal-3454 89 30 scientific scientific ADJ american_scientific_journal-3454 89 31 research research NOUN american_scientific_journal-3454 89 32 journal journal NOUN american_scientific_journal-3454 89 33 for for ADP american_scientific_journal-3454 89 34 engineering engineering NOUN american_scientific_journal-3454 89 35 , , PUNCT american_scientific_journal-3454 89 36 technology technology NOUN american_scientific_journal-3454 89 37 , , PUNCT american_scientific_journal-3454 89 38 and and CCONJ american_scientific_journal-3454 89 39 sciences science NOUN american_scientific_journal-3454 89 40 ( ( PUNCT american_scientific_journal-3454 89 41 asrjets asrjet NOUN american_scientific_journal-3454 89 42 ) ) PUNCT american_scientific_journal-3454 89 43 ( ( PUNCT american_scientific_journal-3454 89 44 2017 2017 NUM american_scientific_journal-3454 89 45 ) ) PUNCT american_scientific_journal-3454 89 46 volume volume NOUN american_scientific_journal-3454 89 47 37 37 NUM american_scientific_journal-3454 89 48 , , PUNCT american_scientific_journal-3454 89 49 no no DET american_scientific_journal-3454 89 50 1 1 NUM american_scientific_journal-3454 89 51 , , PUNCT american_scientific_journal-3454 89 52 pp pp ADV american_scientific_journal-3454 89 53 118 118 NUM american_scientific_journal-3454 89 54 - - SYM american_scientific_journal-3454 89 55 128 128 NUM american_scientific_journal-3454 89 56 125 125 NUM american_scientific_journal-3454 89 57 3 3 NUM american_scientific_journal-3454 89 58 . . PUNCT american_scientific_journal-3454 89 59 illustrative illustrative ADJ american_scientific_journal-3454 89 60 example example NOUN american_scientific_journal-3454 89 61 a a DET american_scientific_journal-3454 89 62 multivariable multivariable ADJ american_scientific_journal-3454 89 63 active active ADJ american_scientific_journal-3454 89 64 suspension suspension NOUN american_scientific_journal-3454 89 65 system system NOUN american_scientific_journal-3454 89 66 , , PUNCT american_scientific_journal-3454 89 67 shown show VERB american_scientific_journal-3454 89 68 in in ADP american_scientific_journal-3454 89 69 figure figure NOUN american_scientific_journal-3454 89 70 1 1 NUM american_scientific_journal-3454 89 71 is be AUX american_scientific_journal-3454 89 72 used use VERB american_scientific_journal-3454 89 73 to to PART american_scientific_journal-3454 89 74 show show VERB american_scientific_journal-3454 89 75 the the DET american_scientific_journal-3454 89 76 effectiveness effectiveness NOUN american_scientific_journal-3454 89 77 of of ADP american_scientific_journal-3454 89 78 the the DET american_scientific_journal-3454 89 79 proposed propose VERB american_scientific_journal-3454 89 80 controllers controller NOUN american_scientific_journal-3454 89 81 . . PUNCT american_scientific_journal-3454 90 1 the the DET american_scientific_journal-3454 90 2 system system NOUN american_scientific_journal-3454 90 3 dynamics dynamic NOUN american_scientific_journal-3454 90 4 can can AUX american_scientific_journal-3454 90 5 be be AUX american_scientific_journal-3454 90 6 represented represent VERB american_scientific_journal-3454 90 7 by by ADP american_scientific_journal-3454 90 8 a a DET american_scientific_journal-3454 90 9 state state NOUN american_scientific_journal-3454 90 10 space space NOUN american_scientific_journal-3454 90 11 model model NOUN american_scientific_journal-3454 90 12 as as ADP american_scientific_journal-3454 90 13 [ [ X american_scientific_journal-3454 90 14 7 7 NUM american_scientific_journal-3454 90 15 ] ] X american_scientific_journal-3454 90 16 : : PUNCT american_scientific_journal-3454 90 17 โŽฃ โŽฃ ADV american_scientific_journal-3454 90 18 โŽข โŽข NOUN american_scientific_journal-3454 90 19 โŽข โŽข NOUN american_scientific_journal-3454 90 20 โŽก โŽก PROPN american_scientific_journal-3454 90 21 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 90 22 ฬ‡ ฬ‡ NOUN american_scientific_journal-3454 90 23 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 90 24 ๐‘ฅ1(๐‘ก๐‘ก ๐‘ฅ1(๐‘ก๐‘ก PROPN american_scientific_journal-3454 90 25 ) ) PUNCT american_scientific_journal-3454 90 26 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 90 27 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 90 28 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 90 29 ๐‘ฅ2(๐‘ก๐‘ก ๐‘ฅ2(๐‘ก๐‘ก PROPN american_scientific_journal-3454 90 30 ) ) PUNCT american_scientific_journal-3454 90 31 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 90 32 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 90 33 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 90 34 ๐‘ฅ3(๐‘ก๐‘ก ๐‘ฅ3(๐‘ก๐‘ก PROPN american_scientific_journal-3454 90 35 ) ) PUNCT american_scientific_journal-3454 90 36 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 90 37 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 90 38 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 90 39 ๐‘ฅ4(๐‘ก๐‘ก)โŽฆ ๐‘ฅ4(๐‘ก๐‘ก)โŽฆ PART american_scientific_journal-3454 90 40 โŽฅ โŽฅ PROPN american_scientific_journal-3454 90 41 โŽฅ โŽฅ PROPN american_scientific_journal-3454 90 42 โŽค โŽค PROPN american_scientific_journal-3454 90 43 = = PUNCT american_scientific_journal-3454 91 1 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 91 2 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 91 3 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 91 4 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 91 5 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 91 6 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 91 7 ๏ฃป ๏ฃป PROPN american_scientific_journal-3454 91 8 ๏ฃน ๏ฃน PROPN american_scientific_journal-3454 91 9 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 91 10 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 91 11 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 91 12 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 91 13 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 91 14 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 91 15 ๏ฃฐ ๏ฃฐ NUM american_scientific_journal-3454 91 16 ๏ฃฎ ๏ฃฎ VERB american_scientific_journal-3454 91 17 โˆ’โˆ’ โˆ’โˆ’ NOUN american_scientific_journal-3454 91 18 โˆ’โˆ’โˆ’โˆ’ โˆ’โˆ’โˆ’โˆ’ NUM american_scientific_journal-3454 91 19 ssss ssss NOUN american_scientific_journal-3454 91 20 cccc cccc PROPN american_scientific_journal-3454 91 21 m m PROPN american_scientific_journal-3454 91 22 b b PROPN american_scientific_journal-3454 91 23 m m PROPN american_scientific_journal-3454 91 24 b b NOUN american_scientific_journal-3454 91 25 m m VERB american_scientific_journal-3454 91 26 k k NOUN american_scientific_journal-3454 91 27 m m VERB american_scientific_journal-3454 91 28 k k PROPN american_scientific_journal-3454 91 29 m m PROPN american_scientific_journal-3454 91 30 b b PROPN american_scientific_journal-3454 91 31 m m VERB american_scientific_journal-3454 91 32 bb bb INTJ american_scientific_journal-3454 91 33 m m NOUN american_scientific_journal-3454 91 34 k k NOUN american_scientific_journal-3454 91 35 m m VERB american_scientific_journal-3454 91 36 kk kk PROPN american_scientific_journal-3454 91 37 2222 2222 NUM american_scientific_journal-3454 91 38 221221 221221 NUM american_scientific_journal-3454 91 39 1000 1000 NUM american_scientific_journal-3454 91 40 0100 0100 NUM american_scientific_journal-3454 92 1 โŽฃ โŽฃ ADV american_scientific_journal-3454 92 2 โŽข โŽข NOUN american_scientific_journal-3454 92 3 โŽข โŽข NOUN american_scientific_journal-3454 92 4 โŽก๐‘ฅ๐‘ฅ1 โŽก๐‘ฅ๐‘ฅ1 PROPN american_scientific_journal-3454 92 5 ( ( PUNCT american_scientific_journal-3454 92 6 ๐‘ก๐‘ก ๐‘ก๐‘ก ADJ american_scientific_journal-3454 92 7 ) ) PUNCT american_scientific_journal-3454 92 8 ๐‘ฅ๐‘ฅ2(๐‘ก๐‘ก ๐‘ฅ๐‘ฅ2(๐‘ก๐‘ก NOUN american_scientific_journal-3454 92 9 ) ) PUNCT american_scientific_journal-3454 92 10 ๐‘ฅ๐‘ฅ3(๐‘ก๐‘ก ๐‘ฅ๐‘ฅ3(๐‘ก๐‘ก NOUN american_scientific_journal-3454 92 11 ) ) PUNCT american_scientific_journal-3454 92 12 ๐‘ฅ๐‘ฅ4(๐‘ก๐‘ก)โŽฆ ๐‘ฅ๐‘ฅ4(๐‘ก๐‘ก)โŽฆ VERB american_scientific_journal-3454 92 13 โŽฅ โŽฅ PROPN american_scientific_journal-3454 92 14 โŽฅ โŽฅ PROPN american_scientific_journal-3454 92 15 โŽค โŽค PROPN american_scientific_journal-3454 93 1 + + CCONJ american_scientific_journal-3454 93 2 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 93 3 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 93 4 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 93 5 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 93 6 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 93 7 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 93 8 ๏ฃป ๏ฃป PROPN american_scientific_journal-3454 93 9 ๏ฃน ๏ฃน PROPN american_scientific_journal-3454 93 10 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 93 11 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 93 12 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 93 13 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 93 14 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 93 15 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 93 16 ๏ฃฐ ๏ฃฐ NUM american_scientific_journal-3454 93 17 ๏ฃฎ ๏ฃฎ VERB american_scientific_journal-3454 93 18 โˆ’ โˆ’ PROPN american_scientific_journal-3454 93 19 s s NOUN american_scientific_journal-3454 93 20 cc cc NOUN american_scientific_journal-3454 93 21 m m NOUN american_scientific_journal-3454 93 22 mm mm PROPN american_scientific_journal-3454 93 23 10 10 NUM american_scientific_journal-3454 93 24 11 11 NUM american_scientific_journal-3454 93 25 00 00 NUM american_scientific_journal-3454 93 26 00 00 NUM american_scientific_journal-3454 94 1 ๐ต๐ต(๐‘ก๐‘ก ๐ต๐ต(๐‘ก๐‘ก NOUN american_scientific_journal-3454 94 2 ) ) PUNCT american_scientific_journal-3454 94 3 ( ( PUNCT american_scientific_journal-3454 94 4 59 59 NUM american_scientific_journal-3454 94 5 ) ) PUNCT american_scientific_journal-3454 94 6 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 94 7 ๐‘ฆ๐‘ฆ1 ๐‘ฆ๐‘ฆ1 PROPN american_scientific_journal-3454 94 8 ( ( PUNCT american_scientific_journal-3454 94 9 ๐‘ก๐‘ก ๐‘ก๐‘ก ADJ american_scientific_journal-3454 94 10 ) ) PUNCT american_scientific_journal-3454 94 11 ๐‘ฆ๐‘ฆ2(๐‘ก๐‘ก ๐‘ฆ๐‘ฆ2(๐‘ก๐‘ก NOUN american_scientific_journal-3454 94 12 ) ) PUNCT american_scientific_journal-3454 94 13 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 94 14 = = PUNCT american_scientific_journal-3454 95 1 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 95 2 ๏ฃป ๏ฃป PROPN american_scientific_journal-3454 95 3 ๏ฃน ๏ฃน PROPN american_scientific_journal-3454 95 4 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 95 5 ๏ฃฐ ๏ฃฐ NUM american_scientific_journal-3454 95 6 ๏ฃฎ ๏ฃฎ NOUN american_scientific_journal-3454 95 7 0010 0010 NUM american_scientific_journal-3454 95 8 0001 0001 NUM american_scientific_journal-3454 96 1 โŽฃ โŽฃ ADJ american_scientific_journal-3454 96 2 โŽข โŽข NOUN american_scientific_journal-3454 96 3 โŽข โŽข NOUN american_scientific_journal-3454 96 4 โŽก๐‘ฅ๐‘ฅ1 โŽก๐‘ฅ๐‘ฅ1 PROPN american_scientific_journal-3454 96 5 ( ( PUNCT american_scientific_journal-3454 96 6 ๐‘ก๐‘ก ๐‘ก๐‘ก ADJ american_scientific_journal-3454 96 7 ) ) PUNCT american_scientific_journal-3454 96 8 ๐‘ฅ๐‘ฅ2(๐‘ก๐‘ก ๐‘ฅ๐‘ฅ2(๐‘ก๐‘ก NOUN american_scientific_journal-3454 96 9 ) ) PUNCT american_scientific_journal-3454 96 10 ๐‘ฅ๐‘ฅ3(๐‘ก๐‘ก ๐‘ฅ๐‘ฅ3(๐‘ก๐‘ก NOUN american_scientific_journal-3454 96 11 ) ) PUNCT american_scientific_journal-3454 96 12 ๐‘ฅ๐‘ฅ4(๐‘ก๐‘ก)โŽฆ ๐‘ฅ๐‘ฅ4(๐‘ก๐‘ก)โŽฆ VERB american_scientific_journal-3454 96 13 โŽฅ โŽฅ PROPN american_scientific_journal-3454 96 14 โŽฅ โŽฅ PROPN american_scientific_journal-3454 96 15 โŽค โŽค PROPN american_scientific_journal-3454 96 16 ( ( PUNCT american_scientific_journal-3454 96 17 60 60 NUM american_scientific_journal-3454 96 18 ) ) PUNCT american_scientific_journal-3454 96 19 where where SCONJ american_scientific_journal-3454 96 20 ๐‘€๐‘€๐‘๐‘ ๐‘€๐‘€๐‘๐‘ PROPN american_scientific_journal-3454 96 21 represents represent VERB american_scientific_journal-3454 96 22 a a DET american_scientific_journal-3454 96 23 car car NOUN american_scientific_journal-3454 96 24 mass mass NOUN american_scientific_journal-3454 96 25 , , PUNCT american_scientific_journal-3454 96 26 ๐‘š๐‘š๐‘ ๐‘  ๐‘š๐‘š๐‘ ๐‘  NOUN american_scientific_journal-3454 96 27 represents represent VERB american_scientific_journal-3454 96 28 the the DET american_scientific_journal-3454 96 29 driver driver NOUN american_scientific_journal-3454 96 30 plus plus CCONJ american_scientific_journal-3454 96 31 seat seat NOUN american_scientific_journal-3454 96 32 mass mass PROPN american_scientific_journal-3454 96 33 . . PUNCT american_scientific_journal-3454 97 1 the the DET american_scientific_journal-3454 97 2 stiffness stiffness NOUN american_scientific_journal-3454 97 3 ๐‘˜๐‘˜1 ๐‘˜๐‘˜1 PROPN american_scientific_journal-3454 97 4 and and CCONJ american_scientific_journal-3454 97 5 the the DET american_scientific_journal-3454 97 6 damping damp VERB american_scientific_journal-3454 97 7 ๐‘๐‘1 ๐‘๐‘1 NOUN american_scientific_journal-3454 97 8 represent represent VERB american_scientific_journal-3454 97 9 the the DET american_scientific_journal-3454 97 10 shock shock NOUN american_scientific_journal-3454 97 11 absorbers absorber NOUN american_scientific_journal-3454 97 12 by by ADP american_scientific_journal-3454 97 13 which which PRON american_scientific_journal-3454 97 14 the the DET american_scientific_journal-3454 97 15 vertical vertical ADJ american_scientific_journal-3454 97 16 vibration vibration NOUN american_scientific_journal-3454 97 17 caused cause VERB american_scientific_journal-3454 97 18 by by ADP american_scientific_journal-3454 97 19 a a DET american_scientific_journal-3454 97 20 street street NOUN american_scientific_journal-3454 97 21 may may AUX american_scientific_journal-3454 97 22 be be AUX american_scientific_journal-3454 97 23 partially partially ADV american_scientific_journal-3454 97 24 attenuated attenuate VERB american_scientific_journal-3454 97 25 . . PUNCT american_scientific_journal-3454 98 1 the the DET american_scientific_journal-3454 98 2 stiffness stiffness NOUN american_scientific_journal-3454 98 3 ๐‘˜๐‘˜2 ๐‘˜๐‘˜2 PROPN american_scientific_journal-3454 98 4 and and CCONJ american_scientific_journal-3454 98 5 the the DET american_scientific_journal-3454 98 6 damping damp VERB american_scientific_journal-3454 98 7 b2 b2 NOUN american_scientific_journal-3454 98 8 represent represent VERB american_scientific_journal-3454 98 9 the the DET american_scientific_journal-3454 98 10 car car NOUN american_scientific_journal-3454 98 11 seat seat NOUN american_scientific_journal-3454 98 12 suspension suspension NOUN american_scientific_journal-3454 98 13 elements element NOUN american_scientific_journal-3454 98 14 by by ADP american_scientific_journal-3454 98 15 which which PRON american_scientific_journal-3454 98 16 the the DET american_scientific_journal-3454 98 17 undesirable undesirable ADJ american_scientific_journal-3454 98 18 vibrations vibration NOUN american_scientific_journal-3454 98 19 subjected subject VERB american_scientific_journal-3454 98 20 to to ADP american_scientific_journal-3454 98 21 the the DET american_scientific_journal-3454 98 22 driver driver NOUN american_scientific_journal-3454 98 23 can can AUX american_scientific_journal-3454 98 24 be be AUX american_scientific_journal-3454 98 25 reduced reduce VERB american_scientific_journal-3454 98 26 . . PUNCT american_scientific_journal-3454 99 1 the the DET american_scientific_journal-3454 99 2 control control NOUN american_scientific_journal-3454 99 3 inputs input NOUN american_scientific_journal-3454 99 4 ๐ต๐ต1(๐‘ก๐‘ก ๐ต๐ต1(๐‘ก๐‘ก PUNCT american_scientific_journal-3454 99 5 ) ) PUNCT american_scientific_journal-3454 99 6 and and CCONJ american_scientific_journal-3454 99 7 ๐ต๐ต2(๐‘ก๐‘ก).can ๐ต๐ต2(๐‘ก๐‘ก).can AUX american_scientific_journal-3454 99 8 be be AUX american_scientific_journal-3454 99 9 changed change VERB american_scientific_journal-3454 99 10 to to PART american_scientific_journal-3454 99 11 increase increase VERB american_scientific_journal-3454 99 12 the the DET american_scientific_journal-3454 99 13 damping damping NOUN american_scientific_journal-3454 99 14 of of ADP american_scientific_journal-3454 99 15 vibration vibration NOUN american_scientific_journal-3454 99 16 of of ADP american_scientific_journal-3454 99 17 the the DET american_scientific_journal-3454 99 18 masses masse NOUN american_scientific_journal-3454 99 19 ๐‘€๐‘€๐‘๐‘ ๐‘€๐‘€๐‘๐‘ ADJ american_scientific_journal-3454 99 20 and and CCONJ american_scientific_journal-3454 99 21 ๐‘š๐‘š๐‘ ๐‘ . ๐‘š๐‘š๐‘ ๐‘ . ADJ american_scientific_journal-3454 99 22 the the DET american_scientific_journal-3454 99 23 accelerations acceleration NOUN american_scientific_journal-3454 99 24 signals signal VERB american_scientific_journal-3454 99 25 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 99 26 ฬˆ ฬˆ NOUN american_scientific_journal-3454 99 27 ๏ฟฝ ๏ฟฝ NOUN american_scientific_journal-3454 99 28 ๐‘ฅ1(๐‘ก๐‘ก ๐‘ฅ1(๐‘ก๐‘ก NOUN american_scientific_journal-3454 99 29 ) ) PUNCT american_scientific_journal-3454 99 30 and and CCONJ american_scientific_journal-3454 99 31 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 99 32 ฬˆ ฬˆ X american_scientific_journal-3454 99 33 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 99 34 ๐‘ฅ2(๐‘ก๐‘ก ๐‘ฅ2(๐‘ก๐‘ก NUM american_scientific_journal-3454 99 35 ) ) PUNCT american_scientific_journal-3454 99 36 are be AUX american_scientific_journal-3454 99 37 only only ADV american_scientific_journal-3454 99 38 available available ADJ american_scientific_journal-3454 99 39 for for ADP american_scientific_journal-3454 99 40 feedback feedback NOUN american_scientific_journal-3454 99 41 because because SCONJ american_scientific_journal-3454 99 42 they they PRON american_scientific_journal-3454 99 43 are be AUX american_scientific_journal-3454 99 44 measured measure VERB american_scientific_journal-3454 99 45 by by ADP american_scientific_journal-3454 99 46 accelerometers accelerometer NOUN american_scientific_journal-3454 99 47 sensors sensor NOUN american_scientific_journal-3454 99 48 . . PUNCT american_scientific_journal-3454 100 1 depending depend VERB american_scientific_journal-3454 100 2 on on ADP american_scientific_journal-3454 100 3 their their PRON american_scientific_journal-3454 100 4 measured measure VERB american_scientific_journal-3454 100 5 time time NOUN american_scientific_journal-3454 100 6 derivatives derivative NOUN american_scientific_journal-3454 100 7 , , PUNCT american_scientific_journal-3454 100 8 the the DET american_scientific_journal-3454 100 9 velocities velocity NOUN american_scientific_journal-3454 100 10 ๏ฟฝ ๏ฟฝ VERB american_scientific_journal-3454 100 11 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 100 12 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 100 13 ๐‘ฅ1(๐‘ก๐‘ก ๐‘ฅ1(๐‘ก๐‘ก PROPN american_scientific_journal-3454 100 14 ) ) PUNCT american_scientific_journal-3454 100 15 and and CCONJ american_scientific_journal-3454 100 16 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 100 17 ฬ‡ ฬ‡ PROPN american_scientific_journal-3454 100 18 ๏ฟฝ ๏ฟฝ PROPN american_scientific_journal-3454 100 19 ๐‘ฅ2(๐‘ก๐‘ก ๐‘ฅ2(๐‘ก๐‘ก NUM american_scientific_journal-3454 100 20 ) ) PUNCT american_scientific_journal-3454 100 21 can can AUX american_scientific_journal-3454 100 22 be be AUX american_scientific_journal-3454 100 23 estimated estimate VERB american_scientific_journal-3454 100 24 . . PUNCT american_scientific_journal-3454 101 1 now now ADV american_scientific_journal-3454 101 2 , , PUNCT american_scientific_journal-3454 101 3 the the DET american_scientific_journal-3454 101 4 accelerations acceleration NOUN american_scientific_journal-3454 101 5 and and CCONJ american_scientific_journal-3454 101 6 velocities velocity NOUN american_scientific_journal-3454 101 7 signals signal NOUN american_scientific_journal-3454 101 8 are be AUX american_scientific_journal-3454 101 9 available available ADJ american_scientific_journal-3454 101 10 and and CCONJ american_scientific_journal-3454 101 11 the the DET american_scientific_journal-3454 101 12 proposed propose VERB american_scientific_journal-3454 101 13 method method NOUN american_scientific_journal-3454 101 14 can can AUX american_scientific_journal-3454 101 15 be be AUX american_scientific_journal-3454 101 16 used use VERB american_scientific_journal-3454 101 17 to to PART american_scientific_journal-3454 101 18 solve solve VERB american_scientific_journal-3454 101 19 the the DET american_scientific_journal-3454 101 20 problem problem NOUN american_scientific_journal-3454 101 21 . . PUNCT american_scientific_journal-3454 102 1 figure figure NOUN american_scientific_journal-3454 102 2 1 1 NUM american_scientific_journal-3454 102 3 : : PUNCT american_scientific_journal-3454 102 4 active active ADJ american_scientific_journal-3454 102 5 suspension suspension NOUN american_scientific_journal-3454 102 6 of of ADP american_scientific_journal-3454 102 7 a a DET american_scientific_journal-3454 102 8 car car NOUN american_scientific_journal-3454 102 9 seat seat NOUN american_scientific_journal-3454 103 1 [ [ X american_scientific_journal-3454 103 2 7 7 NUM american_scientific_journal-3454 103 3 ] ] PUNCT american_scientific_journal-3454 103 4 . . PUNCT american_scientific_journal-3454 104 1 american american PROPN american_scientific_journal-3454 104 2 scientific scientific ADJ american_scientific_journal-3454 104 3 research research PROPN american_scientific_journal-3454 104 4 journal journal NOUN american_scientific_journal-3454 104 5 for for ADP american_scientific_journal-3454 104 6 engineering engineering NOUN american_scientific_journal-3454 104 7 , , PUNCT american_scientific_journal-3454 104 8 technology technology NOUN american_scientific_journal-3454 104 9 , , PUNCT american_scientific_journal-3454 104 10 and and CCONJ american_scientific_journal-3454 104 11 sciences science NOUN american_scientific_journal-3454 104 12 ( ( PUNCT american_scientific_journal-3454 104 13 asrjets asrjet NOUN american_scientific_journal-3454 104 14 ) ) PUNCT american_scientific_journal-3454 104 15 ( ( PUNCT american_scientific_journal-3454 104 16 2017 2017 NUM american_scientific_journal-3454 104 17 ) ) PUNCT american_scientific_journal-3454 104 18 volume volume NOUN american_scientific_journal-3454 104 19 37 37 NUM american_scientific_journal-3454 104 20 , , PUNCT american_scientific_journal-3454 104 21 no no DET american_scientific_journal-3454 104 22 1 1 NUM american_scientific_journal-3454 104 23 , , PUNCT american_scientific_journal-3454 104 24 pp pp ADV american_scientific_journal-3454 104 25 118 118 NUM american_scientific_journal-3454 104 26 - - SYM american_scientific_journal-3454 104 27 128 128 NUM american_scientific_journal-3454 104 28 126 126 NUM american_scientific_journal-3454 104 29 the the DET american_scientific_journal-3454 104 30 nominal nominal ADJ american_scientific_journal-3454 104 31 system system NOUN american_scientific_journal-3454 104 32 parameters parameter NOUN american_scientific_journal-3454 104 33 are be AUX american_scientific_journal-3454 104 34 taken take VERB american_scientific_journal-3454 104 35 as as SCONJ american_scientific_journal-3454 104 36 follows follow VERB american_scientific_journal-3454 104 37 [ [ X american_scientific_journal-3454 104 38 7 7 NUM american_scientific_journal-3454 104 39 ] ] X american_scientific_journal-3454 104 40 : : PUNCT american_scientific_journal-3454 104 41 ๐‘๐‘1(damping ๐‘๐‘1(dampe VERB american_scientific_journal-3454 104 42 ) ) PUNCT american_scientific_journal-3454 104 43 = = SYM american_scientific_journal-3454 104 44 4 4 NUM american_scientific_journal-3454 104 45 ร— ร— NOUN american_scientific_journal-3454 104 46 103 103 NUM american_scientific_journal-3454 104 47 ns ns PROPN american_scientific_journal-3454 104 48 / / SYM american_scientific_journal-3454 104 49 m m PROPN american_scientific_journal-3454 104 50 , , PUNCT american_scientific_journal-3454 104 51 ๐‘๐‘2(damper ๐‘๐‘2(damper PRON american_scientific_journal-3454 104 52 of of ADP american_scientific_journal-3454 104 53 the the DET american_scientific_journal-3454 104 54 seat seat NOUN american_scientific_journal-3454 104 55 suspension suspension NOUN american_scientific_journal-3454 104 56 ) ) PUNCT american_scientific_journal-3454 105 1 = = SYM american_scientific_journal-3454 105 2 5 5 NUM american_scientific_journal-3454 105 3 ร— ร— NOUN american_scientific_journal-3454 105 4 102 102 NUM american_scientific_journal-3454 105 5 ns ns NUM american_scientific_journal-3454 105 6 / / SYM american_scientific_journal-3454 105 7 m m PROPN american_scientific_journal-3454 105 8 , , PUNCT american_scientific_journal-3454 105 9 ๐‘˜๐‘˜1 ๐‘˜๐‘˜1 PROPN american_scientific_journal-3454 105 10 ( ( PUNCT american_scientific_journal-3454 105 11 stiffness)= stiffness)= ADJ american_scientific_journal-3454 105 12 4 4 NUM american_scientific_journal-3454 105 13 ร— ร— NOUN american_scientific_journal-3454 105 14 104 104 NUM american_scientific_journal-3454 105 15 n n CCONJ american_scientific_journal-3454 105 16 / / SYM american_scientific_journal-3454 105 17 m m PROPN american_scientific_journal-3454 105 18 , , PUNCT american_scientific_journal-3454 105 19 ๐‘˜๐‘˜2 ๐‘˜๐‘˜2 PROPN american_scientific_journal-3454 105 20 ( ( PUNCT american_scientific_journal-3454 105 21 stiffness)= stiffness)= ADJ american_scientific_journal-3454 105 22 5 5 NUM american_scientific_journal-3454 105 23 ร— ร— NOUN american_scientific_journal-3454 105 24 103 103 NUM american_scientific_journal-3454 105 25 n n CCONJ american_scientific_journal-3454 105 26 / / SYM american_scientific_journal-3454 105 27 m m PROPN american_scientific_journal-3454 105 28 , , PUNCT american_scientific_journal-3454 105 29 ๐‘€๐‘€๐ถ๐ถ ๐‘€๐‘€๐ถ๐ถ PROPN american_scientific_journal-3454 105 30 ( ( PUNCT american_scientific_journal-3454 105 31 mass mass NOUN american_scientific_journal-3454 105 32 of of ADP american_scientific_journal-3454 105 33 the the DET american_scientific_journal-3454 105 34 car)= car)= PROPN american_scientific_journal-3454 105 35 1500 1500 NUM american_scientific_journal-3454 105 36 kg kg NOUN american_scientific_journal-3454 105 37 , , PUNCT american_scientific_journal-3454 105 38 ๐‘š๐‘š๐‘ ๐‘ (mass ๐‘š๐‘š๐‘ ๐‘ (mass PROPN american_scientific_journal-3454 105 39 of of ADP american_scientific_journal-3454 105 40 the the DET american_scientific_journal-3454 105 41 driver driver NOUN american_scientific_journal-3454 105 42 ) ) PUNCT american_scientific_journal-3454 105 43 = = PUNCT american_scientific_journal-3454 106 1 70 70 NUM american_scientific_journal-3454 106 2 kg kg NOUN american_scientific_journal-3454 106 3 . . PROPN american_scientific_journal-3454 106 4 3.1 3.1 NUM american_scientific_journal-3454 106 5 . . PROPN american_scientific_journal-3454 106 6 lqr lqr PROPN american_scientific_journal-3454 106 7 controller controller PROPN american_scientific_journal-3454 106 8 results result NOUN american_scientific_journal-3454 106 9 figure figure VERB american_scientific_journal-3454 106 10 2 2 NUM american_scientific_journal-3454 106 11 shows show VERB american_scientific_journal-3454 106 12 the the DET american_scientific_journal-3454 106 13 system system NOUN american_scientific_journal-3454 106 14 states state VERB american_scientific_journal-3454 106 15 trajectories trajectory NOUN american_scientific_journal-3454 106 16 when when SCONJ american_scientific_journal-3454 106 17 state state NOUN american_scientific_journal-3454 106 18 feedback feedback NOUN american_scientific_journal-3454 106 19 lqr lqr VERB american_scientific_journal-3454 106 20 control control NOUN american_scientific_journal-3454 106 21 and and CCONJ american_scientific_journal-3454 106 22 state state NOUN american_scientific_journal-3454 106 23 derivative derivative ADJ american_scientific_journal-3454 106 24 feedback feedback NOUN american_scientific_journal-3454 106 25 lqr lqr NOUN american_scientific_journal-3454 106 26 control control NOUN american_scientific_journal-3454 106 27 are be AUX american_scientific_journal-3454 106 28 applied apply VERB american_scientific_journal-3454 106 29 . . PUNCT american_scientific_journal-3454 107 1 it it PRON american_scientific_journal-3454 107 2 shows show VERB american_scientific_journal-3454 107 3 that that SCONJ american_scientific_journal-3454 107 4 the the DET american_scientific_journal-3454 107 5 response response NOUN american_scientific_journal-3454 107 6 obtained obtain VERB american_scientific_journal-3454 107 7 using use VERB american_scientific_journal-3454 107 8 state state NOUN american_scientific_journal-3454 107 9 derivative derivative ADJ american_scientific_journal-3454 107 10 feedback feedback NOUN american_scientific_journal-3454 107 11 lqr lqr NOUN american_scientific_journal-3454 107 12 control control NOUN american_scientific_journal-3454 107 13 is be AUX american_scientific_journal-3454 107 14 fast fast ADJ american_scientific_journal-3454 107 15 with with ADP american_scientific_journal-3454 107 16 small small ADJ american_scientific_journal-3454 107 17 oscillation oscillation NOUN american_scientific_journal-3454 107 18 amplitudes amplitude NOUN american_scientific_journal-3454 107 19 in in ADP american_scientific_journal-3454 107 20 comparison comparison NOUN american_scientific_journal-3454 107 21 to to ADP american_scientific_journal-3454 107 22 that that PRON american_scientific_journal-3454 107 23 obtained obtain VERB american_scientific_journal-3454 107 24 using use VERB american_scientific_journal-3454 107 25 state state NOUN american_scientific_journal-3454 107 26 feedback feedback NOUN american_scientific_journal-3454 107 27 lqr lqr NOUN american_scientific_journal-3454 107 28 control control NOUN american_scientific_journal-3454 107 29 . . PUNCT american_scientific_journal-3454 108 1 the the DET american_scientific_journal-3454 108 2 performance performance NOUN american_scientific_journal-3454 108 3 index index NOUN american_scientific_journal-3454 108 4 weighting weight VERB american_scientific_journal-3454 108 5 matrices matrix NOUN american_scientific_journal-3454 108 6 q q NOUN american_scientific_journal-3454 108 7 and and CCONJ american_scientific_journal-3454 108 8 r r NOUN american_scientific_journal-3454 108 9 for for ADP american_scientific_journal-3454 108 10 state state NOUN american_scientific_journal-3454 108 11 feedback feedback NOUN american_scientific_journal-3454 108 12 lqr lqr VERB american_scientific_journal-3454 108 13 control control NOUN american_scientific_journal-3454 108 14 and and CCONJ american_scientific_journal-3454 108 15 state state NOUN american_scientific_journal-3454 108 16 derivative derivative ADJ american_scientific_journal-3454 108 17 feedback feedback NOUN american_scientific_journal-3454 108 18 lqr lqr NOUN american_scientific_journal-3454 108 19 control control NOUN american_scientific_journal-3454 108 20 are be AUX american_scientific_journal-3454 108 21 chosen choose VERB american_scientific_journal-3454 108 22 as as ADP american_scientific_journal-3454 108 23 q q NOUN american_scientific_journal-3454 108 24 = = PRON american_scientific_journal-3454 108 25 diag{8 diag{8 VERB american_scientific_journal-3454 108 26 ร— ร— PROPN american_scientific_journal-3454 108 27 107 107 NUM american_scientific_journal-3454 108 28 , , PUNCT american_scientific_journal-3454 108 29 0.568475001 0.568475001 NUM american_scientific_journal-3454 108 30 , , PUNCT american_scientific_journal-3454 108 31 0.2 0.2 NUM american_scientific_journal-3454 108 32 ร— ร— NOUN american_scientific_journal-3454 108 33 10โˆ’8 10โˆ’8 NUM american_scientific_journal-3454 108 34 , , PUNCT american_scientific_journal-3454 108 35 0.8521111 0.8521111 NUM american_scientific_journal-3454 108 36 } } PUNCT american_scientific_journal-3454 108 37 and and CCONJ american_scientific_journal-3454 108 38 r r NOUN american_scientific_journal-3454 108 39 = = SYM american_scientific_journal-3454 108 40 diag{1 diag{1 ADJ american_scientific_journal-3454 108 41 , , PUNCT american_scientific_journal-3454 108 42 1 1 NUM american_scientific_journal-3454 108 43 } } PUNCT american_scientific_journal-3454 108 44 . . PUNCT american_scientific_journal-3454 109 1 the the DET american_scientific_journal-3454 109 2 resulting result VERB american_scientific_journal-3454 109 3 feedback feedback NOUN american_scientific_journal-3454 109 4 gain gain NOUN american_scientific_journal-3454 109 5 matrices matrix NOUN american_scientific_journal-3454 109 6 in in ADP american_scientific_journal-3454 109 7 cases case NOUN american_scientific_journal-3454 109 8 , , PUNCT american_scientific_journal-3454 109 9 state state NOUN american_scientific_journal-3454 109 10 feedback feedback NOUN american_scientific_journal-3454 109 11 lqr lqr VERB american_scientific_journal-3454 109 12 control control NOUN american_scientific_journal-3454 109 13 and and CCONJ american_scientific_journal-3454 109 14 state state NOUN american_scientific_journal-3454 109 15 derivative derivative ADJ american_scientific_journal-3454 109 16 feedback feedback NOUN american_scientific_journal-3454 109 17 lqr lqr VERB american_scientific_journal-3454 109 18 control control NOUN american_scientific_journal-3454 109 19 respectively respectively ADV american_scientific_journal-3454 109 20 are be AUX american_scientific_journal-3454 109 21 : : PUNCT american_scientific_journal-3454 109 22 ๐พ๐พ ๐พ๐พ PROPN american_scientific_journal-3454 109 23 = = PUNCT american_scientific_journal-3454 109 24 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 109 25 ๏ฃป ๏ฃป PROPN american_scientific_journal-3454 109 26 ๏ฃน ๏ฃน PROPN american_scientific_journal-3454 109 27 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 109 28 ๏ฃฐ ๏ฃฐ NUM american_scientific_journal-3454 109 29 ๏ฃฎ ๏ฃฎ PROPN american_scientific_journal-3454 109 30 โˆ’โˆ’ โˆ’โˆ’ PROPN american_scientific_journal-3454 109 31 4995.68865.622854.04379.417 4995.68865.622854.04379.417 NUM american_scientific_journal-3454 109 32 9456.182930.3438625.501726.935 9456.182930.3438625.501726.935 NUM american_scientific_journal-3454 109 33 ๐พ๐พ ๐พ๐พ NOUN american_scientific_journal-3454 109 34 = = PUNCT american_scientific_journal-3454 109 35 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 109 36 ๏ฃป ๏ฃป PROPN american_scientific_journal-3454 109 37 ๏ฃน ๏ฃน PROPN american_scientific_journal-3454 109 38 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 109 39 ๏ฃฐ ๏ฃฐ NOUN american_scientific_journal-3454 109 40 ๏ฃฎ ๏ฃฎ VERB american_scientific_journal-3454 109 41 ร—โˆ’ร—ร—ร— ร—โˆ’ร—ร—ร— NOUN american_scientific_journal-3454 109 42 ร—โˆ’ร—โˆ’ร—โˆ’ร— ร—โˆ’ร—โˆ’ร—โˆ’ร— ADP american_scientific_journal-3454 109 43 3333 3333 NUM american_scientific_journal-3454 109 44 3333 3333 NUM american_scientific_journal-3454 109 45 100072.0101273.0100629.0101000.1 100072.0101273.0100629.0101000.1 NOUN american_scientific_journal-3454 109 46 100582.0104695.1102590.0106024.4 100582.0104695.1102590.0106024.4 NUM american_scientific_journal-3454 109 47 figure figure NOUN american_scientific_journal-3454 109 48 2 2 NUM american_scientific_journal-3454 109 49 : : PUNCT american_scientific_journal-3454 109 50 system system NOUN american_scientific_journal-3454 109 51 trajectories trajectory NOUN american_scientific_journal-3454 109 52 using use VERB american_scientific_journal-3454 109 53 state state NOUN american_scientific_journal-3454 109 54 feedback feedback NOUN american_scientific_journal-3454 109 55 lqr lqr NOUN american_scientific_journal-3454 109 56 control control NOUN american_scientific_journal-3454 109 57 ( ( PUNCT american_scientific_journal-3454 109 58 dotted dotted ADJ american_scientific_journal-3454 109 59 line line NOUN american_scientific_journal-3454 109 60 ) ) PUNCT american_scientific_journal-3454 109 61 and and CCONJ american_scientific_journal-3454 109 62 state state NOUN american_scientific_journal-3454 109 63 derivative derivative ADJ american_scientific_journal-3454 109 64 feedback feedback NOUN american_scientific_journal-3454 109 65 lqr lqr NOUN american_scientific_journal-3454 109 66 control control NOUN american_scientific_journal-3454 109 67 ( ( PUNCT american_scientific_journal-3454 109 68 solid solid ADJ american_scientific_journal-3454 109 69 line line NOUN american_scientific_journal-3454 109 70 ) ) PUNCT american_scientific_journal-3454 109 71 . . PUNCT american_scientific_journal-3454 110 1 american american PROPN american_scientific_journal-3454 110 2 scientific scientific ADJ american_scientific_journal-3454 110 3 research research PROPN american_scientific_journal-3454 110 4 journal journal NOUN american_scientific_journal-3454 110 5 for for ADP american_scientific_journal-3454 110 6 engineering engineering NOUN american_scientific_journal-3454 110 7 , , PUNCT american_scientific_journal-3454 110 8 technology technology NOUN american_scientific_journal-3454 110 9 , , PUNCT american_scientific_journal-3454 110 10 and and CCONJ american_scientific_journal-3454 110 11 sciences science NOUN american_scientific_journal-3454 110 12 ( ( PUNCT american_scientific_journal-3454 110 13 asrjets asrjet NOUN american_scientific_journal-3454 110 14 ) ) PUNCT american_scientific_journal-3454 110 15 ( ( PUNCT american_scientific_journal-3454 110 16 2017 2017 NUM american_scientific_journal-3454 110 17 ) ) PUNCT american_scientific_journal-3454 110 18 volume volume NOUN american_scientific_journal-3454 110 19 37 37 NUM american_scientific_journal-3454 110 20 , , PUNCT american_scientific_journal-3454 110 21 no no DET american_scientific_journal-3454 110 22 1 1 NUM american_scientific_journal-3454 110 23 , , PUNCT american_scientific_journal-3454 110 24 pp pp ADV american_scientific_journal-3454 110 25 118 118 NUM american_scientific_journal-3454 110 26 - - SYM american_scientific_journal-3454 110 27 128 128 NUM american_scientific_journal-3454 110 28 127 127 NUM american_scientific_journal-3454 110 29 3.2 3.2 NUM american_scientific_journal-3454 110 30 . . PUNCT american_scientific_journal-3454 111 1 ๐‘ฏ๐‘ฏ๐Ÿ๐Ÿ ๐‘ฏ๐‘ฏ๐Ÿ๐Ÿ ADJ american_scientific_journal-3454 111 2 controller controller NOUN american_scientific_journal-3454 111 3 results result NOUN american_scientific_journal-3454 111 4 figure figure VERB american_scientific_journal-3454 111 5 4 4 NUM american_scientific_journal-3454 111 6 shows show VERB american_scientific_journal-3454 111 7 the the DET american_scientific_journal-3454 111 8 system system NOUN american_scientific_journal-3454 111 9 states state VERB american_scientific_journal-3454 111 10 trajectories trajectory NOUN american_scientific_journal-3454 111 11 when when SCONJ american_scientific_journal-3454 111 12 state state NOUN american_scientific_journal-3454 111 13 feedback feedback NOUN american_scientific_journal-3454 111 14 h2 h2 NOUN american_scientific_journal-3454 111 15 control control NOUN american_scientific_journal-3454 111 16 and and CCONJ american_scientific_journal-3454 111 17 state state NOUN american_scientific_journal-3454 111 18 derivative derivative ADJ american_scientific_journal-3454 111 19 feedback feedback NOUN american_scientific_journal-3454 111 20 h2 h2 NOUN american_scientific_journal-3454 111 21 control control NOUN american_scientific_journal-3454 111 22 are be AUX american_scientific_journal-3454 111 23 applied apply VERB american_scientific_journal-3454 111 24 . . PUNCT american_scientific_journal-3454 112 1 it it PRON american_scientific_journal-3454 112 2 shows show VERB american_scientific_journal-3454 112 3 that that SCONJ american_scientific_journal-3454 112 4 the the DET american_scientific_journal-3454 112 5 response response NOUN american_scientific_journal-3454 112 6 obtained obtain VERB american_scientific_journal-3454 112 7 using use VERB american_scientific_journal-3454 112 8 state state NOUN american_scientific_journal-3454 112 9 derivative derivative ADJ american_scientific_journal-3454 112 10 feedback feedback NOUN american_scientific_journal-3454 112 11 h2 h2 NOUN american_scientific_journal-3454 112 12 control control NOUN american_scientific_journal-3454 112 13 is be AUX american_scientific_journal-3454 112 14 fast fast ADJ american_scientific_journal-3454 112 15 with with ADP american_scientific_journal-3454 112 16 small small ADJ american_scientific_journal-3454 112 17 oscillation oscillation NOUN american_scientific_journal-3454 112 18 amplitudes amplitude NOUN american_scientific_journal-3454 112 19 in in ADP american_scientific_journal-3454 112 20 comparison comparison NOUN american_scientific_journal-3454 112 21 to to ADP american_scientific_journal-3454 112 22 that that PRON american_scientific_journal-3454 112 23 obtained obtain VERB american_scientific_journal-3454 112 24 using use VERB american_scientific_journal-3454 112 25 state state NOUN american_scientific_journal-3454 112 26 feedback feedback NOUN american_scientific_journal-3454 112 27 h2 h2 NOUN american_scientific_journal-3454 112 28 control control NOUN american_scientific_journal-3454 112 29 . . PUNCT american_scientific_journal-3454 113 1 the the DET american_scientific_journal-3454 113 2 performance performance NOUN american_scientific_journal-3454 113 3 index index NOUN american_scientific_journal-3454 113 4 weighting weight VERB american_scientific_journal-3454 113 5 matrices matrix NOUN american_scientific_journal-3454 113 6 q q NOUN american_scientific_journal-3454 113 7 and and CCONJ american_scientific_journal-3454 113 8 r r NOUN american_scientific_journal-3454 113 9 for for ADP american_scientific_journal-3454 113 10 state state NOUN american_scientific_journal-3454 113 11 feedback feedback NOUN american_scientific_journal-3454 113 12 h2 h2 NOUN american_scientific_journal-3454 113 13 control control NOUN american_scientific_journal-3454 113 14 and and CCONJ american_scientific_journal-3454 113 15 state state NOUN american_scientific_journal-3454 113 16 derivative derivative ADJ american_scientific_journal-3454 113 17 feedback feedback NOUN american_scientific_journal-3454 113 18 h2 h2 NOUN american_scientific_journal-3454 113 19 control control NOUN american_scientific_journal-3454 113 20 are be AUX american_scientific_journal-3454 113 21 chosen choose VERB american_scientific_journal-3454 113 22 as as ADP american_scientific_journal-3454 113 23 q q NOUN american_scientific_journal-3454 113 24 = = SYM american_scientific_journal-3454 113 25 diag{100,100 diag{100,100 NOUN american_scientific_journal-3454 113 26 , , PUNCT american_scientific_journal-3454 113 27 1 1 NUM american_scientific_journal-3454 113 28 , , PUNCT american_scientific_journal-3454 113 29 1 1 NUM american_scientific_journal-3454 113 30 } } PUNCT american_scientific_journal-3454 113 31 and and CCONJ american_scientific_journal-3454 113 32 r r NOUN american_scientific_journal-3454 113 33 = = SYM american_scientific_journal-3454 113 34 diag{0.01 diag{0.01 PROPN american_scientific_journal-3454 113 35 , , PUNCT american_scientific_journal-3454 113 36 100 100 NUM american_scientific_journal-3454 113 37 } } PUNCT american_scientific_journal-3454 113 38 . . PUNCT american_scientific_journal-3454 114 1 the the DET american_scientific_journal-3454 114 2 resulting result VERB american_scientific_journal-3454 114 3 feedback feedback NOUN american_scientific_journal-3454 114 4 gain gain NOUN american_scientific_journal-3454 114 5 matrices matrix NOUN american_scientific_journal-3454 114 6 in in ADP american_scientific_journal-3454 114 7 cases case NOUN american_scientific_journal-3454 114 8 , , PUNCT american_scientific_journal-3454 114 9 state state NOUN american_scientific_journal-3454 114 10 feedback feedback NOUN american_scientific_journal-3454 114 11 h2 h2 NOUN american_scientific_journal-3454 114 12 control control NOUN american_scientific_journal-3454 114 13 and and CCONJ american_scientific_journal-3454 114 14 state state NOUN american_scientific_journal-3454 114 15 derivative derivative ADJ american_scientific_journal-3454 114 16 feedback feedback NOUN american_scientific_journal-3454 114 17 h2 h2 NOUN american_scientific_journal-3454 114 18 control control NOUN american_scientific_journal-3454 114 19 respectively respectively ADV american_scientific_journal-3454 114 20 are be AUX american_scientific_journal-3454 114 21 : : PUNCT american_scientific_journal-3454 114 22 ๐พ๐พ ๐พ๐พ PROPN american_scientific_journal-3454 114 23 = = PUNCT american_scientific_journal-3454 115 1 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 115 2 ๏ฃป ๏ฃป PROPN american_scientific_journal-3454 115 3 ๏ฃน ๏ฃน PROPN american_scientific_journal-3454 115 4 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 115 5 ๏ฃฐ ๏ฃฐ NUM american_scientific_journal-3454 115 6 ๏ฃฎ ๏ฃฎ PROPN american_scientific_journal-3454 115 7 ร—ร—ร—ร— ร—ร—ร—ร— NOUN american_scientific_journal-3454 115 8 ร—ร—ร—ร— ร—ร—ร—ร— VERB american_scientific_journal-3454 115 9 3333 3333 NUM american_scientific_journal-3454 115 10 3333 3333 NUM american_scientific_journal-3454 115 11 100001.0100012.0100011.0100021.0 100001.0100012.0100011.0100021.0 PROPN american_scientific_journal-3454 115 12 101164.0109903.0103209.9104641.6 101164.0109903.0103209.9104641.6 PROPN american_scientific_journal-3454 115 13 ๐พ๐พ ๐พ๐พ NOUN american_scientific_journal-3454 115 14 = = PUNCT american_scientific_journal-3454 116 1 ๏ฃบ ๏ฃบ PROPN american_scientific_journal-3454 116 2 ๏ฃป ๏ฃป PROPN american_scientific_journal-3454 116 3 ๏ฃน ๏ฃน PROPN american_scientific_journal-3454 116 4 ๏ฃฏ ๏ฃฏ ADJ american_scientific_journal-3454 116 5 ๏ฃฐ ๏ฃฐ NUM american_scientific_journal-3454 116 6 ๏ฃฎ ๏ฃฎ NOUN american_scientific_journal-3454 116 7 ร—โˆ’ร—ร—โˆ’ร—โˆ’ ร—โˆ’ร—ร—โˆ’ร—โˆ’ VERB american_scientific_journal-3454 116 8 ร—โˆ’ร—โˆ’ร—ร— ร—โˆ’ร—โˆ’ร—ร— PROPN american_scientific_journal-3454 116 9 3333 3333 NUM american_scientific_journal-3454 116 10 3333 3333 NUM american_scientific_journal-3454 116 11 100005.0100008.0100119.0100101.0 100005.0100008.0100119.0100101.0 NUM american_scientific_journal-3454 116 12 102162.0101078.1106049.9109414.2 102162.0101078.1106049.9109414.2 PROPN american_scientific_journal-3454 116 13 figure figure VERB american_scientific_journal-3454 116 14 4 4 NUM american_scientific_journal-3454 116 15 : : PUNCT american_scientific_journal-3454 116 16 system system NOUN american_scientific_journal-3454 116 17 trajectories trajectory NOUN american_scientific_journal-3454 116 18 using use VERB american_scientific_journal-3454 116 19 state state NOUN american_scientific_journal-3454 116 20 feedback feedback NOUN american_scientific_journal-3454 116 21 h2 h2 NOUN american_scientific_journal-3454 116 22 control control NOUN american_scientific_journal-3454 116 23 ( ( PUNCT american_scientific_journal-3454 116 24 dotted dotted ADJ american_scientific_journal-3454 116 25 line line NOUN american_scientific_journal-3454 116 26 ) ) PUNCT american_scientific_journal-3454 116 27 and and CCONJ american_scientific_journal-3454 116 28 state state NOUN american_scientific_journal-3454 116 29 derivative derivative ADJ american_scientific_journal-3454 116 30 feedback feedback NOUN american_scientific_journal-3454 116 31 h2 h2 NOUN american_scientific_journal-3454 116 32 control control NOUN american_scientific_journal-3454 116 33 ( ( PUNCT american_scientific_journal-3454 116 34 solid solid ADJ american_scientific_journal-3454 116 35 line line NOUN american_scientific_journal-3454 116 36 ) ) PUNCT american_scientific_journal-3454 116 37 . . PUNCT american_scientific_journal-3454 117 1 4 4 X american_scientific_journal-3454 117 2 . . X american_scientific_journal-3454 117 3 conclusion conclusion NOUN american_scientific_journal-3454 117 4 in in ADP american_scientific_journal-3454 117 5 this this DET american_scientific_journal-3454 117 6 paper paper NOUN american_scientific_journal-3454 117 7 the the DET american_scientific_journal-3454 117 8 lqr lqr PROPN american_scientific_journal-3454 117 9 and and CCONJ american_scientific_journal-3454 117 10 h2 h2 NOUN american_scientific_journal-3454 117 11 controllers controller NOUN american_scientific_journal-3454 117 12 have have AUX american_scientific_journal-3454 117 13 been be AUX american_scientific_journal-3454 117 14 designed design VERB american_scientific_journal-3454 117 15 using use VERB american_scientific_journal-3454 117 16 state state NOUN american_scientific_journal-3454 117 17 derivative derivative ADJ american_scientific_journal-3454 117 18 feedback feedback NOUN american_scientific_journal-3454 117 19 . . PUNCT american_scientific_journal-3454 118 1 the the DET american_scientific_journal-3454 118 2 h2 h2 PROPN american_scientific_journal-3454 118 3 optimal optimal ADJ american_scientific_journal-3454 118 4 control control NOUN american_scientific_journal-3454 118 5 has have AUX american_scientific_journal-3454 118 6 been be AUX american_scientific_journal-3454 118 7 derived derive VERB american_scientific_journal-3454 118 8 using use VERB american_scientific_journal-3454 118 9 state state NOUN american_scientific_journal-3454 118 10 derivative derivative ADJ american_scientific_journal-3454 118 11 feedback feedback NOUN american_scientific_journal-3454 118 12 similar similar ADJ american_scientific_journal-3454 118 13 to to ADP american_scientific_journal-3454 118 14 lqr lqr NOUN american_scientific_journal-3454 118 15 to to PART american_scientific_journal-3454 118 16 find find VERB american_scientific_journal-3454 118 17 the the DET american_scientific_journal-3454 118 18 optimal optimal ADJ american_scientific_journal-3454 118 19 gain gain NOUN american_scientific_journal-3454 118 20 matrices matrix NOUN american_scientific_journal-3454 118 21 that that PRON american_scientific_journal-3454 118 22 american american ADJ american_scientific_journal-3454 118 23 scientific scientific ADJ american_scientific_journal-3454 118 24 research research NOUN american_scientific_journal-3454 118 25 journal journal NOUN american_scientific_journal-3454 118 26 for for ADP american_scientific_journal-3454 118 27 engineering engineering NOUN american_scientific_journal-3454 118 28 , , PUNCT american_scientific_journal-3454 118 29 technology technology NOUN american_scientific_journal-3454 118 30 , , PUNCT american_scientific_journal-3454 118 31 and and CCONJ american_scientific_journal-3454 118 32 sciences science NOUN american_scientific_journal-3454 118 33 ( ( PUNCT american_scientific_journal-3454 118 34 asrjets asrjet NOUN american_scientific_journal-3454 118 35 ) ) PUNCT american_scientific_journal-3454 118 36 ( ( PUNCT american_scientific_journal-3454 118 37 2017 2017 NUM american_scientific_journal-3454 118 38 ) ) PUNCT american_scientific_journal-3454 118 39 volume volume NOUN american_scientific_journal-3454 118 40 37 37 NUM american_scientific_journal-3454 118 41 , , PUNCT american_scientific_journal-3454 118 42 no no DET american_scientific_journal-3454 118 43 1 1 NUM american_scientific_journal-3454 118 44 , , PUNCT american_scientific_journal-3454 118 45 pp pp ADV american_scientific_journal-3454 118 46 118 118 NUM american_scientific_journal-3454 118 47 - - SYM american_scientific_journal-3454 118 48 128 128 NUM american_scientific_journal-3454 118 49 128 128 NUM american_scientific_journal-3454 118 50 achieve achieve VERB american_scientific_journal-3454 118 51 the the DET american_scientific_journal-3454 118 52 desired desire VERB american_scientific_journal-3454 118 53 performance performance NOUN american_scientific_journal-3454 118 54 . . PUNCT american_scientific_journal-3454 119 1 the the DET american_scientific_journal-3454 119 2 two two NUM american_scientific_journal-3454 119 3 designed design VERB american_scientific_journal-3454 119 4 approaches approach NOUN american_scientific_journal-3454 119 5 were be AUX american_scientific_journal-3454 119 6 applied apply VERB american_scientific_journal-3454 119 7 to to ADP american_scientific_journal-3454 119 8 a a DET american_scientific_journal-3454 119 9 multivariable multivariable ADJ american_scientific_journal-3454 119 10 active active ADJ american_scientific_journal-3454 119 11 suspension suspension NOUN american_scientific_journal-3454 119 12 system system NOUN american_scientific_journal-3454 119 13 . . PUNCT american_scientific_journal-3454 120 1 it it PRON american_scientific_journal-3454 120 2 was be AUX american_scientific_journal-3454 120 3 found find VERB american_scientific_journal-3454 120 4 that that SCONJ american_scientific_journal-3454 120 5 the the DET american_scientific_journal-3454 120 6 designed design VERB american_scientific_journal-3454 120 7 lqr lqr NOUN american_scientific_journal-3454 120 8 and and CCONJ american_scientific_journal-3454 120 9 h2 h2 NOUN american_scientific_journal-3454 120 10 controllers controller NOUN american_scientific_journal-3454 120 11 using use VERB american_scientific_journal-3454 120 12 state state NOUN american_scientific_journal-3454 120 13 derivative derivative ADJ american_scientific_journal-3454 120 14 feedback feedback NOUN american_scientific_journal-3454 120 15 can can AUX american_scientific_journal-3454 120 16 given give VERB american_scientific_journal-3454 120 17 a a DET american_scientific_journal-3454 120 18 better well ADJ american_scientific_journal-3454 120 19 performance performance NOUN american_scientific_journal-3454 120 20 in in ADP american_scientific_journal-3454 120 21 comparison comparison NOUN american_scientific_journal-3454 120 22 to to ADP american_scientific_journal-3454 120 23 the the DET american_scientific_journal-3454 120 24 same same ADJ american_scientific_journal-3454 120 25 approaches approach NOUN american_scientific_journal-3454 120 26 using use VERB american_scientific_journal-3454 120 27 state state NOUN american_scientific_journal-3454 120 28 feedback feedback NOUN american_scientific_journal-3454 120 29 . . PUNCT american_scientific_journal-3454 121 1 references reference NOUN american_scientific_journal-3454 121 2 [ [ X american_scientific_journal-3454 121 3 1 1 NUM american_scientific_journal-3454 121 4 ] ] PUNCT american_scientific_journal-3454 121 5 . . PUNCT american_scientific_journal-3454 122 1 t. t. PROPN american_scientific_journal-3454 122 2 h. h. PROPN american_scientific_journal-3454 122 3 s. s. PROPN american_scientific_journal-3454 122 4 abdelaziz abdelaziz PROPN american_scientific_journal-3454 122 5 and and CCONJ american_scientific_journal-3454 122 6 m. m. NOUN american_scientific_journal-3454 122 7 valask valask PROPN american_scientific_journal-3454 122 8 , , PUNCT american_scientific_journal-3454 122 9 โ€œ " PUNCT american_scientific_journal-3454 122 10 state state NOUN american_scientific_journal-3454 122 11 derivative derivative ADJ american_scientific_journal-3454 122 12 feedback feedback NOUN american_scientific_journal-3454 122 13 by by ADP american_scientific_journal-3454 122 14 lqr lqr NOUN american_scientific_journal-3454 122 15 for for ADP american_scientific_journal-3454 122 16 linear linear ADJ american_scientific_journal-3454 122 17 time time NOUN american_scientific_journal-3454 122 18 - - PUNCT american_scientific_journal-3454 122 19 invariant invariant ADJ american_scientific_journal-3454 122 20 system system NOUN american_scientific_journal-3454 122 21 โ€ " PUNCT american_scientific_journal-3454 122 22 , , PUNCT american_scientific_journal-3454 122 23 proceedings proceeding NOUN american_scientific_journal-3454 122 24 of of ADP american_scientific_journal-3454 122 25 the the DET american_scientific_journal-3454 122 26 16th 16th ADJ american_scientific_journal-3454 122 27 ifac ifac NOUN american_scientific_journal-3454 122 28 world world PROPN american_scientific_journal-3454 122 29 congress congress PROPN american_scientific_journal-3454 122 30 , , PUNCT american_scientific_journal-3454 122 31 czech czech PROPN american_scientific_journal-3454 122 32 republic republic NOUN american_scientific_journal-3454 122 33 , , PUNCT american_scientific_journal-3454 122 34 2005 2005 NUM american_scientific_journal-3454 122 35 , , PUNCT american_scientific_journal-3454 122 36 pp pp ADJ american_scientific_journal-3454 122 37 . . PUNCT american_scientific_journal-3454 123 1 933 933 NUM american_scientific_journal-3454 123 2 - - SYM american_scientific_journal-3454 123 3 938 938 NUM american_scientific_journal-3454 123 4 . . PUNCT american_scientific_journal-3454 124 1 [ [ X american_scientific_journal-3454 124 2 2 2 NUM american_scientific_journal-3454 124 3 ] ] PUNCT american_scientific_journal-3454 124 4 . . PUNCT american_scientific_journal-3454 125 1 m. m. NOUN american_scientific_journal-3454 125 2 pourebrahim pourebrahim PROPN american_scientific_journal-3454 125 3 and and CCONJ american_scientific_journal-3454 125 4 a. a. NOUN american_scientific_journal-3454 125 5 s. s. PROPN american_scientific_journal-3454 125 6 ghafari ghafari PROPN american_scientific_journal-3454 125 7 , , PUNCT american_scientific_journal-3454 125 8 โ€œ " PUNCT american_scientific_journal-3454 125 9 designing design VERB american_scientific_journal-3454 125 10 a a DET american_scientific_journal-3454 125 11 lqr lqr NOUN american_scientific_journal-3454 125 12 controller controller NOUN american_scientific_journal-3454 125 13 for for ADP american_scientific_journal-3454 125 14 an an DET american_scientific_journal-3454 125 15 electro electro NOUN american_scientific_journal-3454 125 16 - - PUNCT american_scientific_journal-3454 125 17 hydraulic hydraulic NOUN american_scientific_journal-3454 125 18 - - PUNCT american_scientific_journal-3454 125 19 actuatedclutch actuatedclutch NOUN american_scientific_journal-3454 125 20 model model NOUN american_scientific_journal-3454 125 21 โ€ " PUNCT american_scientific_journal-3454 125 22 , , PUNCT american_scientific_journal-3454 125 23 international international ADJ american_scientific_journal-3454 125 24 conference conference NOUN american_scientific_journal-3454 125 25 on on ADP american_scientific_journal-3454 125 26 control control NOUN american_scientific_journal-3454 125 27 science science NOUN american_scientific_journal-3454 125 28 and and CCONJ american_scientific_journal-3454 125 29 systems system NOUN american_scientific_journal-3454 125 30 engineering engineering NOUN american_scientific_journal-3454 125 31 , , PUNCT american_scientific_journal-3454 125 32 2016 2016 NUM american_scientific_journal-3454 125 33 . . PUNCT american_scientific_journal-3454 126 1 [ [ X american_scientific_journal-3454 126 2 3 3 NUM american_scientific_journal-3454 126 3 ] ] PUNCT american_scientific_journal-3454 126 4 . . PUNCT american_scientific_journal-3454 127 1 h. h. PROPN american_scientific_journal-3454 127 2 i. i. PROPN american_scientific_journal-3454 127 3 ali ali PROPN american_scientific_journal-3454 127 4 , , PUNCT american_scientific_journal-3454 127 5 โ€œ " PUNCT american_scientific_journal-3454 127 6 mixed mixed ADJ american_scientific_journal-3454 127 7 lqr lqr NOUN american_scientific_journal-3454 127 8 / / SYM american_scientific_journal-3454 127 9 h h NOUN american_scientific_journal-3454 127 10 - - PUNCT american_scientific_journal-3454 127 11 infinity infinity NOUN american_scientific_journal-3454 127 12 controller controller NOUN american_scientific_journal-3454 127 13 design design NOUN american_scientific_journal-3454 127 14 for for ADP american_scientific_journal-3454 127 15 uncertain uncertain ADJ american_scientific_journal-3454 127 16 multivariable multivariable ADJ american_scientific_journal-3454 127 17 systems system NOUN american_scientific_journal-3454 127 18 โ€ " PUNCT american_scientific_journal-3454 127 19 , , PUNCT american_scientific_journal-3454 127 20 emirates emirates PROPN american_scientific_journal-3454 127 21 journal journal PROPN american_scientific_journal-3454 127 22 for for ADP american_scientific_journal-3454 127 23 engineering engineering NOUN american_scientific_journal-3454 127 24 research research NOUN american_scientific_journal-3454 127 25 , , PUNCT american_scientific_journal-3454 127 26 2015 2015 NUM american_scientific_journal-3454 127 27 , , PUNCT american_scientific_journal-3454 127 28 vol vol NOUN american_scientific_journal-3454 127 29 . . PROPN american_scientific_journal-3454 127 30 20 20 NUM american_scientific_journal-3454 127 31 , , PUNCT american_scientific_journal-3454 127 32 no no INTJ american_scientific_journal-3454 127 33 . . NOUN american_scientific_journal-3454 127 34 1 1 NUM american_scientific_journal-3454 127 35 , , PUNCT american_scientific_journal-3454 127 36 pp pp ADJ american_scientific_journal-3454 127 37 . . PUNCT american_scientific_journal-3454 128 1 79 79 NUM american_scientific_journal-3454 128 2 - - SYM american_scientific_journal-3454 128 3 85 85 NUM american_scientific_journal-3454 128 4 . . PUNCT american_scientific_journal-3454 129 1 [ [ X american_scientific_journal-3454 129 2 4 4 NUM american_scientific_journal-3454 129 3 ] ] PUNCT american_scientific_journal-3454 129 4 . . PUNCT american_scientific_journal-3454 130 1 rodrigues rodrigues PROPN american_scientific_journal-3454 130 2 c. c. PROPN american_scientific_journal-3454 130 3 r. r. PROPN american_scientific_journal-3454 130 4 and and CCONJ american_scientific_journal-3454 130 5 kuiava kuiava PROPN american_scientific_journal-3454 130 6 r. r. PROPN american_scientific_journal-3454 130 7 and and CCONJ american_scientific_journal-3454 130 8 ramos ramos PROPN american_scientific_journal-3454 130 9 r.a r.a PROPN american_scientific_journal-3454 130 10 . . PROPN american_scientific_journal-3454 130 11 , , PUNCT american_scientific_journal-3454 130 12 โ€œ " PUNCT american_scientific_journal-3454 130 13 design design NOUN american_scientific_journal-3454 130 14 of of ADP american_scientific_journal-3454 130 15 a a DET american_scientific_journal-3454 130 16 linear linear ADJ american_scientific_journal-3454 130 17 quadratic quadratic ADJ american_scientific_journal-3454 130 18 regulator regulator NOUN american_scientific_journal-3454 130 19 for for ADP american_scientific_journal-3454 130 20 nonlinear nonlinear ADJ american_scientific_journal-3454 130 21 systems system NOUN american_scientific_journal-3454 130 22 modeled model VERB american_scientific_journal-3454 130 23 via via ADP american_scientific_journal-3454 130 24 norm norm NOUN american_scientific_journal-3454 130 25 bounded bound VERB american_scientific_journal-3454 130 26 linear linear PROPN american_scientific_journal-3454 130 27 differential differential ADJ american_scientific_journal-3454 130 28 inclusions inclusion NOUN american_scientific_journal-3454 130 29 โ€ " PUNCT american_scientific_journal-3454 130 30 , , PUNCT american_scientific_journal-3454 130 31 proceedings proceeding NOUN american_scientific_journal-3454 130 32 of of ADP american_scientific_journal-3454 130 33 the the DET american_scientific_journal-3454 130 34 18th 18th ADJ american_scientific_journal-3454 130 35 world world NOUN american_scientific_journal-3454 130 36 congress congress PROPN american_scientific_journal-3454 130 37 , , PUNCT american_scientific_journal-3454 130 38 milano(italy milano(italy PROPN american_scientific_journal-3454 130 39 ) ) PUNCT american_scientific_journal-3454 130 40 , , PUNCT american_scientific_journal-3454 130 41 2011 2011 NUM american_scientific_journal-3454 130 42 . . PUNCT american_scientific_journal-3454 131 1 [ [ X american_scientific_journal-3454 131 2 5 5 NUM american_scientific_journal-3454 131 3 ] ] PUNCT american_scientific_journal-3454 131 4 . . PUNCT american_scientific_journal-3454 132 1 t. t. PROPN american_scientific_journal-3454 132 2 h. h. PROPN american_scientific_journal-3454 132 3 s. s. PROPN american_scientific_journal-3454 132 4 abdelaziz abdelaziz PROPN american_scientific_journal-3454 132 5 and and CCONJ american_scientific_journal-3454 132 6 m.valask m.valask PROPN american_scientific_journal-3454 132 7 , , PUNCT american_scientific_journal-3454 132 8 โ€œ " PUNCT american_scientific_journal-3454 132 9 direct direct ADJ american_scientific_journal-3454 132 10 algorithm algorithm NOUN american_scientific_journal-3454 132 11 for for ADP american_scientific_journal-3454 132 12 pole pole ADJ american_scientific_journal-3454 132 13 placement placement NOUN american_scientific_journal-3454 132 14 by by ADP american_scientific_journal-3454 132 15 state state NOUN american_scientific_journal-3454 132 16 - - PUNCT american_scientific_journal-3454 132 17 derivative derivative ADJ american_scientific_journal-3454 132 18 feedback feedback NOUN american_scientific_journal-3454 132 19 for for ADP american_scientific_journal-3454 132 20 multi multi ADJ american_scientific_journal-3454 132 21 - - ADJ american_scientific_journal-3454 132 22 input input ADJ american_scientific_journal-3454 132 23 linear linear PROPN american_scientific_journal-3454 132 24 systems system NOUN american_scientific_journal-3454 132 25 nonsingular nonsingular ADJ american_scientific_journal-3454 132 26 case case NOUN american_scientific_journal-3454 132 27 โ€ " PUNCT american_scientific_journal-3454 132 28 , , PUNCT american_scientific_journal-3454 132 29 kybernetika kybernetika NOUN american_scientific_journal-3454 132 30 , , PUNCT american_scientific_journal-3454 132 31 2005 2005 NUM american_scientific_journal-3454 132 32 , , PUNCT american_scientific_journal-3454 132 33 vol vol NOUN american_scientific_journal-3454 132 34 . . PROPN american_scientific_journal-3454 132 35 41 41 NUM american_scientific_journal-3454 132 36 , , PUNCT american_scientific_journal-3454 132 37 no no INTJ american_scientific_journal-3454 132 38 . . NOUN american_scientific_journal-3454 132 39 5 5 NUM american_scientific_journal-3454 132 40 , , PUNCT american_scientific_journal-3454 132 41 pp pp ADJ american_scientific_journal-3454 132 42 . . PUNCT american_scientific_journal-3454 133 1 637 637 NUM american_scientific_journal-3454 133 2 - - SYM american_scientific_journal-3454 133 3 660 660 NUM american_scientific_journal-3454 133 4 . . PUNCT american_scientific_journal-3454 134 1 [ [ X american_scientific_journal-3454 134 2 6 6 NUM american_scientific_journal-3454 134 3 ] ] PUNCT american_scientific_journal-3454 134 4 . . PUNCT american_scientific_journal-3454 135 1 t. t. PROPN american_scientific_journal-3454 135 2 h. h. PROPN american_scientific_journal-3454 135 3 s. s. PROPN american_scientific_journal-3454 135 4 abdelaziz abdelaziz PROPN american_scientific_journal-3454 135 5 and and CCONJ american_scientific_journal-3454 135 6 m.valask m.valask PROPN american_scientific_journal-3454 135 7 , , PUNCT american_scientific_journal-3454 135 8 โ€œ " PUNCT american_scientific_journal-3454 135 9 pole pole NOUN american_scientific_journal-3454 135 10 - - PUNCT american_scientific_journal-3454 135 11 placement placement NOUN american_scientific_journal-3454 135 12 for for ADP american_scientific_journal-3454 135 13 siso siso NOUN american_scientific_journal-3454 135 14 linear linear PROPN american_scientific_journal-3454 135 15 systems system NOUN american_scientific_journal-3454 135 16 by by ADP american_scientific_journal-3454 135 17 state state NOUN american_scientific_journal-3454 135 18 - - PUNCT american_scientific_journal-3454 135 19 derivative derivative ADJ american_scientific_journal-3454 135 20 feedback feedback NOUN american_scientific_journal-3454 135 21 โ€ " PUNCT american_scientific_journal-3454 135 22 , , PUNCT american_scientific_journal-3454 135 23 acta acta PROPN american_scientific_journal-3454 135 24 polytechnica polytechnica PROPN american_scientific_journal-3454 135 25 , , PUNCT american_scientific_journal-3454 135 26 2003 2003 NUM american_scientific_journal-3454 135 27 , , PUNCT american_scientific_journal-3454 135 28 vol vol NOUN american_scientific_journal-3454 135 29 . . PROPN american_scientific_journal-3454 135 30 43 43 NUM american_scientific_journal-3454 135 31 , , PUNCT american_scientific_journal-3454 135 32 no no INTJ american_scientific_journal-3454 135 33 . . NOUN american_scientific_journal-3454 135 34 6 6 NUM american_scientific_journal-3454 135 35 , , PUNCT american_scientific_journal-3454 135 36 pp pp ADJ american_scientific_journal-3454 135 37 . . PUNCT american_scientific_journal-3454 136 1 52 52 NUM american_scientific_journal-3454 136 2 - - SYM american_scientific_journal-3454 136 3 60 60 NUM american_scientific_journal-3454 136 4 . . PUNCT american_scientific_journal-3454 137 1 [ [ X american_scientific_journal-3454 137 2 7 7 NUM american_scientific_journal-3454 137 3 ] ] PUNCT american_scientific_journal-3454 137 4 . . PUNCT american_scientific_journal-3454 138 1 r. r. PROPN american_scientific_journal-3454 138 2 cardim cardim PROPN american_scientific_journal-3454 138 3 , , PUNCT american_scientific_journal-3454 138 4 m. m. NOUN american_scientific_journal-3454 138 5 c. c. PROPN american_scientific_journal-3454 138 6 m. m. PROPN american_scientific_journal-3454 138 7 teixeira teixeira PROPN american_scientific_journal-3454 138 8 , , PUNCT american_scientific_journal-3454 138 9 e. e. PROPN american_scientific_journal-3454 138 10 assuncao assuncao PROPN american_scientific_journal-3454 138 11 and and CCONJ american_scientific_journal-3454 138 12 f. f. PROPN american_scientific_journal-3454 138 13 a. a. PROPN american_scientific_journal-3454 138 14 faria faria PROPN american_scientific_journal-3454 138 15 , , PUNCT american_scientific_journal-3454 138 16 โ€œ " PUNCT american_scientific_journal-3454 138 17 control control NOUN american_scientific_journal-3454 138 18 designs design NOUN american_scientific_journal-3454 138 19 for for ADP american_scientific_journal-3454 138 20 linear linear NOUN american_scientific_journal-3454 138 21 systems system NOUN american_scientific_journal-3454 138 22 using use VERB american_scientific_journal-3454 138 23 state state NOUN american_scientific_journal-3454 138 24 - - PUNCT american_scientific_journal-3454 138 25 derivative derivative ADJ american_scientific_journal-3454 138 26 feedback feedback NOUN american_scientific_journal-3454 138 27 โ€ " PUNCT american_scientific_journal-3454 138 28 , , PUNCT american_scientific_journal-3454 138 29 systems system NOUN american_scientific_journal-3454 138 30 structure structure NOUN american_scientific_journal-3454 138 31 and and CCONJ american_scientific_journal-3454 138 32 control control NOUN american_scientific_journal-3454 138 33 , , PUNCT american_scientific_journal-3454 138 34 pert pert ADJ american_scientific_journal-3454 138 35 husek husek NOUN american_scientific_journal-3454 138 36 , , PUNCT american_scientific_journal-3454 138 37 2008 2008 NUM american_scientific_journal-3454 138 38 . . PUNCT american_scientific_journal-3454 139 1 [ [ X american_scientific_journal-3454 139 2 8 8 NUM american_scientific_journal-3454 139 3 ] ] PUNCT american_scientific_journal-3454 139 4 . . PUNCT american_scientific_journal-3454 140 1 j. j. PROPN american_scientific_journal-3454 140 2 kataria kataria PROPN american_scientific_journal-3454 140 3 , , PUNCT american_scientific_journal-3454 140 4 m. m. PROPN american_scientific_journal-3454 140 5 k. k. PROPN american_scientific_journal-3454 140 6 madhav madhav PROPN american_scientific_journal-3454 140 7 and and CCONJ american_scientific_journal-3454 140 8 a. a. PROPN american_scientific_journal-3454 140 9 kumar kumar PROPN american_scientific_journal-3454 140 10 , , PUNCT american_scientific_journal-3454 140 11 โ€œ " PUNCT american_scientific_journal-3454 140 12 state state NOUN american_scientific_journal-3454 140 13 derivative derivative ADJ american_scientific_journal-3454 140 14 feedback feedback NOUN american_scientific_journal-3454 140 15 control control NOUN american_scientific_journal-3454 140 16 application application NOUN american_scientific_journal-3454 140 17 for for ADP american_scientific_journal-3454 140 18 pole pole ADJ american_scientific_journal-3454 140 19 placement placement NOUN american_scientific_journal-3454 140 20 problem problem NOUN american_scientific_journal-3454 140 21 โ€ " PUNCT american_scientific_journal-3454 140 22 , , PUNCT american_scientific_journal-3454 140 23 international international ADJ american_scientific_journal-3454 140 24 journal journal NOUN american_scientific_journal-3454 140 25 of of ADP american_scientific_journal-3454 140 26 emerging emerge VERB american_scientific_journal-3454 140 27 technology technology NOUN american_scientific_journal-3454 140 28 , , PUNCT american_scientific_journal-3454 140 29 2014 2014 NUM american_scientific_journal-3454 140 30 , , PUNCT american_scientific_journal-3454 140 31 vol vol NOUN american_scientific_journal-3454 140 32 . . PROPN american_scientific_journal-3454 140 33 4 4 NUM american_scientific_journal-3454 140 34 , , PUNCT american_scientific_journal-3454 140 35 no no INTJ american_scientific_journal-3454 140 36 . . NOUN american_scientific_journal-3454 140 37 4 4 NUM american_scientific_journal-3454 140 38 , , PUNCT american_scientific_journal-3454 140 39 pp pp ADJ american_scientific_journal-3454 140 40 . . PUNCT american_scientific_journal-3454 141 1 79 79 NUM american_scientific_journal-3454 141 2 - - SYM american_scientific_journal-3454 141 3 85 85 NUM american_scientific_journal-3454 141 4 . . PUNCT american_scientific_journal-3454 142 1 [ [ X american_scientific_journal-3454 142 2 9 9 NUM american_scientific_journal-3454 142 3 ] ] PUNCT american_scientific_journal-3454 142 4 . . PUNCT american_scientific_journal-3454 143 1 g. g. PROPN american_scientific_journal-3454 143 2 s. s. PROPN american_scientific_journal-3454 143 3 wang wang PROPN american_scientific_journal-3454 143 4 , , PUNCT american_scientific_journal-3454 143 5 b. b. PROPN american_scientific_journal-3454 143 6 liang liang PROPN american_scientific_journal-3454 143 7 and and CCONJ american_scientific_journal-3454 143 8 g. g. PROPN american_scientific_journal-3454 143 9 r. r. PROPN american_scientific_journal-3454 143 10 duan duan PROPN american_scientific_journal-3454 143 11 , , PUNCT american_scientific_journal-3454 143 12 โ€œ " PUNCT american_scientific_journal-3454 143 13 h2 h2 NOUN american_scientific_journal-3454 143 14 - - PUNCT american_scientific_journal-3454 143 15 optimal optimal ADJ american_scientific_journal-3454 143 16 control control NOUN american_scientific_journal-3454 143 17 with with ADP american_scientific_journal-3454 143 18 regional regional ADJ american_scientific_journal-3454 143 19 pole pole NOUN american_scientific_journal-3454 143 20 assignment assignment NOUN american_scientific_journal-3454 143 21 via via ADP american_scientific_journal-3454 143 22 state state NOUN american_scientific_journal-3454 143 23 feedback feedback NOUN american_scientific_journal-3454 143 24 , , PUNCT american_scientific_journal-3454 143 25 international international ADJ american_scientific_journal-3454 143 26 journal journal NOUN american_scientific_journal-3454 143 27 of of ADP american_scientific_journal-3454 143 28 control control PROPN american_scientific_journal-3454 143 29 โ€ " PUNCT american_scientific_journal-3454 143 30 , , PUNCT american_scientific_journal-3454 143 31 automation automation NOUN american_scientific_journal-3454 143 32 , , PUNCT american_scientific_journal-3454 143 33 and and CCONJ american_scientific_journal-3454 143 34 systems system NOUN american_scientific_journal-3454 143 35 , , PUNCT american_scientific_journal-3454 143 36 2006 2006 NUM american_scientific_journal-3454 143 37 , , PUNCT american_scientific_journal-3454 143 38 vol vol NOUN american_scientific_journal-3454 143 39 . . PROPN american_scientific_journal-3454 143 40 4 4 NUM american_scientific_journal-3454 143 41 , , PUNCT american_scientific_journal-3454 143 42 no no INTJ american_scientific_journal-3454 143 43 . . NOUN american_scientific_journal-3454 143 44 5 5 NUM american_scientific_journal-3454 143 45 , , PUNCT american_scientific_journal-3454 143 46 pp pp ADJ american_scientific_journal-3454 143 47 . . PUNCT american_scientific_journal-3454 143 48 653659 653659 NUM american_scientific_journal-3454 143 49 . . PUNCT american_scientific_journal-3454 144 1 [ [ X american_scientific_journal-3454 144 2 10 10 NUM american_scientific_journal-3454 144 3 ] ] PUNCT american_scientific_journal-3454 144 4 . . PUNCT american_scientific_journal-3454 145 1 e. e. PROPN american_scientific_journal-3454 145 2 reithmeier reithmeier PROPN american_scientific_journal-3454 145 3 and and CCONJ american_scientific_journal-3454 145 4 g. g. PROPN american_scientific_journal-3454 145 5 leitmann leitmann PROPN american_scientific_journal-3454 145 6 , , PUNCT american_scientific_journal-3454 145 7 โ€œ " PUNCT american_scientific_journal-3454 145 8 robust robust ADJ american_scientific_journal-3454 145 9 vibration vibration NOUN american_scientific_journal-3454 145 10 control control NOUN american_scientific_journal-3454 145 11 of of ADP american_scientific_journal-3454 145 12 dynamical dynamical ADJ american_scientific_journal-3454 145 13 systems system NOUN american_scientific_journal-3454 145 14 based base VERB american_scientific_journal-3454 145 15 on on ADP american_scientific_journal-3454 145 16 derivative derivative NOUN american_scientific_journal-3454 145 17 of of ADP american_scientific_journal-3454 145 18 the the DET american_scientific_journal-3454 145 19 state state NOUN american_scientific_journal-3454 145 20 โ€ " PUNCT american_scientific_journal-3454 145 21 , , PUNCT american_scientific_journal-3454 145 22 archive archive NOUN american_scientific_journal-3454 145 23 appl appl NOUN american_scientific_journal-3454 145 24 . . PUNCT american_scientific_journal-3454 146 1 mechanics mechanic NOUN american_scientific_journal-3454 146 2 , , PUNCT american_scientific_journal-3454 146 3 , , PUNCT american_scientific_journal-3454 146 4 2003 2003 NUM american_scientific_journal-3454 146 5 , , PUNCT american_scientific_journal-3454 146 6 vol vol NOUN american_scientific_journal-3454 146 7 . . PROPN american_scientific_journal-3454 146 8 72 72 NUM american_scientific_journal-3454 146 9 , , PUNCT american_scientific_journal-3454 146 10 pp pp ADJ american_scientific_journal-3454 146 11 . . PUNCT american_scientific_journal-3454 147 1 856 856 NUM american_scientific_journal-3454 147 2 - - SYM american_scientific_journal-3454 147 3 864 864 NUM american_scientific_journal-3454 147 4 . . PUNCT american_scientific_journal-3454 148 1 [ [ X american_scientific_journal-3454 148 2 11 11 NUM american_scientific_journal-3454 148 3 ] ] PUNCT american_scientific_journal-3454 148 4 . . PUNCT american_scientific_journal-3454 149 1 a. a. PROPN american_scientific_journal-3454 149 2 sinha sinha PROPN american_scientific_journal-3454 149 3 , , PUNCT american_scientific_journal-3454 149 4 โ€œ " PUNCT american_scientific_journal-3454 149 5 linear linear ADJ american_scientific_journal-3454 149 6 systems system NOUN american_scientific_journal-3454 149 7 optimal optimal ADJ american_scientific_journal-3454 149 8 and and CCONJ american_scientific_journal-3454 149 9 robust robust ADJ american_scientific_journal-3454 149 10 control control NOUN american_scientific_journal-3454 149 11 โ€ " PUNCT american_scientific_journal-3454 149 12 , , PUNCT american_scientific_journal-3454 149 13 taylor taylor PROPN american_scientific_journal-3454 149 14 and and CCONJ american_scientific_journal-3454 149 15 francis francis PROPN american_scientific_journal-3454 149 16 group group PROPN american_scientific_journal-3454 149 17 , , PUNCT american_scientific_journal-3454 149 18 llc llc PROPN american_scientific_journal-3454 149 19 , , PUNCT american_scientific_journal-3454 149 20 2007 2007 NUM american_scientific_journal-3454 149 21 . . PUNCT