id sid tid token lemma pos hjic-493 1 1 hungarian hungarian ADJ hjic-493 1 2 journal journal NOUN hjic-493 1 3 of of ADP hjic-493 1 4 industry industry NOUN hjic-493 1 5 and and CCONJ hjic-493 1 6 chemistry chemistry NOUN hjic-493 1 7 veszprém veszprém NOUN hjic-493 1 8 vol vol NOUN hjic-493 1 9 . . PUNCT hjic-493 2 1 42(2 42(2 NUM hjic-493 2 2 ) ) PUNCT hjic-493 3 1 pp pp ADP hjic-493 3 2 . . PUNCT hjic-493 4 1 103–107 103–107 NUM hjic-493 4 2 ( ( PUNCT hjic-493 4 3 2014 2014 NUM hjic-493 4 4 ) ) PUNCT hjic-493 4 5 on on ADP hjic-493 4 6 the the DET hjic-493 4 7 parametric parametric ADJ hjic-493 4 8 uncertainty uncertainty NOUN hjic-493 4 9 of of ADP hjic-493 4 10 weakly weakly ADJ hjic-493 4 11 reversible reversible ADJ hjic-493 4 12 realizations realization NOUN hjic-493 4 13 of of ADP hjic-493 4 14 kinetic kinetic ADJ hjic-493 4 15 systems system NOUN hjic-493 4 16 györgy györgy PROPN hjic-493 4 17 lipták lipták PROPN hjic-493 4 18 b1 b1 PROPN hjic-493 4 19 , , PUNCT hjic-493 4 20 gábor gábor PROPN hjic-493 4 21 szederkényi1,2 szederkényi1,2 PROPN hjic-493 4 22 and and CCONJ hjic-493 4 23 katalin katalin PROPN hjic-493 4 24 m. m. NOUN hjic-493 4 25 hangos1,3 hangos1,3 PROPN hjic-493 4 26 1process 1process NUM hjic-493 4 27 control control NOUN hjic-493 4 28 research research NOUN hjic-493 4 29 group group NOUN hjic-493 4 30 , , PUNCT hjic-493 4 31 mta mta PROPN hjic-493 4 32 sztaki sztaki PROPN hjic-493 4 33 , , PUNCT hjic-493 4 34 kende kende VERB hjic-493 4 35 u. u. PROPN hjic-493 4 36 13 13 NUM hjic-493 4 37 - - SYM hjic-493 4 38 17 17 NUM hjic-493 4 39 , , PUNCT hjic-493 4 40 budapest budapest NOUN hjic-493 4 41 , , PUNCT hjic-493 4 42 1111 1111 NUM hjic-493 4 43 , , PUNCT hjic-493 4 44 hungary hungary PROPN hjic-493 4 45 2faculty 2faculty NUM hjic-493 4 46 of of ADP hjic-493 4 47 information information NOUN hjic-493 4 48 technology technology NOUN hjic-493 4 49 , , PUNCT hjic-493 4 50 péter péter PROPN hjic-493 4 51 pázmány pázmány PROPN hjic-493 4 52 catholic catholic PROPN hjic-493 4 53 university university PROPN hjic-493 4 54 , , PUNCT hjic-493 4 55 práter práter NOUN hjic-493 4 56 u. u. PROPN hjic-493 4 57 50 50 NUM hjic-493 4 58 / / SYM hjic-493 4 59 a a PRON hjic-493 4 60 , , PUNCT hjic-493 4 61 budapest budapest ADJ hjic-493 4 62 , , PUNCT hjic-493 4 63 1083 1083 NUM hjic-493 4 64 , , PUNCT hjic-493 4 65 hungary hungary PROPN hjic-493 4 66 3department 3department NUM hjic-493 4 67 of of ADP hjic-493 4 68 electrical electrical ADJ hjic-493 4 69 engineering engineering NOUN hjic-493 4 70 and and CCONJ hjic-493 4 71 information information NOUN hjic-493 4 72 systems system NOUN hjic-493 4 73 , , PUNCT hjic-493 4 74 university university NOUN hjic-493 4 75 of of ADP hjic-493 4 76 pannonia pannonia PROPN hjic-493 4 77 , , PUNCT hjic-493 4 78 egyetem egyetem NOUN hjic-493 4 79 u. u. PROPN hjic-493 4 80 10 10 NUM hjic-493 4 81 , , PUNCT hjic-493 4 82 veszprém veszprém NOUN hjic-493 4 83 , , PUNCT hjic-493 4 84 8200 8200 NUM hjic-493 4 85 , , PUNCT hjic-493 4 86 hungary hungary NOUN hjic-493 4 87 be be NOUN hjic-493 4 88 - - PUNCT hjic-493 4 89 mail mail NOUN hjic-493 4 90 : : PUNCT hjic-493 5 1 lipgyorgy@gmail.com lipgyorgy@gmail.com X hjic-493 6 1 the the DET hjic-493 6 2 existence existence NOUN hjic-493 6 3 of of ADP hjic-493 6 4 weakly weakly ADJ hjic-493 6 5 reversible reversible ADJ hjic-493 6 6 realizations realization NOUN hjic-493 6 7 within within ADP hjic-493 6 8 a a DET hjic-493 6 9 given give VERB hjic-493 6 10 convex convex ADJ hjic-493 6 11 domain domain NOUN hjic-493 6 12 is be AUX hjic-493 6 13 investigated investigate VERB hjic-493 6 14 . . PUNCT hjic-493 7 1 it it PRON hjic-493 7 2 is be AUX hjic-493 7 3 shown show VERB hjic-493 7 4 that that SCONJ hjic-493 7 5 the the DET hjic-493 7 6 domain domain NOUN hjic-493 7 7 of of ADP hjic-493 7 8 weakly weakly ADJ hjic-493 7 9 reversible reversible ADJ hjic-493 7 10 realizations realization NOUN hjic-493 7 11 is be AUX hjic-493 7 12 convex convex ADJ hjic-493 7 13 in in ADP hjic-493 7 14 the the DET hjic-493 7 15 parameter parameter NOUN hjic-493 7 16 space space NOUN hjic-493 7 17 . . PUNCT hjic-493 8 1 a a DET hjic-493 8 2 lp lp ADV hjic-493 8 3 - - PUNCT hjic-493 8 4 based base VERB hjic-493 8 5 method method NOUN hjic-493 8 6 of of ADP hjic-493 8 7 testing testing NOUN hjic-493 8 8 if if SCONJ hjic-493 8 9 every every DET hjic-493 8 10 element element NOUN hjic-493 8 11 of of ADP hjic-493 8 12 a a DET hjic-493 8 13 convex convex NOUN hjic-493 8 14 domain domain NOUN hjic-493 8 15 admits admit VERB hjic-493 8 16 weakly weakly ADJ hjic-493 8 17 reversible reversible ADJ hjic-493 8 18 realizations realization NOUN hjic-493 8 19 is be AUX hjic-493 8 20 proposed propose VERB hjic-493 8 21 . . PUNCT hjic-493 9 1 a a DET hjic-493 9 2 linear linear ADJ hjic-493 9 3 programming programming NOUN hjic-493 9 4 method method NOUN hjic-493 9 5 is be AUX hjic-493 9 6 also also ADV hjic-493 9 7 presented present VERB hjic-493 9 8 to to PART hjic-493 9 9 compute compute VERB hjic-493 9 10 a a DET hjic-493 9 11 stabilizing stabilize VERB hjic-493 9 12 kinetic kinetic ADJ hjic-493 9 13 feedback feedback NOUN hjic-493 9 14 controller controller NOUN hjic-493 9 15 for for ADP hjic-493 9 16 polynomial polynomial ADJ hjic-493 9 17 systems system NOUN hjic-493 9 18 with with ADP hjic-493 9 19 parametric parametric ADJ hjic-493 9 20 uncertainty uncertainty NOUN hjic-493 9 21 . . PUNCT hjic-493 10 1 the the DET hjic-493 10 2 proposed propose VERB hjic-493 10 3 methods method NOUN hjic-493 10 4 are be AUX hjic-493 10 5 illustrated illustrate VERB hjic-493 10 6 using use VERB hjic-493 10 7 simple simple ADJ hjic-493 10 8 examples example NOUN hjic-493 10 9 . . PUNCT hjic-493 11 1 keywords keyword NOUN hjic-493 11 2 : : PUNCT hjic-493 11 3 parametric parametric ADJ hjic-493 11 4 uncertainty uncertainty NOUN hjic-493 11 5 ; ; PUNCT hjic-493 11 6 computational computational ADJ hjic-493 11 7 methods method NOUN hjic-493 11 8 ; ; PUNCT hjic-493 11 9 optimization optimization NOUN hjic-493 11 10 ; ; PUNCT hjic-493 11 11 kinetic kinetic ADJ hjic-493 11 12 systems system NOUN hjic-493 11 13 introduction introduction NOUN hjic-493 11 14 the the DET hjic-493 11 15 notion notion NOUN hjic-493 11 16 of of ADP hjic-493 11 17 parametric parametric ADJ hjic-493 11 18 robustness robustness NOUN hjic-493 11 19 is be AUX hjic-493 11 20 well well ADV hjic-493 11 21 - - PUNCT hjic-493 11 22 known know VERB hjic-493 11 23 and and CCONJ hjic-493 11 24 central central ADJ hjic-493 11 25 in in ADP hjic-493 11 26 linear linear ADJ hjic-493 11 27 and and CCONJ hjic-493 11 28 nonlinear nonlinear ADJ hjic-493 11 29 systems system NOUN hjic-493 11 30 and and CCONJ hjic-493 11 31 control control PROPN hjic-493 11 32 theory theory NOUN hjic-493 11 33 [ [ X hjic-493 11 34 1 1 NUM hjic-493 11 35 ] ] PUNCT hjic-493 11 36 . . PUNCT hjic-493 12 1 it it PRON hjic-493 12 2 is be AUX hjic-493 12 3 used use VERB hjic-493 12 4 for for ADP hjic-493 12 5 ensuring ensure VERB hjic-493 12 6 a a DET hjic-493 12 7 desirable desirable ADJ hjic-493 12 8 property property NOUN hjic-493 12 9 , , PUNCT hjic-493 12 10 such such ADJ hjic-493 12 11 as as ADP hjic-493 12 12 stability stability NOUN hjic-493 12 13 , , PUNCT hjic-493 12 14 in in ADP hjic-493 12 15 a a DET hjic-493 12 16 given give VERB hjic-493 12 17 domain domain NOUN hjic-493 12 18 in in ADP hjic-493 12 19 the the DET hjic-493 12 20 parameter parameter NOUN hjic-493 12 21 space space NOUN hjic-493 12 22 around around ADP hjic-493 12 23 a a DET hjic-493 12 24 nominal nominal ADJ hjic-493 12 25 realization realization NOUN hjic-493 12 26 having have VERB hjic-493 12 27 the the DET hjic-493 12 28 desired desire VERB hjic-493 12 29 property property NOUN hjic-493 12 30 . . PUNCT hjic-493 13 1 the the DET hjic-493 13 2 aim aim NOUN hjic-493 13 3 of of ADP hjic-493 13 4 the the DET hjic-493 13 5 paper paper NOUN hjic-493 13 6 is be AUX hjic-493 13 7 to to PART hjic-493 13 8 extend extend VERB hjic-493 13 9 the the DET hjic-493 13 10 notions notion NOUN hjic-493 13 11 and and CCONJ hjic-493 13 12 tools tool NOUN hjic-493 13 13 of of ADP hjic-493 13 14 parametric parametric ADJ hjic-493 13 15 robustness robustness NOUN hjic-493 13 16 for for ADP hjic-493 13 17 a a DET hjic-493 13 18 class class NOUN hjic-493 13 19 of of ADP hjic-493 13 20 positive positive ADJ hjic-493 13 21 polynomial polynomial ADJ hjic-493 13 22 systems system NOUN hjic-493 13 23 , , PUNCT hjic-493 13 24 namely namely ADV hjic-493 13 25 a a DET hjic-493 13 26 class class NOUN hjic-493 13 27 of of ADP hjic-493 13 28 kinetic kinetic ADJ hjic-493 13 29 systems system NOUN hjic-493 13 30 . . PUNCT hjic-493 14 1 only only ADV hjic-493 14 2 the the DET hjic-493 14 3 very very ADV hjic-493 14 4 first first ADJ hjic-493 14 5 steps step NOUN hjic-493 14 6 are be AUX hjic-493 14 7 reported report VERB hjic-493 14 8 here here ADV hjic-493 14 9 that that PRON hjic-493 14 10 offer offer VERB hjic-493 14 11 a a DET hjic-493 14 12 computationally computationally ADV hjic-493 14 13 efficient efficient ADJ hjic-493 14 14 method method NOUN hjic-493 14 15 for for ADP hjic-493 14 16 checking check VERB hjic-493 14 17 one one NUM hjic-493 14 18 of of ADP hjic-493 14 19 the the DET hjic-493 14 20 many many ADJ hjic-493 14 21 important important ADJ hjic-493 14 22 properties property NOUN hjic-493 14 23 of of ADP hjic-493 14 24 kinetic kinetic ADJ hjic-493 14 25 systems system NOUN hjic-493 14 26 , , PUNCT hjic-493 14 27 their their PRON hjic-493 14 28 weak weak ADJ hjic-493 14 29 reversibility reversibility NOUN hjic-493 14 30 . . PUNCT hjic-493 15 1 basic basic ADJ hjic-493 15 2 notions notion NOUN hjic-493 15 3 and and CCONJ hjic-493 15 4 methods method NOUN hjic-493 15 5 the the DET hjic-493 15 6 basic basic ADJ hjic-493 15 7 notions notion NOUN hjic-493 15 8 and and CCONJ hjic-493 15 9 tools tool NOUN hjic-493 15 10 related relate VERB hjic-493 15 11 to to ADP hjic-493 15 12 reaction reaction NOUN hjic-493 15 13 kinetic kinetic NOUN hjic-493 15 14 systems system NOUN hjic-493 15 15 and and CCONJ hjic-493 15 16 their their PRON hjic-493 15 17 realizations realization NOUN hjic-493 15 18 are be AUX hjic-493 15 19 briefly briefly ADV hjic-493 15 20 summarized summarize VERB hjic-493 15 21 in in ADP hjic-493 15 22 this this DET hjic-493 15 23 section section NOUN hjic-493 15 24 . . PUNCT hjic-493 16 1 kinetic kinetic ADJ hjic-493 16 2 systems system NOUN hjic-493 16 3 , , PUNCT hjic-493 16 4 their their PRON hjic-493 16 5 dynamics dynamic NOUN hjic-493 16 6 and and CCONJ hjic-493 16 7 structure structure NOUN hjic-493 16 8 deterministic deterministic ADJ hjic-493 16 9 kinetic kinetic NOUN hjic-493 16 10 systems system NOUN hjic-493 16 11 with with ADP hjic-493 16 12 mass mass ADJ hjic-493 16 13 action action NOUN hjic-493 16 14 kinetics kinetic NOUN hjic-493 16 15 or or CCONJ hjic-493 16 16 simply simply ADV hjic-493 16 17 chemical chemical ADJ hjic-493 16 18 reaction reaction NOUN hjic-493 16 19 networks network NOUN hjic-493 16 20 ( ( PUNCT hjic-493 16 21 crns crn NOUN hjic-493 16 22 ) ) PUNCT hjic-493 16 23 form form NOUN hjic-493 16 24 a a DET hjic-493 16 25 wide wide ADJ hjic-493 16 26 class class NOUN hjic-493 16 27 of of ADP hjic-493 16 28 non non ADJ hjic-493 16 29 - - ADJ hjic-493 16 30 negative negative ADJ hjic-493 16 31 polynomial polynomial ADJ hjic-493 16 32 systems system NOUN hjic-493 16 33 , , PUNCT hjic-493 16 34 that that PRON hjic-493 16 35 are be AUX hjic-493 16 36 able able ADJ hjic-493 16 37 to to PART hjic-493 16 38 produce produce VERB hjic-493 16 39 all all DET hjic-493 16 40 the the DET hjic-493 16 41 important important ADJ hjic-493 16 42 qualitative qualitative ADJ hjic-493 16 43 phenomena phenomenon NOUN hjic-493 16 44 ( ( PUNCT hjic-493 16 45 e.g. e.g. ADV hjic-493 16 46 stable stable ADJ hjic-493 16 47 / / SYM hjic-493 16 48 unstable unstable ADJ hjic-493 16 49 equilibria equilibrium NOUN hjic-493 16 50 , , PUNCT hjic-493 16 51 oscillations oscillation NOUN hjic-493 16 52 , , PUNCT hjic-493 16 53 limit limit NOUN hjic-493 16 54 cycles cycle NOUN hjic-493 16 55 , , PUNCT hjic-493 16 56 multiplicity multiplicity NOUN hjic-493 16 57 of of ADP hjic-493 16 58 equilibrium equilibrium NOUN hjic-493 16 59 points point NOUN hjic-493 16 60 and and CCONJ hjic-493 16 61 even even ADV hjic-493 16 62 chaotic chaotic ADJ hjic-493 16 63 behaviour behaviour NOUN hjic-493 16 64 ) ) PUNCT hjic-493 16 65 present present ADJ hjic-493 16 66 in in ADP hjic-493 16 67 the the DET hjic-493 16 68 dynamics dynamic NOUN hjic-493 16 69 of of ADP hjic-493 16 70 nonlinear nonlinear ADJ hjic-493 16 71 processes process NOUN hjic-493 16 72 [ [ X hjic-493 16 73 2 2 NUM hjic-493 16 74 ] ] PUNCT hjic-493 16 75 . . PUNCT hjic-493 17 1 the the DET hjic-493 17 2 general general ADJ hjic-493 17 3 form form NOUN hjic-493 17 4 of of ADP hjic-493 17 5 dynamic dynamic ADJ hjic-493 17 6 models model NOUN hjic-493 17 7 studied study VERB hjic-493 17 8 in in ADP hjic-493 17 9 this this DET hjic-493 17 10 paper paper NOUN hjic-493 17 11 is be AUX hjic-493 17 12 the the DET hjic-493 17 13 following follow VERB hjic-493 17 14 ẋ ẋ PUNCT hjic-493 18 1 = = ADJ hjic-493 18 2 m m PROPN hjic-493 18 3 · · PUNCT hjic-493 18 4 ψ(x ψ(x NOUN hjic-493 18 5 ) ) PUNCT hjic-493 18 6 , , PUNCT hjic-493 18 7 ( ( PUNCT hjic-493 18 8 1 1 X hjic-493 18 9 ) ) PUNCT hjic-493 18 10 where where SCONJ hjic-493 18 11 x x SYM hjic-493 18 12 ∈ ∈ PROPN hjic-493 18 13 rn rn PROPN hjic-493 18 14 is be AUX hjic-493 18 15 the the DET hjic-493 18 16 state state NOUN hjic-493 18 17 variable variable NOUN hjic-493 18 18 and and CCONJ hjic-493 18 19 m m PROPN hjic-493 18 20 ∈ ∈ PROPN hjic-493 18 21 rn×m rn×m NOUN hjic-493 18 22 . . PUNCT hjic-493 19 1 the the DET hjic-493 19 2 monomial monomial ADJ hjic-493 19 3 vector vector PROPN hjic-493 19 4 function function NOUN hjic-493 19 5 ψ ψ PROPN hjic-493 19 6 : : PUNCT hjic-493 19 7 rn rn PROPN hjic-493 19 8 → → SYM hjic-493 19 9 rm rm PROPN hjic-493 19 10 is be AUX hjic-493 19 11 defined define VERB hjic-493 19 12 as as ADP hjic-493 19 13 ψj(x ψj(x PUNCT hjic-493 19 14 ) ) PUNCT hjic-493 20 1 = = PUNCT hjic-493 20 2 n∏ n∏ NOUN hjic-493 20 3 i=1 i=1 NOUN hjic-493 20 4 x x X hjic-493 20 5 yij yij NOUN hjic-493 20 6 i i PRON hjic-493 20 7 , , PUNCT hjic-493 20 8 j j PROPN hjic-493 20 9 = = SYM hjic-493 20 10 1 1 NUM hjic-493 20 11 , , PUNCT hjic-493 20 12 . . PUNCT hjic-493 20 13 . . PUNCT hjic-493 21 1 . . PUNCT hjic-493 22 1 , , PUNCT hjic-493 22 2 m m PROPN hjic-493 22 3 ( ( PUNCT hjic-493 22 4 2 2 NUM hjic-493 22 5 ) ) PUNCT hjic-493 22 6 where where SCONJ hjic-493 22 7 y y PROPN hjic-493 22 8 ∈ ∈ PROPN hjic-493 22 9 nn×m nn×m PROPN hjic-493 22 10 0 0 NUM hjic-493 22 11 . . PUNCT hjic-493 23 1 the the DET hjic-493 23 2 system system NOUN hjic-493 23 3 eq.(1 eq.(1 ADJ hjic-493 23 4 ) ) PUNCT hjic-493 23 5 is be AUX hjic-493 23 6 kinetic kinetic ADJ hjic-493 23 7 if if SCONJ hjic-493 23 8 and and CCONJ hjic-493 23 9 only only ADV hjic-493 23 10 if if SCONJ hjic-493 23 11 the the DET hjic-493 23 12 matrix matrix NOUN hjic-493 23 13 m m AUX hjic-493 23 14 has have VERB hjic-493 23 15 a a DET hjic-493 23 16 factorization factorization NOUN hjic-493 23 17 m m ADJ hjic-493 23 18 = = SYM hjic-493 23 19 y y PROPN hjic-493 23 20 · · PROPN hjic-493 23 21 ak ak PROPN hjic-493 23 22 . . PROPN hjic-493 24 1 ( ( PUNCT hjic-493 24 2 3 3 X hjic-493 24 3 ) ) PUNCT hjic-493 24 4 the the DET hjic-493 24 5 kirchhoff kirchhoff NOUN hjic-493 24 6 - - PUNCT hjic-493 24 7 matrix matrix NOUN hjic-493 24 8 ak ak PROPN hjic-493 24 9 has have VERB hjic-493 24 10 non non ADJ hjic-493 24 11 - - ADJ hjic-493 24 12 positive positive ADJ hjic-493 24 13 diagonal diagonal ADJ hjic-493 24 14 and and CCONJ hjic-493 24 15 non non ADJ hjic-493 24 16 - - ADJ hjic-493 24 17 negative negative ADJ hjic-493 24 18 off off ADP hjic-493 24 19 - - PUNCT hjic-493 24 20 diagonal diagonal ADJ hjic-493 24 21 elements element NOUN hjic-493 24 22 and and CCONJ hjic-493 24 23 zero zero NUM hjic-493 24 24 column column NOUN hjic-493 24 25 sums sum NOUN hjic-493 24 26 . . PUNCT hjic-493 25 1 the the DET hjic-493 25 2 matrix matrix NOUN hjic-493 25 3 pair pair NOUN hjic-493 25 4 ( ( PUNCT hjic-493 25 5 y y PROPN hjic-493 25 6 , , PUNCT hjic-493 25 7 ak ak PROPN hjic-493 25 8 ) ) PUNCT hjic-493 25 9 is be AUX hjic-493 25 10 called call VERB hjic-493 25 11 the the DET hjic-493 25 12 realization realization NOUN hjic-493 25 13 of of ADP hjic-493 25 14 the the DET hjic-493 25 15 system system NOUN hjic-493 25 16 eq.(1 eq.(1 ADJ hjic-493 25 17 ) ) PUNCT hjic-493 25 18 . . PUNCT hjic-493 26 1 the the DET hjic-493 26 2 chemically chemically ADV hjic-493 26 3 originated originate VERB hjic-493 26 4 notions notion NOUN hjic-493 26 5 : : PUNCT hjic-493 26 6 the the DET hjic-493 26 7 chemically chemically ADV hjic-493 26 8 originated originate VERB hjic-493 26 9 notions notion NOUN hjic-493 26 10 of of ADP hjic-493 26 11 kinetic kinetic ADJ hjic-493 26 12 systems system NOUN hjic-493 26 13 are be AUX hjic-493 26 14 as as SCONJ hjic-493 26 15 follows follow VERB hjic-493 26 16 : : PUNCT hjic-493 26 17 the the DET hjic-493 26 18 species specie NOUN hjic-493 26 19 of of ADP hjic-493 26 20 the the DET hjic-493 26 21 system system NOUN hjic-493 26 22 are be AUX hjic-493 26 23 denoted denote VERB hjic-493 26 24 by by ADP hjic-493 26 25 x1 x1 PROPN hjic-493 26 26 , , PUNCT hjic-493 26 27 . . PUNCT hjic-493 26 28 . . PUNCT hjic-493 27 1 . . PUNCT hjic-493 28 1 , , PUNCT hjic-493 28 2 xn xn PROPN hjic-493 28 3 , , PUNCT hjic-493 28 4 and and CCONJ hjic-493 28 5 the the DET hjic-493 28 6 concentrations concentration NOUN hjic-493 28 7 of of ADP hjic-493 28 8 the the DET hjic-493 28 9 species specie NOUN hjic-493 28 10 are be AUX hjic-493 28 11 the the DET hjic-493 28 12 state state NOUN hjic-493 28 13 variables variable NOUN hjic-493 28 14 of of ADP hjic-493 28 15 eq.(1 eq.(1 ADJ hjic-493 28 16 ) ) PUNCT hjic-493 28 17 , , PUNCT hjic-493 28 18 i.e. i.e. X hjic-493 28 19 xi xi X hjic-493 28 20 = = PUNCT hjic-493 29 1 [ [ X hjic-493 29 2 xi xi X hjic-493 29 3 ] ] X hjic-493 29 4 ≥ ≥ X hjic-493 29 5 0 0 NUM hjic-493 29 6 for for ADP hjic-493 29 7 i i PRON hjic-493 29 8 = = NOUN hjic-493 29 9 1 1 NUM hjic-493 29 10 , , PUNCT hjic-493 29 11 . . PUNCT hjic-493 29 12 . . PUNCT hjic-493 30 1 . . PUNCT hjic-493 31 1 , , PUNCT hjic-493 31 2 n. n. VERB hjic-493 31 3 the the DET hjic-493 31 4 structure structure NOUN hjic-493 31 5 of of ADP hjic-493 31 6 kinetic kinetic ADJ hjic-493 31 7 systems system NOUN hjic-493 31 8 is be AUX hjic-493 31 9 given give VERB hjic-493 31 10 in in ADP hjic-493 31 11 terms term NOUN hjic-493 31 12 of of ADP hjic-493 31 13 its its PRON hjic-493 31 14 complexes complex NOUN hjic-493 31 15 ci ci NOUN hjic-493 31 16 , , PUNCT hjic-493 31 17 i i PRON hjic-493 31 18 = = NOUN hjic-493 31 19 1 1 NUM hjic-493 31 20 , , PUNCT hjic-493 31 21 . . PUNCT hjic-493 31 22 . . PUNCT hjic-493 32 1 . . PUNCT hjic-493 33 1 , , PUNCT hjic-493 33 2 m m VERB hjic-493 33 3 that that PRON hjic-493 33 4 are be AUX hjic-493 33 5 non non ADJ hjic-493 33 6 - - ADJ hjic-493 33 7 negative negative ADJ hjic-493 33 8 linear linear ADJ hjic-493 33 9 combinations combination NOUN hjic-493 33 10 of of ADP hjic-493 33 11 the the DET hjic-493 33 12 species specie NOUN hjic-493 34 1 i.e. i.e. X hjic-493 34 2 ci ci X hjic-493 34 3 = = SYM hjic-493 34 4 ∑n ∑n PROPN hjic-493 34 5 j=1[y j=1[y X hjic-493 34 6 ] ] PUNCT hjic-493 34 7 jixj jixj ADJ hjic-493 34 8 for for ADP hjic-493 34 9 i i PROPN hjic-493 34 10 = = NOUN hjic-493 34 11 1 1 NUM hjic-493 34 12 , , PUNCT hjic-493 34 13 . . PUNCT hjic-493 34 14 . . PUNCT hjic-493 34 15 . . PUNCT hjic-493 35 1 , , PUNCT hjic-493 35 2 m m PROPN hjic-493 35 3 , , PUNCT hjic-493 35 4 and and CCONJ hjic-493 35 5 therefore therefore ADV hjic-493 35 6 y y PROPN hjic-493 35 7 is be AUX hjic-493 35 8 also also ADV hjic-493 35 9 called call VERB hjic-493 35 10 the the DET hjic-493 35 11 complex complex ADJ hjic-493 35 12 composition composition NOUN hjic-493 35 13 matrix matrix NOUN hjic-493 35 14 . . PUNCT hjic-493 36 1 the the DET hjic-493 36 2 reaction reaction NOUN hjic-493 36 3 graph graph NOUN hjic-493 36 4 : : PUNCT hjic-493 36 5 the the DET hjic-493 36 6 weighted weight VERB hjic-493 36 7 directed direct VERB hjic-493 36 8 graph graph NOUN hjic-493 36 9 ( ( PUNCT hjic-493 36 10 or or CCONJ hjic-493 36 11 reaction reaction NOUN hjic-493 36 12 graph graph NOUN hjic-493 36 13 ) ) PUNCT hjic-493 36 14 of of ADP hjic-493 36 15 kinetic kinetic ADJ hjic-493 36 16 systems system NOUN hjic-493 36 17 is be AUX hjic-493 36 18 g g NOUN hjic-493 36 19 = = SYM hjic-493 36 20 ( ( PUNCT hjic-493 36 21 v v NOUN hjic-493 36 22 , , PUNCT hjic-493 36 23 e e NOUN hjic-493 36 24 ) ) PUNCT hjic-493 36 25 , , PUNCT hjic-493 36 26 where where SCONJ hjic-493 36 27 104 104 NUM hjic-493 36 28 v v NOUN hjic-493 36 29 = = SYM hjic-493 36 30 { { PUNCT hjic-493 36 31 c1 c1 PROPN hjic-493 36 32 , , PUNCT hjic-493 36 33 c2 c2 PROPN hjic-493 36 34 , , PUNCT hjic-493 36 35 . . PUNCT hjic-493 36 36 . . PUNCT hjic-493 36 37 . . PUNCT hjic-493 37 1 , , PUNCT hjic-493 37 2 cm cm NOUN hjic-493 37 3 } } PUNCT hjic-493 37 4 and and CCONJ hjic-493 37 5 e e NOUN hjic-493 37 6 denote denote VERB hjic-493 37 7 the the DET hjic-493 37 8 set set NOUN hjic-493 37 9 of of ADP hjic-493 37 10 vertices vertex NOUN hjic-493 37 11 and and CCONJ hjic-493 37 12 directed direct VERB hjic-493 37 13 edges edge NOUN hjic-493 37 14 , , PUNCT hjic-493 37 15 respectively respectively ADV hjic-493 37 16 . . PUNCT hjic-493 38 1 the the DET hjic-493 38 2 directed direct VERB hjic-493 38 3 edge edge NOUN hjic-493 38 4 ( ( PUNCT hjic-493 38 5 ci ci NOUN hjic-493 38 6 , , PUNCT hjic-493 38 7 cj cj PROPN hjic-493 38 8 ) ) PUNCT hjic-493 38 9 ( ( PUNCT hjic-493 38 10 also also ADV hjic-493 38 11 denoted denote VERB hjic-493 38 12 by by ADP hjic-493 38 13 ci ci PROPN hjic-493 38 14 → → SYM hjic-493 38 15 cj cj NOUN hjic-493 38 16 ) ) PUNCT hjic-493 38 17 belongs belong VERB hjic-493 38 18 to to ADP hjic-493 38 19 the the DET hjic-493 38 20 reaction reaction NOUN hjic-493 38 21 graph graph NOUN hjic-493 38 22 if if SCONJ hjic-493 38 23 and and CCONJ hjic-493 38 24 only only ADV hjic-493 38 25 if if SCONJ hjic-493 38 26 [ [ X hjic-493 38 27 ak]j ak]j PROPN hjic-493 38 28 , , PUNCT hjic-493 38 29 i i PRON hjic-493 38 30 > > X hjic-493 38 31 0 0 X hjic-493 38 32 . . PUNCT hjic-493 39 1 in in ADP hjic-493 39 2 this this DET hjic-493 39 3 case case NOUN hjic-493 39 4 , , PUNCT hjic-493 39 5 the the DET hjic-493 39 6 weight weight NOUN hjic-493 39 7 assigned assign VERB hjic-493 39 8 to to ADP hjic-493 39 9 the the DET hjic-493 39 10 directed direct VERB hjic-493 39 11 edge edge NOUN hjic-493 39 12 is be AUX hjic-493 39 13 ci ci NOUN hjic-493 39 14 → → SYM hjic-493 39 15 cj cj PROPN hjic-493 39 16 is be AUX hjic-493 39 17 [ [ X hjic-493 39 18 ak]j ak]j PROPN hjic-493 39 19 , , PUNCT hjic-493 39 20 i. i. NOUN hjic-493 39 21 stoichiometric stoichiometric NOUN hjic-493 39 22 subspace subspace NOUN hjic-493 39 23 : : PUNCT hjic-493 39 24 stoichiometric stoichiometric NOUN hjic-493 39 25 subspace subspace NOUN hjic-493 39 26 s s PART hjic-493 39 27 is be AUX hjic-493 39 28 given give VERB hjic-493 39 29 by by ADP hjic-493 39 30 the the DET hjic-493 39 31 span span NOUN hjic-493 39 32 of of ADP hjic-493 39 33 the the DET hjic-493 39 34 reaction reaction NOUN hjic-493 39 35 vectors vector NOUN hjic-493 39 36 s s PART hjic-493 39 37 = = PUNCT hjic-493 39 38 { { PUNCT hjic-493 40 1 [ [ X hjic-493 40 2 y y X hjic-493 40 3 ] ] X hjic-493 40 4 · · PUNCT hjic-493 40 5 i i PRON hjic-493 40 6 − − VERB hjic-493 41 1 [ [ X hjic-493 41 2 y y X hjic-493 41 3 ] ] X hjic-493 41 4 · · PUNCT hjic-493 41 5 j j PROPN hjic-493 41 6 | | ADV hjic-493 41 7 [ [ X hjic-493 41 8 ak]ij ak]ij VERB hjic-493 41 9 > > X hjic-493 41 10 0 0 NUM hjic-493 41 11 } } PUNCT hjic-493 41 12 . . PUNCT hjic-493 42 1 ( ( PUNCT hjic-493 42 2 4 4 X hjic-493 42 3 ) ) PUNCT hjic-493 42 4 the the DET hjic-493 42 5 stoichiometric stoichiometric ADJ hjic-493 42 6 compatibility compatibility NOUN hjic-493 42 7 classes class NOUN hjic-493 42 8 of of ADP hjic-493 42 9 a a DET hjic-493 42 10 kinetic kinetic ADJ hjic-493 42 11 system system NOUN hjic-493 42 12 are be AUX hjic-493 42 13 the the DET hjic-493 42 14 affine affine ADJ hjic-493 42 15 translations translation NOUN hjic-493 42 16 of of ADP hjic-493 42 17 the the DET hjic-493 42 18 stoichiometric stoichiometric ADJ hjic-493 42 19 subspace subspace NOUN hjic-493 42 20 : : PUNCT hjic-493 42 21 ( ( PUNCT hjic-493 42 22 x0 x0 PROPN hjic-493 42 23 + + PROPN hjic-493 42 24 s s X hjic-493 42 25 ) ) PUNCT hjic-493 42 26 ∩ ∩ PROPN hjic-493 42 27 rn rn PROPN hjic-493 42 28 ≥0 ≥0 NOUN hjic-493 42 29 . . PUNCT hjic-493 42 30 structural structural ADJ hjic-493 42 31 properties property NOUN hjic-493 42 32 and and CCONJ hjic-493 42 33 dynamical dynamical ADJ hjic-493 42 34 behaviour behaviour NOUN hjic-493 42 35 it it PRON hjic-493 42 36 is be AUX hjic-493 42 37 possible possible ADJ hjic-493 42 38 to to PART hjic-493 42 39 utilize utilize VERB hjic-493 42 40 certain certain ADJ hjic-493 42 41 structural structural ADJ hjic-493 42 42 properties property NOUN hjic-493 42 43 of of ADP hjic-493 42 44 kinetic kinetic ADJ hjic-493 42 45 systems system NOUN hjic-493 42 46 that that PRON hjic-493 42 47 enable enable VERB hjic-493 42 48 us we PRON hjic-493 42 49 to to PART hjic-493 42 50 effectively effectively ADV hjic-493 42 51 analyze analyze VERB hjic-493 42 52 the the DET hjic-493 42 53 stability stability NOUN hjic-493 42 54 of of ADP hjic-493 42 55 the the DET hjic-493 42 56 system system NOUN hjic-493 42 57 . . PUNCT hjic-493 43 1 deficiency deficiency NOUN hjic-493 43 2 : : PUNCT hjic-493 43 3 there there PRON hjic-493 43 4 are be VERB hjic-493 43 5 several several ADJ hjic-493 43 6 equivalent equivalent ADJ hjic-493 43 7 ways way NOUN hjic-493 43 8 to to PART hjic-493 43 9 define define VERB hjic-493 43 10 deficiency deficiency NOUN hjic-493 43 11 . . PUNCT hjic-493 44 1 we we PRON hjic-493 44 2 will will AUX hjic-493 44 3 use use VERB hjic-493 44 4 the the DET hjic-493 44 5 following follow VERB hjic-493 44 6 definition definition NOUN hjic-493 44 7 δ δ PROPN hjic-493 44 8 = = PUNCT hjic-493 44 9 dim(ker(y dim(ker(y ADJ hjic-493 44 10 ) ) PUNCT hjic-493 44 11 ∩ ∩ NOUN hjic-493 44 12 im(bg im(bg NOUN hjic-493 44 13 ) ) PUNCT hjic-493 44 14 ) ) PUNCT hjic-493 44 15 , , PUNCT hjic-493 44 16 ( ( PUNCT hjic-493 44 17 5 5 X hjic-493 44 18 ) ) PUNCT hjic-493 44 19 where where SCONJ hjic-493 44 20 bg bg PROPN hjic-493 44 21 is be AUX hjic-493 44 22 the the DET hjic-493 44 23 incidence incidence ADJ hjic-493 44 24 matrix matrix NOUN hjic-493 44 25 of of ADP hjic-493 44 26 the the DET hjic-493 44 27 reaction reaction NOUN hjic-493 44 28 graph graph NOUN hjic-493 44 29 . . PUNCT hjic-493 45 1 it it PRON hjic-493 45 2 is be AUX hjic-493 45 3 easy easy ADJ hjic-493 45 4 to to PART hjic-493 45 5 see see VERB hjic-493 45 6 that that DET hjic-493 45 7 deficiency deficiency NOUN hjic-493 45 8 is be AUX hjic-493 45 9 zero zero NUM hjic-493 45 10 if if SCONJ hjic-493 45 11 ker(y ker(y VERB hjic-493 45 12 ) ) PUNCT hjic-493 45 13 = = PUNCT hjic-493 45 14 { { PUNCT hjic-493 45 15 0 0 NUM hjic-493 45 16 } } PUNCT hjic-493 45 17 or or CCONJ hjic-493 45 18 equivalently equivalently ADV hjic-493 45 19 rank(y rank(y X hjic-493 45 20 ) ) PUNCT hjic-493 45 21 = = SYM hjic-493 45 22 m. m. NOUN hjic-493 45 23 weak weak ADJ hjic-493 45 24 reversibility reversibility NOUN hjic-493 45 25 : : PUNCT hjic-493 45 26 a a DET hjic-493 45 27 crn crn NOUN hjic-493 45 28 is be AUX hjic-493 45 29 called call VERB hjic-493 45 30 weakly weakly ADV hjic-493 45 31 reversible reversible ADJ hjic-493 45 32 if if SCONJ hjic-493 45 33 whenever whenever SCONJ hjic-493 45 34 there there PRON hjic-493 45 35 exists exist VERB hjic-493 45 36 a a DET hjic-493 45 37 directed direct VERB hjic-493 45 38 path path NOUN hjic-493 45 39 from from ADP hjic-493 45 40 ci ci PROPN hjic-493 45 41 to to PART hjic-493 45 42 cj cj NOUN hjic-493 45 43 in in ADP hjic-493 45 44 its its PRON hjic-493 45 45 reaction reaction NOUN hjic-493 45 46 graph graph NOUN hjic-493 45 47 , , PUNCT hjic-493 45 48 then then ADV hjic-493 45 49 there there PRON hjic-493 45 50 exists exist VERB hjic-493 45 51 a a DET hjic-493 45 52 directed direct VERB hjic-493 45 53 path path NOUN hjic-493 45 54 from from ADP hjic-493 45 55 cj cj NOUN hjic-493 45 56 to to ADP hjic-493 45 57 ci ci PROPN hjic-493 45 58 . . PUNCT hjic-493 46 1 in in ADP hjic-493 46 2 graph graph NOUN hjic-493 46 3 theoretic theoretic ADJ hjic-493 46 4 terms term NOUN hjic-493 46 5 , , PUNCT hjic-493 46 6 this this PRON hjic-493 46 7 means mean VERB hjic-493 46 8 that that SCONJ hjic-493 46 9 all all DET hjic-493 46 10 components component NOUN hjic-493 46 11 of of ADP hjic-493 46 12 the the DET hjic-493 46 13 reaction reaction NOUN hjic-493 46 14 graph graph NOUN hjic-493 46 15 are be AUX hjic-493 46 16 strongly strongly ADV hjic-493 46 17 connected connect VERB hjic-493 46 18 components component NOUN hjic-493 46 19 . . PUNCT hjic-493 47 1 deficiency deficiency NOUN hjic-493 47 2 zero zero NUM hjic-493 47 3 theorem theorem VERB hjic-493 47 4 : : PUNCT hjic-493 47 5 a a DET hjic-493 47 6 weakly weakly ADJ hjic-493 47 7 reversible reversible ADJ hjic-493 47 8 kinetic kinetic NOUN hjic-493 47 9 system system NOUN hjic-493 47 10 with with ADP hjic-493 47 11 zero zero NUM hjic-493 47 12 deficiency deficiency NOUN hjic-493 47 13 has have VERB hjic-493 47 14 precisely precisely ADV hjic-493 47 15 one one NUM hjic-493 47 16 equilibrium equilibrium NOUN hjic-493 47 17 point point NOUN hjic-493 47 18 in in ADP hjic-493 47 19 each each DET hjic-493 47 20 positive positive ADJ hjic-493 47 21 stoichiometric stoichiometric NOUN hjic-493 47 22 compatibility compatibility NOUN hjic-493 47 23 class class NOUN hjic-493 47 24 that that PRON hjic-493 47 25 is be AUX hjic-493 47 26 locally locally ADV hjic-493 47 27 asymptotically asymptotically ADV hjic-493 47 28 stable stable ADJ hjic-493 47 29 ( ( PUNCT hjic-493 47 30 conjecture conjecture NOUN hjic-493 47 31 : : PUNCT hjic-493 47 32 globally globally ADV hjic-493 47 33 asymptotically asymptotically ADV hjic-493 47 34 stable stable ADJ hjic-493 47 35 ) ) PUNCT hjic-493 47 36 . . PUNCT hjic-493 48 1 computing compute VERB hjic-493 48 2 weakly weakly ADJ hjic-493 48 3 reversible reversible ADJ hjic-493 48 4 realizations realization NOUN hjic-493 48 5 formulated formulate VERB hjic-493 48 6 as as ADP hjic-493 48 7 an an DET hjic-493 48 8 optimization optimization NOUN hjic-493 48 9 problem problem NOUN hjic-493 48 10 in in ADP hjic-493 48 11 this this DET hjic-493 48 12 section section NOUN hjic-493 48 13 , , PUNCT hjic-493 48 14 first first ADV hjic-493 48 15 a a DET hjic-493 48 16 method method NOUN hjic-493 48 17 for for ADP hjic-493 48 18 computing compute VERB hjic-493 48 19 weakly weakly ADJ hjic-493 48 20 reversible reversible ADJ hjic-493 48 21 realization realization NOUN hjic-493 48 22 based base VERB hjic-493 48 23 on on ADP hjic-493 48 24 ref.[3 ref.[3 NOUN hjic-493 48 25 ] ] PUNCT hjic-493 48 26 is be AUX hjic-493 48 27 briefly briefly ADV hjic-493 48 28 presented present VERB hjic-493 48 29 . . PUNCT hjic-493 49 1 we we PRON hjic-493 49 2 assume assume VERB hjic-493 49 3 that that SCONJ hjic-493 49 4 we we PRON hjic-493 49 5 have have VERB hjic-493 49 6 a a DET hjic-493 49 7 kinetic kinetic ADJ hjic-493 49 8 polynomial polynomial ADJ hjic-493 49 9 system system NOUN hjic-493 49 10 of of ADP hjic-493 49 11 the the DET hjic-493 49 12 form form NOUN hjic-493 49 13 eq.(1 eq.(1 ADJ hjic-493 49 14 ) ) PUNCT hjic-493 49 15 . . PUNCT hjic-493 50 1 we we PRON hjic-493 50 2 use use VERB hjic-493 50 3 the the DET hjic-493 50 4 fact fact NOUN hjic-493 50 5 known know VERB hjic-493 50 6 from from ADP hjic-493 50 7 the the DET hjic-493 50 8 literature literature NOUN hjic-493 50 9 that that PRON hjic-493 50 10 a a DET hjic-493 50 11 realization realization NOUN hjic-493 50 12 of of ADP hjic-493 50 13 a a DET hjic-493 50 14 crn crn NOUN hjic-493 50 15 is be AUX hjic-493 50 16 weakly weakly ADV hjic-493 50 17 reversible reversible ADJ hjic-493 50 18 if if SCONJ hjic-493 50 19 and and CCONJ hjic-493 50 20 only only ADV hjic-493 50 21 if if SCONJ hjic-493 50 22 there there PRON hjic-493 50 23 exists exist VERB hjic-493 50 24 a a DET hjic-493 50 25 vector vector NOUN hjic-493 50 26 with with ADP hjic-493 50 27 strictly strictly ADV hjic-493 50 28 positive positive ADJ hjic-493 50 29 elements element NOUN hjic-493 50 30 in in ADP hjic-493 50 31 the the DET hjic-493 50 32 kernel kernel NOUN hjic-493 50 33 of of ADP hjic-493 50 34 ak ak PROPN hjic-493 50 35 , , PUNCT hjic-493 50 36 i.e. i.e. X hjic-493 50 37 there there PRON hjic-493 50 38 exists exist VERB hjic-493 50 39 b b PROPN hjic-493 50 40 ∈ ∈ PROPN hjic-493 50 41 rn rn PROPN hjic-493 50 42 + + CCONJ hjic-493 50 43 such such ADJ hjic-493 50 44 that that SCONJ hjic-493 50 45 ak ak PROPN hjic-493 50 46 · · PUNCT hjic-493 50 47 b b X hjic-493 51 1 = = SYM hjic-493 51 2 0 0 PUNCT hjic-493 52 1 [ [ X hjic-493 52 2 4 4 NUM hjic-493 52 3 ] ] PUNCT hjic-493 52 4 . . PUNCT hjic-493 53 1 since since SCONJ hjic-493 53 2 b b PROPN hjic-493 53 3 is be AUX hjic-493 53 4 unknown unknown ADJ hjic-493 53 5 , , PUNCT hjic-493 53 6 too too ADV hjic-493 53 7 , , PUNCT hjic-493 53 8 this this DET hjic-493 53 9 condition condition NOUN hjic-493 53 10 in in ADP hjic-493 53 11 this this DET hjic-493 53 12 form form NOUN hjic-493 53 13 is be AUX hjic-493 53 14 not not PART hjic-493 53 15 linear linear ADJ hjic-493 53 16 . . PUNCT hjic-493 54 1 therefore therefore ADV hjic-493 54 2 , , PUNCT hjic-493 54 3 we we PRON hjic-493 54 4 introduce introduce VERB hjic-493 54 5 a a DET hjic-493 54 6 scaled scale VERB hjic-493 54 7 matrix matrix NOUN hjic-493 54 8 ãk ãk PRON hjic-493 54 9 ãk ãk PROPN hjic-493 54 10 = = SYM hjic-493 54 11 ak ak PROPN hjic-493 54 12 · · PUNCT hjic-493 54 13 diag(b diag(b PROPN hjic-493 54 14 ) ) PUNCT hjic-493 54 15 ( ( PUNCT hjic-493 54 16 6 6 NUM hjic-493 54 17 ) ) PUNCT hjic-493 54 18 where where SCONJ hjic-493 54 19 diag(b diag(b VERB hjic-493 54 20 ) ) PUNCT hjic-493 54 21 is be AUX hjic-493 54 22 a a DET hjic-493 54 23 diagonal diagonal ADJ hjic-493 54 24 matrix matrix NOUN hjic-493 54 25 with with ADP hjic-493 54 26 elements element NOUN hjic-493 54 27 of of ADP hjic-493 54 28 b. b. PROPN hjic-493 54 29 it it PRON hjic-493 54 30 is be AUX hjic-493 54 31 clear clear ADJ hjic-493 54 32 from from ADP hjic-493 54 33 eq.(6 eq.(6 ADJ hjic-493 54 34 ) ) PUNCT hjic-493 54 35 that that PRON hjic-493 54 36 ãk ãk PRON hjic-493 54 37 is be AUX hjic-493 54 38 also also ADV hjic-493 54 39 a a DET hjic-493 54 40 kirchhoff kirchhoff NOUN hjic-493 54 41 matrix matrix NOUN hjic-493 54 42 and and CCONJ hjic-493 54 43 that that SCONJ hjic-493 54 44 1 1 NUM hjic-493 54 45 ∈ ∈ PROPN hjic-493 54 46 rm rm NOUN hjic-493 54 47 ( ( PUNCT hjic-493 54 48 the the DET hjic-493 54 49 m m ADJ hjic-493 54 50 - - ADJ hjic-493 54 51 dimensional dimensional ADJ hjic-493 54 52 vector vector NOUN hjic-493 54 53 containing contain VERB hjic-493 54 54 only only ADJ hjic-493 54 55 ones one NOUN hjic-493 54 56 ) ) PUNCT hjic-493 54 57 lies lie VERB hjic-493 54 58 in in ADP hjic-493 54 59 kernel kernel NOUN hjic-493 54 60 of of ADP hjic-493 54 61 ãk ãk PROPN hjic-493 54 62 . . PUNCT hjic-493 55 1 moreover moreover ADV hjic-493 55 2 , , PUNCT hjic-493 55 3 it it PRON hjic-493 55 4 is be AUX hjic-493 55 5 easy easy ADJ hjic-493 55 6 to to PART hjic-493 55 7 see see VERB hjic-493 55 8 that that SCONJ hjic-493 55 9 ãk ãk PROPN hjic-493 55 10 defines define VERB hjic-493 55 11 a a DET hjic-493 55 12 weakly weakly ADJ hjic-493 55 13 reversible reversible ADJ hjic-493 55 14 network network NOUN hjic-493 55 15 if if SCONJ hjic-493 55 16 and and CCONJ hjic-493 55 17 only only ADV hjic-493 55 18 if if SCONJ hjic-493 55 19 ak ak PROPN hjic-493 55 20 corresponds correspond VERB hjic-493 55 21 to to ADP hjic-493 55 22 a a DET hjic-493 55 23 weakly weakly ADJ hjic-493 55 24 reversible reversible ADJ hjic-493 55 25 network network NOUN hjic-493 55 26 . . PUNCT hjic-493 56 1 then then ADV hjic-493 56 2 , , PUNCT hjic-493 56 3 the the DET hjic-493 56 4 weak weak ADJ hjic-493 56 5 reversibility reversibility NOUN hjic-493 56 6 and and CCONJ hjic-493 56 7 the the DET hjic-493 56 8 kirchhoff kirchhoff NOUN hjic-493 56 9 property property NOUN hjic-493 56 10 of of ADP hjic-493 56 11 ãk ãk PRON hjic-493 56 12 can can AUX hjic-493 56 13 be be AUX hjic-493 56 14 expressed express VERB hjic-493 56 15 using use VERB hjic-493 56 16 the the DET hjic-493 56 17 following follow VERB hjic-493 56 18 linear linear NOUN hjic-493 56 19 constraints constraint NOUN hjic-493 56 20 m∑ m∑ ADP hjic-493 56 21 i=1 i=1 PROPN hjic-493 56 22 [ [ PUNCT hjic-493 56 23 ãk ãk X hjic-493 56 24 ] ] PUNCT hjic-493 56 25 ij ij NOUN hjic-493 56 26 = = SYM hjic-493 56 27 0 0 PROPN hjic-493 56 28 , , PUNCT hjic-493 56 29 j j PROPN hjic-493 56 30 = = SYM hjic-493 56 31 1 1 NUM hjic-493 56 32 , , PUNCT hjic-493 56 33 . . PUNCT hjic-493 56 34 . . PUNCT hjic-493 56 35 . . PUNCT hjic-493 57 1 , , PUNCT hjic-493 57 2 m m VERB hjic-493 57 3 m∑ m∑ INTJ hjic-493 57 4 i=1 i=1 PROPN hjic-493 58 1 [ [ PUNCT hjic-493 58 2 ãk ãk X hjic-493 58 3 ] ] PUNCT hjic-493 58 4 ji ji PROPN hjic-493 58 5 = = NOUN hjic-493 58 6 0 0 PROPN hjic-493 58 7 , , PUNCT hjic-493 58 8 j j PROPN hjic-493 58 9 = = SYM hjic-493 58 10 1 1 NUM hjic-493 58 11 , , PUNCT hjic-493 58 12 . . PUNCT hjic-493 58 13 . . PUNCT hjic-493 58 14 . . PUNCT hjic-493 59 1 , , PUNCT hjic-493 59 2 m m PRON hjic-493 59 3 [ [ X hjic-493 59 4 ãk ãk PRON hjic-493 59 5 ] ] PUNCT hjic-493 59 6 ij ij X hjic-493 59 7 ≥ ≥ NOUN hjic-493 59 8 0 0 NUM hjic-493 59 9 , , PUNCT hjic-493 59 10 i i PRON hjic-493 59 11 , , PUNCT hjic-493 59 12 j j PROPN hjic-493 59 13 = = SYM hjic-493 59 14 1 1 NUM hjic-493 59 15 , , PUNCT hjic-493 59 16 . . PUNCT hjic-493 59 17 . . PUNCT hjic-493 59 18 . . PUNCT hjic-493 60 1 , , PUNCT hjic-493 60 2 m m PROPN hjic-493 60 3 , , PUNCT hjic-493 60 4 i i PROPN hjic-493 60 5 6= 6= PROPN hjic-493 60 6 j j PROPN hjic-493 60 7 [ [ PUNCT hjic-493 60 8 ãk ãk PRON hjic-493 60 9 ] ] PUNCT hjic-493 60 10 ii ii NOUN hjic-493 60 11 ≤ ≤ NUM hjic-493 60 12 0 0 NUM hjic-493 60 13 , , PUNCT hjic-493 60 14 i i PRON hjic-493 60 15 = = NOUN hjic-493 60 16 1 1 NUM hjic-493 60 17 , , PUNCT hjic-493 60 18 . . PUNCT hjic-493 60 19 . . PUNCT hjic-493 61 1 . . PUNCT hjic-493 62 1 , , PUNCT hjic-493 62 2 m. m. NOUN hjic-493 62 3 ( ( PUNCT hjic-493 62 4 7 7 NUM hjic-493 62 5 ) ) PUNCT hjic-493 62 6 moreover moreover ADV hjic-493 62 7 , , PUNCT hjic-493 62 8 the the DET hjic-493 62 9 equation equation NOUN hjic-493 62 10 eq.(3 eq.(3 NOUN hjic-493 62 11 ) ) PUNCT hjic-493 62 12 is be AUX hjic-493 62 13 transformed transform VERB hjic-493 62 14 by by ADP hjic-493 62 15 diag(b diag(b PROPN hjic-493 62 16 ) ) PUNCT hjic-493 62 17 ( ( PUNCT hjic-493 62 18 we we PRON hjic-493 62 19 can can AUX hjic-493 62 20 do do VERB hjic-493 62 21 this this PRON hjic-493 62 22 , , PUNCT hjic-493 62 23 because because SCONJ hjic-493 62 24 diag(b diag(b VERB hjic-493 62 25 ) ) PUNCT hjic-493 62 26 is be AUX hjic-493 62 27 invertible invertible ADJ hjic-493 62 28 ): ): PUNCT hjic-493 62 29 m m VERB hjic-493 62 30 · · PUNCT hjic-493 62 31 diag(b diag(b ADP hjic-493 62 32 ) ) PUNCT hjic-493 62 33 = = SYM hjic-493 62 34 y y PROPN hjic-493 62 35 · · SYM hjic-493 62 36 ak ak X hjic-493 62 37 · · PUNCT hjic-493 62 38 diag(b)︸ diag(b)︸ PROPN hjic-493 62 39 ︷︷ ︷︷ PROPN hjic-493 62 40 ︸ ︸ PRON hjic-493 63 1 ãk ãk PROPN hjic-493 63 2 ( ( PUNCT hjic-493 63 3 8) 8) NUM hjic-493 63 4 finally finally ADV hjic-493 63 5 , , PUNCT hjic-493 63 6 by by ADP hjic-493 63 7 choosing choose VERB hjic-493 63 8 an an DET hjic-493 63 9 arbitrary arbitrary ADJ hjic-493 63 10 linear linear ADJ hjic-493 63 11 objective objective ADJ hjic-493 63 12 function function NOUN hjic-493 63 13 of of ADP hjic-493 63 14 the the DET hjic-493 63 15 decision decision NOUN hjic-493 63 16 variables variable VERB hjic-493 63 17 ãk ãk PRON hjic-493 63 18 and and CCONJ hjic-493 63 19 b b NOUN hjic-493 63 20 , , PUNCT hjic-493 63 21 weakly weakly ADJ hjic-493 63 22 reversible reversible ADJ hjic-493 63 23 realizations realization NOUN hjic-493 63 24 of of ADP hjic-493 63 25 the the DET hjic-493 63 26 studied study VERB hjic-493 63 27 kinetic kinetic ADJ hjic-493 63 28 system system NOUN hjic-493 63 29 can can AUX hjic-493 63 30 be be AUX hjic-493 63 31 computed compute VERB hjic-493 63 32 ( ( PUNCT hjic-493 63 33 if if SCONJ hjic-493 63 34 any any DET hjic-493 63 35 exist exist NOUN hjic-493 63 36 ) ) PUNCT hjic-493 63 37 in in ADP hjic-493 63 38 a a DET hjic-493 63 39 lp lp NOUN hjic-493 63 40 framework framework NOUN hjic-493 63 41 using use VERB hjic-493 63 42 the the DET hjic-493 63 43 linear linear ADJ hjic-493 63 44 constraints constraint NOUN hjic-493 63 45 eq.(7 eq.(7 NOUN hjic-493 63 46 ) ) PUNCT hjic-493 63 47 and and CCONJ hjic-493 63 48 ( ( PUNCT hjic-493 63 49 8) 8) NUM hjic-493 63 50 . . PUNCT hjic-493 63 51 weakly weakly ADJ hjic-493 63 52 reversible reversible ADJ hjic-493 63 53 crn crn NOUN hjic-493 63 54 realizations realization NOUN hjic-493 63 55 in in ADP hjic-493 63 56 this this DET hjic-493 63 57 section section NOUN hjic-493 63 58 , , PUNCT hjic-493 63 59 first first ADV hjic-493 63 60 the the DET hjic-493 63 61 convexity convexity NOUN hjic-493 63 62 of of ADP hjic-493 63 63 the the DET hjic-493 63 64 weakly weakly ADJ hjic-493 63 65 reversible reversible ADJ hjic-493 63 66 kirchhoff kirchhoff NOUN hjic-493 63 67 matrix matrix NOUN hjic-493 63 68 will will AUX hjic-493 63 69 be be AUX hjic-493 63 70 shown show VERB hjic-493 63 71 . . PUNCT hjic-493 64 1 after after ADP hjic-493 64 2 that that PRON hjic-493 64 3 the the DET hjic-493 64 4 practical practical ADJ hjic-493 64 5 benefits benefit NOUN hjic-493 64 6 of of ADP hjic-493 64 7 this this DET hjic-493 64 8 property property NOUN hjic-493 64 9 will will AUX hjic-493 64 10 be be AUX hjic-493 64 11 demonstrated demonstrate VERB hjic-493 64 12 in in ADP hjic-493 64 13 the the DET hjic-493 64 14 field field NOUN hjic-493 64 15 of of ADP hjic-493 64 16 system system NOUN hjic-493 64 17 analysis analysis NOUN hjic-493 64 18 and and CCONJ hjic-493 64 19 robust robust ADJ hjic-493 64 20 feedback feedback NOUN hjic-493 64 21 design design NOUN hjic-493 64 22 . . PUNCT hjic-493 65 1 convexity convexity NOUN hjic-493 65 2 of of ADP hjic-493 65 3 the the DET hjic-493 65 4 weak weak ADJ hjic-493 65 5 reversibility reversibility NOUN hjic-493 65 6 in in ADP hjic-493 65 7 the the DET hjic-493 65 8 parameter parameter NOUN hjic-493 65 9 space space NOUN hjic-493 65 10 theorem theorem VERB hjic-493 65 11 1 1 X hjic-493 65 12 . . PUNCT hjic-493 66 1 let let VERB hjic-493 66 2 a(1 a(1 NOUN hjic-493 66 3 ) ) PUNCT hjic-493 67 1 k k NOUN hjic-493 67 2 and and CCONJ hjic-493 67 3 a a DET hjic-493 67 4 ( ( PUNCT hjic-493 67 5 2 2 NUM hjic-493 67 6 ) ) PUNCT hjic-493 67 7 k k NOUN hjic-493 67 8 be be VERB hjic-493 67 9 m m PROPN hjic-493 67 10 × × NOUN hjic-493 67 11 m m VERB hjic-493 67 12 weakly weakly ADJ hjic-493 67 13 reversible reversible ADJ hjic-493 67 14 kirchhoff kirchhoff NOUN hjic-493 67 15 matrices matrix NOUN hjic-493 67 16 . . PUNCT hjic-493 68 1 then then ADV hjic-493 68 2 the the DET hjic-493 68 3 convex convex ADJ hjic-493 68 4 combination combination NOUN hjic-493 68 5 of of ADP hjic-493 68 6 the the DET hjic-493 68 7 two two NUM hjic-493 68 8 matrices matrix NOUN hjic-493 68 9 remains remain VERB hjic-493 68 10 weakly weakly ADV hjic-493 68 11 reversible reversible ADJ hjic-493 68 12 . . PUNCT hjic-493 69 1 proof proof NOUN hjic-493 69 2 . . PUNCT hjic-493 70 1 the the DET hjic-493 70 2 idea idea NOUN hjic-493 70 3 behind behind ADP hjic-493 70 4 the the DET hjic-493 70 5 proof proof NOUN hjic-493 70 6 is be AUX hjic-493 70 7 based base VERB hjic-493 70 8 on on ADP hjic-493 70 9 ref.[5 ref.[5 NOUN hjic-493 70 10 ] ] PUNCT hjic-493 70 11 . . PUNCT hjic-493 71 1 a a DET hjic-493 71 2 kirchhoff kirchhoff NOUN hjic-493 71 3 matrix matrix NOUN hjic-493 71 4 is be AUX hjic-493 71 5 weakly weakly ADV hjic-493 71 6 reversible reversible ADJ hjic-493 71 7 if if SCONJ hjic-493 71 8 and and CCONJ hjic-493 71 9 only only ADV hjic-493 71 10 if if SCONJ hjic-493 71 11 there there PRON hjic-493 71 12 is be VERB hjic-493 71 13 a a DET hjic-493 71 14 strictly strictly ADV hjic-493 71 15 positive positive ADJ hjic-493 71 16 vector vector NOUN hjic-493 71 17 in in ADP hjic-493 71 18 its its PRON hjic-493 71 19 kernel kernel NOUN hjic-493 71 20 . . PUNCT hjic-493 72 1 therefore therefore ADV hjic-493 72 2 strictly strictly ADV hjic-493 72 3 positive positive ADJ hjic-493 72 4 vectors vector NOUN hjic-493 72 5 p1 p1 NOUN hjic-493 72 6 , , PUNCT hjic-493 72 7 p2 p2 PROPN hjic-493 72 8 exist exist VERB hjic-493 72 9 such such ADJ hjic-493 72 10 as as ADP hjic-493 72 11 a(1 a(1 NOUN hjic-493 72 12 ) ) PUNCT hjic-493 72 13 k k PROPN hjic-493 72 14 · · PUNCT hjic-493 72 15 p1 p1 NOUN hjic-493 72 16 = = SYM hjic-493 72 17 0 0 PROPN hjic-493 72 18 and and CCONJ hjic-493 72 19 a a DET hjic-493 72 20 ( ( PUNCT hjic-493 72 21 2 2 NUM hjic-493 72 22 ) ) PUNCT hjic-493 72 23 k k NOUN hjic-493 72 24 · · PUNCT hjic-493 72 25 p2 p2 X hjic-493 73 1 = = SYM hjic-493 73 2 0 0 X hjic-493 73 3 . . PUNCT hjic-493 74 1 let let VERB hjic-493 74 2 us we PRON hjic-493 74 3 define define VERB hjic-493 74 4 the the DET hjic-493 74 5 following follow VERB hjic-493 74 6 scaled scale VERB hjic-493 74 7 kirchhoff kirchhoff NOUN hjic-493 74 8 matrix matrix NOUN hjic-493 74 9 : : PUNCT hjic-493 74 10 â(1 â(1 X hjic-493 74 11 ) ) PUNCT hjic-493 75 1 k k NOUN hjic-493 76 1 = = PUNCT hjic-493 76 2 a a PRON hjic-493 76 3 ( ( PUNCT hjic-493 76 4 1 1 NUM hjic-493 76 5 ) ) PUNCT hjic-493 76 6 k k PROPN hjic-493 76 7 · · PUNCT hjic-493 76 8 diag(p1 diag(p1 NOUN hjic-493 76 9 ) ) PUNCT hjic-493 76 10 and and CCONJ hjic-493 76 11 â(2 â(2 NOUN hjic-493 76 12 ) ) PUNCT hjic-493 76 13 k k NOUN hjic-493 77 1 = = PUNCT hjic-493 77 2 a a PRON hjic-493 77 3 ( ( PUNCT hjic-493 77 4 2 2 NUM hjic-493 77 5 ) ) PUNCT hjic-493 77 6 k k PROPN hjic-493 77 7 · · PUNCT hjic-493 77 8 diag(p2 diag(p2 ADJ hjic-493 77 9 ) ) PUNCT hjic-493 77 10 . . PUNCT hjic-493 78 1 these these DET hjic-493 78 2 scaled scale VERB hjic-493 78 3 matrices matrix NOUN hjic-493 78 4 have have VERB hjic-493 78 5 identical identical ADJ hjic-493 78 6 structures structure NOUN hjic-493 78 7 to to ADP hjic-493 78 8 the the DET hjic-493 78 9 original original ADJ hjic-493 78 10 ones one NOUN hjic-493 78 11 . . PUNCT hjic-493 79 1 moreover moreover ADV hjic-493 79 2 , , PUNCT hjic-493 79 3 â(1 â(1 PROPN hjic-493 79 4 ) ) PUNCT hjic-493 79 5 k k X hjic-493 79 6 · · PUNCT hjic-493 79 7 1(m 1(m NUM hjic-493 79 8 ) ) PUNCT hjic-493 79 9 = = SYM hjic-493 79 10 0 0 NUM hjic-493 79 11 and and CCONJ hjic-493 79 12 â(2 â(2 PROPN hjic-493 79 13 ) ) PUNCT hjic-493 79 14 k k X hjic-493 79 15 · · PUNCT hjic-493 79 16 1(m 1(m NUM hjic-493 79 17 ) ) PUNCT hjic-493 80 1 = = SYM hjic-493 80 2 0 0 NUM hjic-493 80 3 where where SCONJ hjic-493 80 4 the the DET hjic-493 80 5 vector vector NOUN hjic-493 80 6 1(m 1(m NUM hjic-493 80 7 ) ) PUNCT hjic-493 80 8 denotes denote VERB hjic-493 80 9 the the DET hjic-493 80 10 m m ADJ hjic-493 80 11 dimensional dimensional ADJ hjic-493 80 12 column column NOUN hjic-493 80 13 vector vector NOUN hjic-493 80 14 composed compose VERB hjic-493 80 15 of of ADP hjic-493 80 16 ones one NOUN hjic-493 80 17 . . PUNCT hjic-493 81 1 for for ADP hjic-493 81 2 that that PRON hjic-493 81 3 ( ( PUNCT hjic-493 81 4 λâ λâ X hjic-493 81 5 ( ( PUNCT hjic-493 81 6 1 1 NUM hjic-493 81 7 ) ) PUNCT hjic-493 81 8 k k NOUN hjic-493 82 1 + + CCONJ hjic-493 82 2 ( ( PUNCT hjic-493 82 3 1− 1− NUM hjic-493 82 4 λ)â(2 λ)â(2 PROPN hjic-493 82 5 ) ) PUNCT hjic-493 82 6 k k NOUN hjic-493 82 7 ) ) PUNCT hjic-493 82 8 · · PUNCT hjic-493 83 1 1(m 1(m NUM hjic-493 83 2 ) ) PUNCT hjic-493 83 3 = = SYM hjic-493 83 4 0 0 X hjic-493 83 5 . . PUNCT hjic-493 83 6 ( ( PUNCT hjic-493 83 7 9 9 NUM hjic-493 83 8 ) ) PUNCT hjic-493 83 9 for for ADP hjic-493 83 10 any any DET hjic-493 83 11 λ λ PROPN hjic-493 83 12 ∈ ∈ PROPN hjic-493 84 1 [ [ X hjic-493 84 2 0 0 NUM hjic-493 84 3 , , PUNCT hjic-493 84 4 1 1 NUM hjic-493 84 5 ] ] PUNCT hjic-493 84 6 . . PUNCT hjic-493 85 1 therefore therefore ADV hjic-493 85 2 the the DET hjic-493 85 3 convex convex ADJ hjic-493 85 4 combination combination NOUN hjic-493 85 5 of of ADP hjic-493 85 6 the the DET hjic-493 85 7 original original ADJ hjic-493 85 8 two two NUM hjic-493 85 9 realizations realization NOUN hjic-493 85 10 has have VERB hjic-493 85 11 to to PART hjic-493 85 12 be be AUX hjic-493 85 13 weakly weakly ADV hjic-493 85 14 reversible reversible ADJ hjic-493 85 15 . . PUNCT hjic-493 86 1 105 105 NUM hjic-493 86 2 ( ( PUNCT hjic-493 86 3 a a NOUN hjic-493 86 4 ) ) PUNCT hjic-493 86 5 ( ( PUNCT hjic-493 86 6 b b X hjic-493 86 7 ) ) PUNCT hjic-493 86 8 ( ( PUNCT hjic-493 86 9 c c X hjic-493 86 10 ) ) PUNCT hjic-493 86 11 figure figure NOUN hjic-493 86 12 1 1 NUM hjic-493 86 13 : : PUNCT hjic-493 86 14 a a DET hjic-493 86 15 weakly weakly ADJ hjic-493 86 16 reversible reversible ADJ hjic-493 86 17 reaction reaction NOUN hjic-493 86 18 graphs graph NOUN hjic-493 86 19 of of ADP hjic-493 86 20 the the DET hjic-493 86 21 three three NUM hjic-493 86 22 realizations realization NOUN hjic-493 86 23 ( ( PUNCT hjic-493 86 24 y y NOUN hjic-493 86 25 , , PUNCT hjic-493 86 26 a(1 a(1 ADJ hjic-493 86 27 ) ) PUNCT hjic-493 86 28 k k NOUN hjic-493 86 29 ) ) PUNCT hjic-493 86 30 , , PUNCT hjic-493 86 31 ( ( PUNCT hjic-493 86 32 y y NOUN hjic-493 86 33 , , PUNCT hjic-493 86 34 a(2 a(2 PROPN hjic-493 86 35 ) ) PUNCT hjic-493 86 36 k k PROPN hjic-493 86 37 ) ) PUNCT hjic-493 87 1 and and CCONJ hjic-493 87 2 ( ( PUNCT hjic-493 87 3 y y PROPN hjic-493 87 4 , , PUNCT hjic-493 87 5 a a DET hjic-493 87 6 ( ( PUNCT hjic-493 87 7 3 3 NUM hjic-493 87 8 ) ) PUNCT hjic-493 87 9 k k NOUN hjic-493 87 10 ) ) PUNCT hjic-493 87 11 weak weak ADJ hjic-493 87 12 reversibility reversibility NOUN hjic-493 87 13 of of ADP hjic-493 87 14 crn crn NOUN hjic-493 87 15 realizations realization NOUN hjic-493 87 16 with with ADP hjic-493 87 17 parametric parametric ADJ hjic-493 87 18 uncertainty uncertainty NOUN hjic-493 87 19 we we PRON hjic-493 87 20 assume assume VERB hjic-493 87 21 that that SCONJ hjic-493 87 22 a a DET hjic-493 87 23 crn crn NOUN hjic-493 87 24 with with ADP hjic-493 87 25 parametric parametric ADJ hjic-493 87 26 uncertainty uncertainty NOUN hjic-493 87 27 is be AUX hjic-493 87 28 given give VERB hjic-493 87 29 as as ADP hjic-493 87 30 ẋ ẋ PROPN hjic-493 87 31 = = PROPN hjic-493 87 32 m m PROPN hjic-493 87 33 · · PUNCT hjic-493 87 34 ψ(x ψ(x NOUN hjic-493 87 35 ) ) PUNCT hjic-493 87 36 , , PUNCT hjic-493 87 37 ( ( PUNCT hjic-493 87 38 10 10 NUM hjic-493 87 39 ) ) PUNCT hjic-493 87 40 where where SCONJ hjic-493 87 41 x x SYM hjic-493 87 42 ∈ ∈ PROPN hjic-493 87 43 rn rn PROPN hjic-493 87 44 is be AUX hjic-493 87 45 the the DET hjic-493 87 46 state state NOUN hjic-493 87 47 variable variable NOUN hjic-493 87 48 , , PUNCT hjic-493 87 49 ψ ψ ADP hjic-493 87 50 ∈ ∈ PROPN hjic-493 87 51 rn rn PROPN hjic-493 87 52 → → SYM hjic-493 87 53 rm rm PROPN hjic-493 87 54 contains contain VERB hjic-493 87 55 the the DET hjic-493 87 56 monomials monomial NOUN hjic-493 87 57 and and CCONJ hjic-493 87 58 the the DET hjic-493 87 59 matrix matrix NOUN hjic-493 87 60 m m VERB hjic-493 87 61 ∈ ∈ PROPN hjic-493 87 62 rn×m rn×m NOUN hjic-493 87 63 is be AUX hjic-493 87 64 an an DET hjic-493 87 65 element element NOUN hjic-493 87 66 of of ADP hjic-493 87 67 the the DET hjic-493 87 68 following following NOUN hjic-493 87 69 set set NOUN hjic-493 87 70 m m PROPN hjic-493 87 71 = = PUNCT hjic-493 87 72 { { PUNCT hjic-493 87 73 l∑ l∑ NUM hjic-493 87 74 i=1 i=1 PROPN hjic-493 87 75 αimi αimi PROPN hjic-493 88 1 | | ADV hjic-493 88 2 ( ( PUNCT hjic-493 88 3 ∀i ∀i NOUN hjic-493 88 4 : : PUNCT hjic-493 88 5 αi αi X hjic-493 88 6 ≥ ≥ NUM hjic-493 88 7 0 0 NUM hjic-493 88 8 ) ) PUNCT hjic-493 89 1 ∧ ∧ NOUN hjic-493 89 2 l∑ l∑ PUNCT hjic-493 90 1 i=1 i=1 PROPN hjic-493 90 2 αi αi X hjic-493 90 3 = = SYM hjic-493 90 4 1 1 X hjic-493 90 5 } } PUNCT hjic-493 90 6 . . PUNCT hjic-493 91 1 ( ( PUNCT hjic-493 91 2 11 11 NUM hjic-493 91 3 ) ) PUNCT hjic-493 91 4 the the DET hjic-493 91 5 goal goal NOUN hjic-493 91 6 is be AUX hjic-493 91 7 to to PART hjic-493 91 8 find find VERB hjic-493 91 9 a a DET hjic-493 91 10 method method NOUN hjic-493 91 11 for for ADP hjic-493 91 12 checking check VERB hjic-493 91 13 the the DET hjic-493 91 14 weak weak ADJ hjic-493 91 15 reversibility reversibility NOUN hjic-493 91 16 of of ADP hjic-493 91 17 the the DET hjic-493 91 18 system system NOUN hjic-493 91 19 eq.(10 eq.(10 NOUN hjic-493 91 20 ) ) PUNCT hjic-493 91 21 for for ADP hjic-493 91 22 all all DET hjic-493 91 23 matricesm matricesm ADJ hjic-493 91 24 ∈m ∈m NOUN hjic-493 91 25 . . PUNCT hjic-493 92 1 when when SCONJ hjic-493 92 2 all all DET hjic-493 92 3 vertices vertice VERB hjic-493 92 4 mi mi PROPN hjic-493 92 5 have have VERB hjic-493 92 6 a a DET hjic-493 92 7 weakly weakly ADJ hjic-493 92 8 reversible reversible ADJ hjic-493 92 9 realization realization NOUN hjic-493 92 10 ( ( PUNCT hjic-493 92 11 y y PROPN hjic-493 92 12 , , PUNCT hjic-493 92 13 a a PRON hjic-493 92 14 ( ( PUNCT hjic-493 92 15 i i NOUN hjic-493 92 16 ) ) PUNCT hjic-493 92 17 k k PROPN hjic-493 92 18 ) ) PUNCT hjic-493 92 19 then then ADV hjic-493 92 20 any any DET hjic-493 92 21 element element NOUN hjic-493 92 22 of of ADP hjic-493 92 23 the the DET hjic-493 92 24 setm setm NOUN hjic-493 92 25 has have VERB hjic-493 92 26 a a DET hjic-493 92 27 realization realization NOUN hjic-493 92 28 ( ( PUNCT hjic-493 92 29 y y PROPN hjic-493 92 30 , , PUNCT hjic-493 92 31 ak ak PROPN hjic-493 92 32 ) ) PUNCT hjic-493 92 33 such such ADJ hjic-493 92 34 that that SCONJ hjic-493 92 35 ak ak PROPN hjic-493 92 36 is be AUX hjic-493 92 37 the the DET hjic-493 92 38 convex convex ADJ hjic-493 92 39 combination combination NOUN hjic-493 92 40 of of ADP hjic-493 92 41 the the DET hjic-493 92 42 kirchhoff kirchhoff NOUN hjic-493 92 43 matrices matrix NOUN hjic-493 92 44 a(i a(i VERB hjic-493 92 45 ) ) PUNCT hjic-493 93 1 k k X hjic-493 93 2 . . PUNCT hjic-493 94 1 the the DET hjic-493 94 2 obtained obtain VERB hjic-493 94 3 realization realization NOUN hjic-493 94 4 ak ak PROPN hjic-493 94 5 will will AUX hjic-493 94 6 be be AUX hjic-493 94 7 weakly weakly ADV hjic-493 94 8 reversible reversible ADJ hjic-493 94 9 due due ADJ hjic-493 94 10 to to ADP hjic-493 94 11 theorem theorem NOUN hjic-493 94 12 1 1 NUM hjic-493 94 13 . . PUNCT hjic-493 95 1 therefore therefore ADV hjic-493 95 2 , , PUNCT hjic-493 95 3 it it PRON hjic-493 95 4 is be AUX hjic-493 95 5 enough enough ADJ hjic-493 95 6 to to PART hjic-493 95 7 compute compute VERB hjic-493 95 8 a a DET hjic-493 95 9 weakly weakly ADV hjic-493 95 10 reversible reversible ADJ hjic-493 95 11 realization realization NOUN hjic-493 95 12 for for ADP hjic-493 95 13 each each DET hjic-493 95 14 matrixmi matrixmi NOUN hjic-493 95 15 by by ADP hjic-493 95 16 using use VERB hjic-493 95 17 the the DET hjic-493 95 18 previously previously ADV hjic-493 95 19 presented present VERB hjic-493 95 20 lp lp ADV hjic-493 95 21 - - PUNCT hjic-493 95 22 based base VERB hjic-493 95 23 method method NOUN hjic-493 95 24 . . PUNCT hjic-493 96 1 a a DET hjic-493 96 2 simple simple ADJ hjic-493 96 3 example example NOUN hjic-493 96 4 let let VERB hjic-493 96 5 us we PRON hjic-493 96 6 consider consider VERB hjic-493 96 7 the the DET hjic-493 96 8 following follow VERB hjic-493 96 9 polynomial polynomial ADJ hjic-493 96 10 system system NOUN hjic-493 96 11 [ [ PUNCT hjic-493 96 12 ẋ1 ẋ1 PROPN hjic-493 96 13 ẋ2 ẋ2 PROPN hjic-493 96 14 ] ] PUNCT hjic-493 97 1 = = X hjic-493 97 2 m m X hjic-493 97 3 · · PUNCT hjic-493 97 4   NOUN hjic-493 97 5 x1 x1 INTJ hjic-493 97 6 x2 x2 NOUN hjic-493 97 7 x1x2 x1x2 PUNCT hjic-493 97 8   NOUN hjic-493 97 9 , , PUNCT hjic-493 97 10 ( ( PUNCT hjic-493 97 11 12 12 NUM hjic-493 97 12 ) ) PUNCT hjic-493 97 13 where where SCONJ hjic-493 97 14 m m NOUN hjic-493 97 15 is be AUX hjic-493 97 16 an an DET hjic-493 97 17 arbitrary arbitrary ADJ hjic-493 97 18 convex convex NOUN hjic-493 97 19 combination combination NOUN hjic-493 97 20 of of ADP hjic-493 97 21 the the DET hjic-493 97 22 following follow VERB hjic-493 97 23 three three NUM hjic-493 97 24 matrices matrix NOUN hjic-493 97 25 m1 m1 NOUN hjic-493 97 26 = = PUNCT hjic-493 98 1 [ [ PUNCT hjic-493 98 2 0 0 NUM hjic-493 98 3 1 1 NUM hjic-493 98 4 −1 −1 NOUN hjic-493 98 5 1 1 NUM hjic-493 98 6 −1 −1 NOUN hjic-493 98 7 0 0 NUM hjic-493 98 8 ] ] PUNCT hjic-493 98 9 , , PUNCT hjic-493 98 10 m2 m2 PROPN hjic-493 98 11 = = PUNCT hjic-493 98 12 [ [ PUNCT hjic-493 98 13 −1 −1 NOUN hjic-493 98 14 1 1 NUM hjic-493 98 15 0 0 NUM hjic-493 98 16 1 1 NUM hjic-493 98 17 −1 −1 NOUN hjic-493 98 18 0 0 NUM hjic-493 98 19 ] ] PUNCT hjic-493 98 20 , , PUNCT hjic-493 98 21 and and CCONJ hjic-493 98 22 m3 m3 PROPN hjic-493 98 23 = = PUNCT hjic-493 98 24 [ [ PUNCT hjic-493 98 25 0 0 NUM hjic-493 98 26 1 1 NUM hjic-493 98 27 −1 −1 NOUN hjic-493 98 28 0 0 NUM hjic-493 98 29 0 0 NUM hjic-493 98 30 0 0 NUM hjic-493 98 31 ] ] PUNCT hjic-493 98 32 . . PUNCT hjic-493 99 1 figure figure NOUN hjic-493 99 2 2 2 NUM hjic-493 99 3 : : PUNCT hjic-493 99 4 a a DET hjic-493 99 5 weakly weakly ADV hjic-493 99 6 reversible reversible ADJ hjic-493 99 7 realization realization NOUN hjic-493 99 8 of of ADP hjic-493 99 9 the the DET hjic-493 99 10 convex convex NOUN hjic-493 99 11 combination combination NOUN hjic-493 99 12 m m VERB hjic-493 99 13 = = NOUN hjic-493 99 14 0.2m1 0.2m1 NUM hjic-493 100 1 + + CCONJ hjic-493 100 2 0.4m2 0.4m2 NUM hjic-493 100 3 + + CCONJ hjic-493 100 4 0.4m3 0.4m3 NUM hjic-493 100 5 in in ADP hjic-493 100 6 order order NOUN hjic-493 100 7 to to PART hjic-493 100 8 show show VERB hjic-493 100 9 weak weak ADJ hjic-493 100 10 reversibility reversibility NOUN hjic-493 100 11 for for ADP hjic-493 100 12 all all DET hjic-493 100 13 possible possible ADJ hjic-493 100 14 convex convex NOUN hjic-493 100 15 combinations combination NOUN hjic-493 100 16 , , PUNCT hjic-493 100 17 we we PRON hjic-493 100 18 have have VERB hjic-493 100 19 to to PART hjic-493 100 20 find find VERB hjic-493 100 21 a a DET hjic-493 100 22 weakly weakly ADJ hjic-493 100 23 reversible reversible ADJ hjic-493 100 24 realization realization NOUN hjic-493 100 25 for for ADP hjic-493 100 26 each each DET hjic-493 100 27 matrix matrix NOUN hjic-493 100 28 m1 m1 NOUN hjic-493 100 29 , , PUNCT hjic-493 100 30 m2 m2 PROPN hjic-493 100 31 and and CCONJ hjic-493 100 32 m3 m3 PROPN hjic-493 100 33 . . PUNCT hjic-493 101 1 the the DET hjic-493 101 2 resulting result VERB hjic-493 101 3 weakly weakly ADJ hjic-493 101 4 reversible reversible ADJ hjic-493 101 5 reaction reaction NOUN hjic-493 101 6 graphs graph NOUN hjic-493 101 7 are be AUX hjic-493 101 8 depicted depict VERB hjic-493 101 9 in in ADP hjic-493 101 10 fig.1 fig.1 PROPN hjic-493 101 11 , , PUNCT hjic-493 101 12 while while SCONJ hjic-493 101 13 fig.2 fig.2 PROPN hjic-493 101 14 illustrates illustrate VERB hjic-493 101 15 an an DET hjic-493 101 16 inner inner ADJ hjic-493 101 17 point point NOUN hjic-493 101 18 realization realization NOUN hjic-493 101 19 which which PRON hjic-493 101 20 is be AUX hjic-493 101 21 weakly weakly ADV hjic-493 101 22 reversible reversible ADJ hjic-493 101 23 too too ADV hjic-493 101 24 . . PUNCT hjic-493 102 1 computing compute VERB hjic-493 102 2 kinetic kinetic ADJ hjic-493 102 3 feedback feedback NOUN hjic-493 102 4 for for ADP hjic-493 102 5 a a DET hjic-493 102 6 polynomial polynomial ADJ hjic-493 102 7 system system NOUN hjic-493 102 8 with with ADP hjic-493 102 9 parametric parametric ADJ hjic-493 102 10 uncertainty uncertainty NOUN hjic-493 102 11 besides besides SCONJ hjic-493 102 12 the the DET hjic-493 102 13 possible possible ADJ hjic-493 102 14 application application NOUN hjic-493 102 15 of of ADP hjic-493 102 16 the the DET hjic-493 102 17 above above ADJ hjic-493 102 18 described describe VERB hjic-493 102 19 lp lp ADV hjic-493 102 20 - - PUNCT hjic-493 102 21 based base VERB hjic-493 102 22 method method NOUN hjic-493 102 23 for for ADP hjic-493 102 24 robust robust ADJ hjic-493 102 25 stability stability NOUN hjic-493 102 26 analysis analysis NOUN hjic-493 102 27 , , PUNCT hjic-493 102 28 it it PRON hjic-493 102 29 can can AUX hjic-493 102 30 also also ADV hjic-493 102 31 be be AUX hjic-493 102 32 used use VERB hjic-493 102 33 for for ADP hjic-493 102 34 stabilizing stabilize VERB hjic-493 102 35 feedback feedback NOUN hjic-493 102 36 controller controller NOUN hjic-493 102 37 design design NOUN hjic-493 102 38 . . PUNCT hjic-493 103 1 for for ADP hjic-493 103 2 this this DET hjic-493 103 3 purpose purpose NOUN hjic-493 103 4 , , PUNCT hjic-493 103 5 a a DET hjic-493 103 6 generalized generalized ADJ hjic-493 103 7 version version NOUN hjic-493 103 8 of of ADP hjic-493 103 9 our our PRON hjic-493 103 10 preliminary preliminary ADJ hjic-493 103 11 work work NOUN hjic-493 103 12 on on ADP hjic-493 103 13 kinetic kinetic ADJ hjic-493 103 14 feedback feedback NOUN hjic-493 103 15 computation computation NOUN hjic-493 103 16 for for ADP hjic-493 103 17 polynomial polynomial ADJ hjic-493 103 18 systems system NOUN hjic-493 103 19 to to PART hjic-493 103 20 achieve achieve VERB hjic-493 103 21 weak weak ADJ hjic-493 103 22 reversibility reversibility NOUN hjic-493 103 23 and and CCONJ hjic-493 103 24 minimal minimal ADJ hjic-493 103 25 deficiency deficiency NOUN hjic-493 104 1 [ [ X hjic-493 104 2 6 6 NUM hjic-493 104 3 ] ] PUNCT hjic-493 104 4 is be AUX hjic-493 104 5 used use VERB hjic-493 104 6 here here ADV hjic-493 104 7 . . PUNCT hjic-493 105 1 the the DET hjic-493 105 2 feedback feedback NOUN hjic-493 105 3 design design NOUN hjic-493 105 4 problem problem NOUN hjic-493 105 5 we we PRON hjic-493 105 6 assume assume VERB hjic-493 105 7 that that SCONJ hjic-493 105 8 the the DET hjic-493 105 9 equation equation NOUN hjic-493 105 10 of of ADP hjic-493 105 11 the the DET hjic-493 105 12 open open ADJ hjic-493 105 13 - - PUNCT hjic-493 105 14 loop loop NOUN hjic-493 105 15 polynomial polynomial ADJ hjic-493 105 16 system system NOUN hjic-493 105 17 with with ADP hjic-493 105 18 linear linear ADJ hjic-493 105 19 constant constant ADJ hjic-493 105 20 parameter parameter NOUN hjic-493 105 21 input input NOUN hjic-493 105 22 structure structure NOUN hjic-493 105 23 is be AUX hjic-493 105 24 given give VERB hjic-493 105 25 as as ADP hjic-493 105 26 ẋ ẋ PROPN hjic-493 105 27 = = PROPN hjic-493 105 28 m m PROPN hjic-493 105 29 · · PUNCT hjic-493 105 30 ψ(x ψ(x NOUN hjic-493 105 31 ) ) PUNCT hjic-493 106 1 + + NOUN hjic-493 106 2 bu bu ADJ hjic-493 106 3 , , PUNCT hjic-493 106 4 ( ( PUNCT hjic-493 106 5 13 13 NUM hjic-493 106 6 ) ) PUNCT hjic-493 106 7 where where SCONJ hjic-493 106 8 x x SYM hjic-493 106 9 ∈ ∈ PROPN hjic-493 106 10 rn rn PROPN hjic-493 106 11 is be AUX hjic-493 106 12 the the DET hjic-493 106 13 state state NOUN hjic-493 106 14 vector vector NOUN hjic-493 106 15 , , PUNCT hjic-493 106 16 u u PROPN hjic-493 106 17 ∈ ∈ NOUN hjic-493 106 18 rp rp NOUN hjic-493 106 19 is be AUX hjic-493 106 20 the the DET hjic-493 106 21 input input NOUN hjic-493 106 22 and and CCONJ hjic-493 106 23 ψ ψ X hjic-493 106 24 ∈ ∈ PROPN hjic-493 106 25 rn rn PROPN hjic-493 106 26 → → SYM hjic-493 106 27 rm rm PROPN hjic-493 106 28 contains contain VERB hjic-493 106 29 the the DET hjic-493 106 30 monomials monomial NOUN hjic-493 106 31 of of ADP hjic-493 106 32 the the DET hjic-493 106 33 open open ADJ hjic-493 106 34 - - PUNCT hjic-493 106 35 loop loop NOUN hjic-493 106 36 system system NOUN hjic-493 106 37 . . PUNCT hjic-493 107 1 the the DET hjic-493 107 2 input input NOUN hjic-493 107 3 matrix matrix NOUN hjic-493 107 4 is be AUX hjic-493 107 5 b b PROPN hjic-493 107 6 ∈ ∈ PROPN hjic-493 107 7 rn×p rn×p NOUN hjic-493 107 8 , , PUNCT hjic-493 107 9 the the DET hjic-493 107 10 corresponding corresponding ADJ hjic-493 107 11 complex complex ADJ hjic-493 107 12 composition composition NOUN hjic-493 107 13 matrix matrix NOUN hjic-493 107 14 is be AUX hjic-493 107 15 y y PROPN hjic-493 107 16 with with ADP hjic-493 107 17 rank rank PROPN hjic-493 107 18 m m PROPN hjic-493 107 19 , , PUNCT hjic-493 107 20 and and CCONJ hjic-493 107 21 m m PROPN hjic-493 107 22 ∈ ∈ PROPN hjic-493 107 23 rn×m rn×m NOUN hjic-493 107 24 is be AUX hjic-493 107 25 an an DET hjic-493 107 26 element element NOUN hjic-493 107 27 of of ADP hjic-493 107 28 the the DET hjic-493 107 29 following following NOUN hjic-493 107 30 set set NOUN hjic-493 107 31 m m PROPN hjic-493 107 32 = = PUNCT hjic-493 107 33 { { PUNCT hjic-493 107 34 l∑ l∑ NUM hjic-493 107 35 i=1 i=1 PROPN hjic-493 107 36 αimi αimi PROPN hjic-493 108 1 | | ADV hjic-493 108 2 ( ( PUNCT hjic-493 108 3 ∀i ∀i NOUN hjic-493 108 4 : : PUNCT hjic-493 108 5 αi αi X hjic-493 108 6 ≥ ≥ NUM hjic-493 108 7 0 0 NUM hjic-493 108 8 ) ) PUNCT hjic-493 109 1 ∧ ∧ NOUN hjic-493 109 2 l∑ l∑ PUNCT hjic-493 110 1 i=1 i=1 PROPN hjic-493 110 2 αi αi X hjic-493 110 3 = = SYM hjic-493 110 4 1 1 X hjic-493 110 5 } } PUNCT hjic-493 110 6 . . PUNCT hjic-493 111 1 ( ( PUNCT hjic-493 111 2 14 14 NUM hjic-493 111 3 ) ) PUNCT hjic-493 111 4 moreover moreover ADV hjic-493 111 5 , , PUNCT hjic-493 111 6 a a DET hjic-493 111 7 positive positive ADJ hjic-493 111 8 vector vector NOUN hjic-493 111 9 x x X hjic-493 111 10 ∈ ∈ PROPN hjic-493 111 11 rn rn PROPN hjic-493 111 12 > > PROPN hjic-493 111 13 0 0 PUNCT hjic-493 112 1 being be AUX hjic-493 112 2 the the DET hjic-493 112 3 desired desire VERB hjic-493 112 4 equilibrium equilibrium NOUN hjic-493 112 5 point point NOUN hjic-493 112 6 is be AUX hjic-493 112 7 given give VERB hjic-493 112 8 as as ADP hjic-493 112 9 a a DET hjic-493 112 10 design design NOUN hjic-493 112 11 parameter parameter NOUN hjic-493 112 12 . . PUNCT hjic-493 113 1 note note VERB hjic-493 113 2 that that SCONJ hjic-493 113 3 the the DET hjic-493 113 4 above above ADJ hjic-493 113 5 polynomial polynomial ADJ hjic-493 113 6 system system NOUN hjic-493 113 7 is be AUX hjic-493 113 8 not not PART hjic-493 113 9 necessarily necessarily ADV hjic-493 113 10 kinetic kinetic ADJ hjic-493 113 11 , , PUNCT hjic-493 113 12 i.e. i.e. X hjic-493 113 13 not not PART hjic-493 113 14 necessarily necessarily ADV hjic-493 113 15 positive positive ADJ hjic-493 113 16 , , PUNCT hjic-493 113 17 and and CCONJ hjic-493 113 18 may may AUX hjic-493 113 19 not not PART hjic-493 113 20 have have VERB hjic-493 113 21 a a DET hjic-493 113 22 positive positive ADJ hjic-493 113 23 equilibrium equilibrium NOUN hjic-493 113 24 point point NOUN hjic-493 113 25 at at ADV hjic-493 113 26 all all ADV hjic-493 113 27 . . PUNCT hjic-493 114 1 106 106 NUM hjic-493 115 1 the the DET hjic-493 115 2 aim aim NOUN hjic-493 115 3 of of ADP hjic-493 115 4 the the DET hjic-493 115 5 feedback feedback NOUN hjic-493 115 6 is be AUX hjic-493 115 7 to to PART hjic-493 115 8 set set VERB hjic-493 115 9 a a DET hjic-493 115 10 region region NOUN hjic-493 115 11 in in ADP hjic-493 115 12 the the DET hjic-493 115 13 state state NOUN hjic-493 115 14 space space NOUN hjic-493 115 15 r r NOUN hjic-493 115 16 ⊆ ⊆ NUM hjic-493 115 17 rn rn X hjic-493 115 18 ≥0 ≥0 NOUN hjic-493 115 19 where where SCONJ hjic-493 115 20 x x PRON hjic-493 115 21 is be AUX hjic-493 115 22 ( ( PUNCT hjic-493 115 23 at at ADP hjic-493 115 24 least least ADJ hjic-493 115 25 ) ) PUNCT hjic-493 115 26 a a DET hjic-493 115 27 locally locally ADV hjic-493 115 28 asymptotically asymptotically ADV hjic-493 115 29 stable stable ADJ hjic-493 115 30 equilibrium equilibrium NOUN hjic-493 115 31 point point NOUN hjic-493 115 32 of of ADP hjic-493 115 33 the the DET hjic-493 115 34 closed closed ADJ hjic-493 115 35 - - PUNCT hjic-493 115 36 loop loop NOUN hjic-493 115 37 system system NOUN hjic-493 115 38 for for ADP hjic-493 115 39 all all DET hjic-493 115 40 m m NOUN hjic-493 115 41 ∈m ∈m NOUN hjic-493 115 42 . . PUNCT hjic-493 116 1 for for ADP hjic-493 116 2 this this DET hjic-493 116 3 purpose purpose NOUN hjic-493 116 4 we we PRON hjic-493 116 5 are be AUX hjic-493 116 6 looking look VERB hjic-493 116 7 for for ADP hjic-493 116 8 a a DET hjic-493 116 9 feedback feedback NOUN hjic-493 116 10 in in ADP hjic-493 116 11 the the DET hjic-493 116 12 form form NOUN hjic-493 116 13 u u NOUN hjic-493 116 14 = = NOUN hjic-493 116 15 kψ(x kψ(x PROPN hjic-493 116 16 ) ) PUNCT hjic-493 116 17 ( ( PUNCT hjic-493 116 18 15 15 NUM hjic-493 116 19 ) ) PUNCT hjic-493 116 20 which which PRON hjic-493 116 21 transforms transform VERB hjic-493 116 22 the the DET hjic-493 116 23 open open ADJ hjic-493 116 24 - - PUNCT hjic-493 116 25 loop loop NOUN hjic-493 116 26 system system NOUN hjic-493 116 27 into into ADP hjic-493 116 28 a a DET hjic-493 116 29 weakly weakly ADJ hjic-493 116 30 reversible reversible ADJ hjic-493 116 31 kinetic kinetic NOUN hjic-493 116 32 system system NOUN hjic-493 116 33 with with ADP hjic-493 116 34 zero zero NUM hjic-493 116 35 deficiency deficiency NOUN hjic-493 116 36 for for ADP hjic-493 116 37 all all DET hjic-493 116 38 m m NOUN hjic-493 116 39 ∈ ∈ NOUN hjic-493 116 40 m m NOUN hjic-493 116 41 with with ADP hjic-493 116 42 the the DET hjic-493 116 43 given give VERB hjic-493 116 44 equilibrium equilibrium NOUN hjic-493 116 45 point point NOUN hjic-493 116 46 x. x. NOUN hjic-493 116 47 feedback feedback NOUN hjic-493 116 48 computation computation NOUN hjic-493 116 49 similarly similarly ADV hjic-493 116 50 to to ADP hjic-493 116 51 the the DET hjic-493 116 52 realization realization NOUN hjic-493 116 53 computation computation NOUN hjic-493 116 54 , , PUNCT hjic-493 116 55 the the DET hjic-493 116 56 matrix matrix NOUN hjic-493 116 57 k k PROPN hjic-493 116 58 will will AUX hjic-493 116 59 be be AUX hjic-493 116 60 determined determine VERB hjic-493 116 61 by by ADP hjic-493 116 62 solving solve VERB hjic-493 116 63 an an DET hjic-493 116 64 lp lp ADJ hjic-493 116 65 problem problem NOUN hjic-493 116 66 . . PUNCT hjic-493 117 1 the the DET hjic-493 117 2 convexity convexity NOUN hjic-493 117 3 result result NOUN hjic-493 117 4 shows show VERB hjic-493 117 5 that that SCONJ hjic-493 117 6 it it PRON hjic-493 117 7 is be AUX hjic-493 117 8 enough enough ADJ hjic-493 117 9 to to PART hjic-493 117 10 compute compute VERB hjic-493 117 11 one one NUM hjic-493 117 12 weakly weakly ADV hjic-493 117 13 reversible reversible ADJ hjic-493 117 14 realization realization NOUN hjic-493 117 15 ( ( PUNCT hjic-493 117 16 y y PROPN hjic-493 117 17 , , PUNCT hjic-493 117 18 a a DET hjic-493 117 19 ( ( PUNCT hjic-493 117 20 r r NOUN hjic-493 117 21 ) ) PUNCT hjic-493 117 22 k k NOUN hjic-493 117 23 ) ) PUNCT hjic-493 117 24 in in ADP hjic-493 117 25 each each DET hjic-493 117 26 vertex vertex NOUN hjic-493 117 27 mr mr PROPN hjic-493 117 28 to to PART hjic-493 117 29 ensure ensure VERB hjic-493 117 30 weak weak ADJ hjic-493 117 31 reversibility reversibility NOUN hjic-493 117 32 for for ADP hjic-493 117 33 all all DET hjic-493 117 34 possible possible ADJ hjic-493 117 35 closed closed ADJ hjic-493 117 36 - - PUNCT hjic-493 117 37 loop loop NOUN hjic-493 117 38 systems system NOUN hjic-493 117 39 . . PUNCT hjic-493 118 1 all all DET hjic-493 118 2 realizations realization NOUN hjic-493 118 3 will will AUX hjic-493 118 4 have have VERB hjic-493 118 5 zero zero NUM hjic-493 118 6 deficiency deficiency NOUN hjic-493 118 7 , , PUNCT hjic-493 118 8 because because SCONJ hjic-493 118 9 of of ADP hjic-493 118 10 the the DET hjic-493 118 11 rank rank NOUN hjic-493 118 12 condition condition NOUN hjic-493 118 13 rank(y rank(y PROPN hjic-493 118 14 ) ) PUNCT hjic-493 118 15 = = PUNCT hjic-493 118 16 m m VERB hjic-493 119 1 [ [ X hjic-493 119 2 7 7 NUM hjic-493 119 3 ] ] PUNCT hjic-493 119 4 . . PUNCT hjic-493 120 1 first first ADV hjic-493 120 2 we we PRON hjic-493 120 3 note note VERB hjic-493 120 4 , , PUNCT hjic-493 120 5 that that SCONJ hjic-493 120 6 the the DET hjic-493 120 7 realization realization NOUN hjic-493 120 8 ( ( PUNCT hjic-493 120 9 y y PROPN hjic-493 120 10 , , PUNCT hjic-493 120 11 a a DET hjic-493 120 12 ( ( PUNCT hjic-493 120 13 r r NOUN hjic-493 120 14 ) ) PUNCT hjic-493 120 15 k k NOUN hjic-493 120 16 ) ) PUNCT hjic-493 120 17 that that PRON hjic-493 120 18 corresponds correspond VERB hjic-493 120 19 to to ADP hjic-493 120 20 the the DET hjic-493 120 21 closed closed ADJ hjic-493 120 22 - - PUNCT hjic-493 120 23 loop loop NOUN hjic-493 120 24 system system NOUN hjic-493 120 25 is be AUX hjic-493 120 26 mr mr PROPN hjic-493 120 27 + + PROPN hjic-493 120 28 b b PROPN hjic-493 120 29 · · SYM hjic-493 120 30 k k X hjic-493 120 31 = = SYM hjic-493 120 32 y y PROPN hjic-493 120 33 · · SYM hjic-493 120 34 a(r a(r NOUN hjic-493 120 35 ) ) PUNCT hjic-493 120 36 k k X hjic-493 120 37 . . PUNCT hjic-493 121 1 ( ( PUNCT hjic-493 121 2 16 16 NUM hjic-493 121 3 ) ) PUNCT hjic-493 121 4 where where SCONJ hjic-493 121 5 the the DET hjic-493 121 6 matrix matrix NOUN hjic-493 121 7 a(r a(r NOUN hjic-493 121 8 ) ) PUNCT hjic-493 121 9 k k PROPN hjic-493 121 10 should should AUX hjic-493 121 11 be be AUX hjic-493 121 12 kirchhoff kirchhoff NOUN hjic-493 121 13 m∑ m∑ X hjic-493 121 14 i=1 i=1 PRON hjic-493 122 1 [ [ X hjic-493 122 2 ãk]ij ãk]ij NOUN hjic-493 122 3 = = SYM hjic-493 122 4 0 0 NUM hjic-493 122 5 , , PUNCT hjic-493 122 6 j j PROPN hjic-493 122 7 = = SYM hjic-493 122 8 1 1 NUM hjic-493 122 9 , , PUNCT hjic-493 122 10 . . PUNCT hjic-493 122 11 . . PUNCT hjic-493 122 12 . . PUNCT hjic-493 123 1 , , PUNCT hjic-493 123 2 m m VERB hjic-493 123 3 [ [ X hjic-493 123 4 ãk]ij ãk]ij VERB hjic-493 123 5 ≥ ≥ NOUN hjic-493 123 6 0 0 NUM hjic-493 123 7 , , PUNCT hjic-493 123 8 i i PRON hjic-493 123 9 , , PUNCT hjic-493 123 10 j j PROPN hjic-493 123 11 = = SYM hjic-493 123 12 1 1 NUM hjic-493 123 13 , , PUNCT hjic-493 123 14 . . PUNCT hjic-493 123 15 . . PUNCT hjic-493 123 16 . . PUNCT hjic-493 124 1 , , PUNCT hjic-493 124 2 m m PROPN hjic-493 124 3 , , PUNCT hjic-493 124 4 i i PROPN hjic-493 124 5 6= 6= NUM hjic-493 124 6 j j PROPN hjic-493 125 1 [ [ X hjic-493 125 2 ãk]ii ãk]ii NOUN hjic-493 125 3 ≤ ≤ NUM hjic-493 125 4 0 0 NUM hjic-493 125 5 , , PUNCT hjic-493 125 6 i i PRON hjic-493 125 7 = = NOUN hjic-493 125 8 1 1 NUM hjic-493 125 9 , , PUNCT hjic-493 125 10 . . PUNCT hjic-493 125 11 . . PUNCT hjic-493 125 12 . . PUNCT hjic-493 126 1 , , PUNCT hjic-493 126 2 m. m. NOUN hjic-493 126 3 ( ( PUNCT hjic-493 126 4 17 17 NUM hjic-493 126 5 ) ) PUNCT hjic-493 126 6 in in ADP hjic-493 126 7 order order NOUN hjic-493 126 8 to to PART hjic-493 126 9 obtain obtain VERB hjic-493 126 10 a a DET hjic-493 126 11 weakly weakly ADV hjic-493 126 12 reversible reversible ADJ hjic-493 126 13 closed closed ADJ hjic-493 126 14 - - PUNCT hjic-493 126 15 loop loop NOUN hjic-493 126 16 system system NOUN hjic-493 126 17 with with ADP hjic-493 126 18 an an DET hjic-493 126 19 equilibrium equilibrium NOUN hjic-493 126 20 point point NOUN hjic-493 126 21 x x NOUN hjic-493 126 22 , , PUNCT hjic-493 126 23 the the DET hjic-493 126 24 matrix matrix NOUN hjic-493 126 25 a(r a(r NOUN hjic-493 126 26 ) ) PUNCT hjic-493 127 1 k k PROPN hjic-493 127 2 should should AUX hjic-493 127 3 be be AUX hjic-493 127 4 weakly weakly ADV hjic-493 127 5 reversible reversible ADJ hjic-493 127 6 and and CCONJ hjic-493 127 7 has have VERB hjic-493 127 8 to to PART hjic-493 127 9 have have VERB hjic-493 127 10 the the DET hjic-493 127 11 vector vector NOUN hjic-493 127 12 ψ(x ψ(x NOUN hjic-493 127 13 ) ) PUNCT hjic-493 127 14 in in ADP hjic-493 127 15 its its PRON hjic-493 127 16 right right ADJ hjic-493 127 17 kernel kernel NOUN hjic-493 127 18 , , PUNCT hjic-493 127 19 i.e. i.e. X hjic-493 127 20 a a DET hjic-493 127 21 ( ( PUNCT hjic-493 127 22 r r NOUN hjic-493 127 23 ) ) PUNCT hjic-493 127 24 k k PROPN hjic-493 127 25 · · PUNCT hjic-493 127 26 ψ(x ψ(x NOUN hjic-493 127 27 ) ) PUNCT hjic-493 127 28 = = SYM hjic-493 128 1 0 0 X hjic-493 128 2 . . PUNCT hjic-493 129 1 ( ( PUNCT hjic-493 129 2 18 18 NUM hjic-493 129 3 ) ) PUNCT hjic-493 129 4 finally finally ADV hjic-493 129 5 , , PUNCT hjic-493 129 6 by by ADP hjic-493 129 7 choosing choose VERB hjic-493 129 8 an an DET hjic-493 129 9 arbitrary arbitrary ADJ hjic-493 129 10 linear linear ADJ hjic-493 129 11 objective objective ADJ hjic-493 129 12 function function NOUN hjic-493 129 13 of of ADP hjic-493 129 14 the the DET hjic-493 129 15 decision decision NOUN hjic-493 129 16 variables variable NOUN hjic-493 129 17 a(1 a(1 ADJ hjic-493 129 18 ) ) PUNCT hjic-493 129 19 k k NOUN hjic-493 129 20 , , PUNCT hjic-493 129 21 . . PUNCT hjic-493 129 22 . . PUNCT hjic-493 130 1 . . PUNCT hjic-493 131 1 , , PUNCT hjic-493 131 2 a a DET hjic-493 131 3 ( ( PUNCT hjic-493 131 4 l l NOUN hjic-493 131 5 ) ) PUNCT hjic-493 131 6 k k PROPN hjic-493 131 7 and and CCONJ hjic-493 131 8 k k NOUN hjic-493 131 9 , , PUNCT hjic-493 131 10 the the DET hjic-493 131 11 feedback feedback NOUN hjic-493 131 12 gain gain NOUN hjic-493 131 13 k k PROPN hjic-493 131 14 can can AUX hjic-493 131 15 be be AUX hjic-493 131 16 computed compute VERB hjic-493 131 17 ( ( PUNCT hjic-493 131 18 if if SCONJ hjic-493 131 19 it it PRON hjic-493 131 20 exists exist VERB hjic-493 131 21 ) ) PUNCT hjic-493 131 22 in in ADP hjic-493 131 23 a a DET hjic-493 131 24 lp lp NOUN hjic-493 131 25 framework framework NOUN hjic-493 131 26 using use VERB hjic-493 131 27 the the DET hjic-493 131 28 linear linear PROPN hjic-493 131 29 constraints constraints PROPN hjic-493 131 30 eqs.(16 eqs.(16 PROPN hjic-493 131 31 - - SYM hjic-493 131 32 18 18 NUM hjic-493 131 33 ) ) PUNCT hjic-493 131 34 . . PUNCT hjic-493 132 1 with with ADP hjic-493 132 2 the the DET hjic-493 132 3 resulting result VERB hjic-493 132 4 feedback feedback NOUN hjic-493 132 5 gain gain NOUN hjic-493 132 6 k k NOUN hjic-493 132 7 , , PUNCT hjic-493 132 8 the the DET hjic-493 132 9 point point NOUN hjic-493 132 10 x x PUNCT hjic-493 132 11 will will AUX hjic-493 132 12 be be AUX hjic-493 132 13 an an DET hjic-493 132 14 equilibrium equilibrium NOUN hjic-493 132 15 point point NOUN hjic-493 132 16 of of ADP hjic-493 132 17 all all DET hjic-493 132 18 possible possible ADJ hjic-493 132 19 closed closed ADJ hjic-493 132 20 - - PUNCT hjic-493 132 21 loop loop NOUN hjic-493 132 22 systems system NOUN hjic-493 132 23 , , PUNCT hjic-493 132 24 and and CCONJ hjic-493 132 25 x x PRON hjic-493 132 26 will will AUX hjic-493 132 27 be be AUX hjic-493 132 28 locally locally ADV hjic-493 132 29 asymptotically asymptotically ADV hjic-493 132 30 stable stable ADJ hjic-493 132 31 in in ADP hjic-493 132 32 the the DET hjic-493 132 33 region region NOUN hjic-493 132 34 s s PART hjic-493 132 35 = = PUNCT hjic-493 132 36 ( ( PUNCT hjic-493 132 37 x+s)∩rn x+s)∩rn X hjic-493 132 38 ≥0 ≥0 NOUN hjic-493 132 39 , , PUNCT hjic-493 132 40 where where SCONJ hjic-493 132 41 s s NOUN hjic-493 132 42 is be AUX hjic-493 132 43 the the DET hjic-493 132 44 stoichiometric stoichiometric ADJ hjic-493 132 45 subspace subspace NOUN hjic-493 132 46 of of ADP hjic-493 132 47 the the DET hjic-493 132 48 closed closed ADJ hjic-493 132 49 - - PUNCT hjic-493 132 50 loop loop NOUN hjic-493 132 51 system system NOUN hjic-493 132 52 . . PUNCT hjic-493 133 1 example example NOUN hjic-493 133 2 let let VERB hjic-493 133 3 the the DET hjic-493 133 4 open open ADJ hjic-493 133 5 - - PUNCT hjic-493 133 6 loop loop NOUN hjic-493 133 7 system system NOUN hjic-493 133 8 be be AUX hjic-493 133 9 given give VERB hjic-493 133 10 as as ADP hjic-493 133 11 ẋ ẋ PROPN hjic-493 133 12 = = PROPN hjic-493 133 13 m m NOUN hjic-493 133 14   NOUN hjic-493 133 15 x1x2 x1x2 X hjic-493 134 1 x2x3 x2x3 PROPN hjic-493 135 1 x1 x1 PROPN hjic-493 135 2 + + PROPN hjic-493 135 3   PROPN hjic-493 135 4 0 0 NUM hjic-493 135 5 1 1 NUM hjic-493 135 6 0 0 NUM hjic-493 135 7 u u NOUN hjic-493 135 8 ( ( PUNCT hjic-493 135 9 19 19 NUM hjic-493 135 10 ) ) PUNCT hjic-493 135 11 figure figure NOUN hjic-493 135 12 3 3 NUM hjic-493 135 13 : : PUNCT hjic-493 135 14 weakly weakly ADJ hjic-493 135 15 reversible reversible ADJ hjic-493 135 16 realization realization NOUN hjic-493 135 17 of of ADP hjic-493 135 18 the the DET hjic-493 135 19 closed closed ADJ hjic-493 135 20 - - PUNCT hjic-493 135 21 loop loop NOUN hjic-493 135 22 system system NOUN hjic-493 135 23 , , PUNCT hjic-493 135 24 where where SCONJ hjic-493 135 25 m m VERB hjic-493 135 26 = = X hjic-493 135 27 0.6m1 0.6m1 NUM hjic-493 135 28 + + NOUN hjic-493 135 29 0.2m2 0.2m2 NUM hjic-493 135 30 + + CCONJ hjic-493 135 31 0.2m3 0.2m3 NUM hjic-493 135 32 where where SCONJ hjic-493 135 33 m m NOUN hjic-493 135 34 is be AUX hjic-493 135 35 an an DET hjic-493 135 36 arbitrary arbitrary ADJ hjic-493 135 37 convex convex NOUN hjic-493 135 38 combination combination NOUN hjic-493 135 39 of of ADP hjic-493 135 40 the the DET hjic-493 135 41 following follow VERB hjic-493 135 42 three three NUM hjic-493 135 43 matrices matrix NOUN hjic-493 135 44 : : PUNCT hjic-493 135 45 m1 m1 NOUN hjic-493 135 46 = = SYM hjic-493 135 47   PROPN hjic-493 135 48 −1 −1 NOUN hjic-493 135 49 1 1 NUM hjic-493 135 50 0 0 NUM hjic-493 135 51 2 2 NUM hjic-493 135 52 1 1 NUM hjic-493 135 53 2 2 NUM hjic-493 135 54 1 1 NUM hjic-493 135 55 −1 −1 NOUN hjic-493 135 56 0 0 NUM hjic-493 135 57   NOUN hjic-493 135 58 , , PUNCT hjic-493 135 59 m2 m2 PROPN hjic-493 135 60 = = SYM hjic-493 135 61   PROPN hjic-493 135 62 0 0 NUM hjic-493 135 63 0 0 NUM hjic-493 135 64 0 0 NUM hjic-493 135 65 1 1 NUM hjic-493 135 66 1 1 NUM hjic-493 135 67 3 3 NUM hjic-493 135 68 0 0 NUM hjic-493 135 69 0 0 NUM hjic-493 135 70 0 0 NUM hjic-493 135 71   NOUN hjic-493 135 72 , , PUNCT hjic-493 135 73 and and CCONJ hjic-493 135 74 m3 m3 PROPN hjic-493 135 75 = = SYM hjic-493 135 76   PROPN hjic-493 135 77 0 0 NUM hjic-493 135 78 1 1 NUM hjic-493 135 79 −1 −1 NOUN hjic-493 135 80 2 2 NUM hjic-493 135 81 0 0 NUM hjic-493 135 82 3 3 NUM hjic-493 135 83 0 0 NUM hjic-493 135 84 −1 −1 NOUN hjic-493 135 85 1 1 NUM hjic-493 135 86   NOUN hjic-493 135 87 . . PUNCT hjic-493 136 1 the the DET hjic-493 136 2 desired desire VERB hjic-493 136 3 equilibrium equilibrium NOUN hjic-493 136 4 point point NOUN hjic-493 136 5 x x PUNCT hjic-493 137 1 = = PUNCT hjic-493 138 1 [ [ X hjic-493 138 2 1 1 NUM hjic-493 138 3 1 1 NUM hjic-493 138 4 1 1 NUM hjic-493 138 5 ] ] PUNCT hjic-493 138 6 t t NOUN hjic-493 138 7 . . PUNCT hjic-493 139 1 we we PRON hjic-493 139 2 are be AUX hjic-493 139 3 looking look VERB hjic-493 139 4 for for ADP hjic-493 139 5 a a DET hjic-493 139 6 feedback feedback NOUN hjic-493 139 7 law law NOUN hjic-493 139 8 with with ADP hjic-493 139 9 gaink gaink NOUN hjic-493 139 10 which which PRON hjic-493 139 11 transforms transform VERB hjic-493 139 12 the the DET hjic-493 139 13 matricesmi matricesmi NOUN hjic-493 139 14 into into ADP hjic-493 139 15 weakly weakly ADJ hjic-493 139 16 reversible reversible ADJ hjic-493 139 17 kinetic kinetic NOUN hjic-493 139 18 systems system NOUN hjic-493 139 19 with with ADP hjic-493 139 20 the the DET hjic-493 139 21 given give VERB hjic-493 139 22 equilibrium equilibrium NOUN hjic-493 139 23 point point NOUN hjic-493 139 24 . . PUNCT hjic-493 140 1 by by ADP hjic-493 140 2 solving solve VERB hjic-493 140 3 the the DET hjic-493 140 4 feedback feedback NOUN hjic-493 140 5 design design NOUN hjic-493 140 6 lp lp NOUN hjic-493 140 7 optimization optimization NOUN hjic-493 140 8 problem problem NOUN hjic-493 140 9 using use VERB hjic-493 140 10 the the DET hjic-493 140 11 linear linear PROPN hjic-493 140 12 constraints constraints PROPN hjic-493 140 13 eqs.(16 eqs.(16 PROPN hjic-493 140 14 - - SYM hjic-493 140 15 18 18 NUM hjic-493 140 16 ) ) PUNCT hjic-493 140 17 , , PUNCT hjic-493 140 18 the the DET hjic-493 140 19 computed computed ADJ hjic-493 140 20 feedback feedback NOUN hjic-493 140 21 is be AUX hjic-493 140 22 in in ADP hjic-493 140 23 the the DET hjic-493 140 24 following follow VERB hjic-493 140 25 form form NOUN hjic-493 140 26 : : PUNCT hjic-493 140 27 u u NOUN hjic-493 140 28 = = X hjic-493 140 29 [ [ PUNCT hjic-493 140 30 2 2 NUM hjic-493 140 31 1 1 NUM hjic-493 140 32 2 2 NUM hjic-493 140 33 ] ] PUNCT hjic-493 140 34 ψ(x ψ(x NOUN hjic-493 140 35 ) ) PUNCT hjic-493 140 36 . . PUNCT hjic-493 141 1 ( ( PUNCT hjic-493 141 2 20 20 X hjic-493 141 3 ) ) PUNCT hjic-493 141 4 fig.3 fig.3 PROPN hjic-493 141 5 depicts depict VERB hjic-493 141 6 a a DET hjic-493 141 7 weakly weakly ADJ hjic-493 141 8 reversible reversible ADJ hjic-493 141 9 realization realization NOUN hjic-493 141 10 of of ADP hjic-493 141 11 the the DET hjic-493 141 12 closed closed ADJ hjic-493 141 13 - - PUNCT hjic-493 141 14 loop loop NOUN hjic-493 141 15 system system NOUN hjic-493 141 16 . . PUNCT hjic-493 142 1 the the DET hjic-493 142 2 obtained obtain VERB hjic-493 142 3 closed close VERB hjic-493 142 4 - - PUNCT hjic-493 142 5 loop loop NOUN hjic-493 142 6 system system NOUN hjic-493 142 7 in in ADP hjic-493 142 8 an an DET hjic-493 142 9 inner inner ADJ hjic-493 142 10 point point NOUN hjic-493 142 11 of of ADP hjic-493 142 12 the the DET hjic-493 142 13 convex convex ADJ hjic-493 142 14 setm setm NOUN hjic-493 142 15 has have VERB hjic-493 142 16 the the DET hjic-493 142 17 following follow VERB hjic-493 142 18 stoichiometric stoichiometric ADJ hjic-493 142 19 subspace subspace NOUN hjic-493 142 20 : : PUNCT hjic-493 142 21 s s X hjic-493 142 22 = = PUNCT hjic-493 142 23 span span NOUN hjic-493 142 24   VERB hjic-493 142 25 1 1 NUM hjic-493 142 26 1 1 NUM hjic-493 142 27 0 0 NUM hjic-493 142 28 − − X hjic-493 142 29   NOUN hjic-493 142 30 0 0 NUM hjic-493 142 31 1 1 NUM hjic-493 142 32 1 1 NUM hjic-493 142 33   NOUN hjic-493 142 34 , , PUNCT hjic-493 142 35   NOUN hjic-493 142 36 1 1 NUM hjic-493 142 37 1 1 NUM hjic-493 142 38 0 0 NUM hjic-493 142 39 − − AUX hjic-493 142 40   NOUN hjic-493 142 41 1 1 NUM hjic-493 142 42 0 0 NUM hjic-493 142 43 0 0 NUM hjic-493 142 44   NOUN hjic-493 142 45 . . PUNCT hjic-493 143 1 ( ( PUNCT hjic-493 143 2 21 21 NUM hjic-493 143 3 ) ) PUNCT hjic-493 143 4 therefore therefore ADV hjic-493 143 5 , , PUNCT hjic-493 143 6 the the DET hjic-493 143 7 equilibrium equilibrium NOUN hjic-493 143 8 point point NOUN hjic-493 143 9 x x PUNCT hjic-493 143 10 will will AUX hjic-493 143 11 be be AUX hjic-493 143 12 asymptotically asymptotically ADV hjic-493 143 13 stable stable ADJ hjic-493 143 14 with with ADP hjic-493 143 15 the the DET hjic-493 143 16 region region NOUN hjic-493 143 17 s s PART hjic-493 143 18 = = PUNCT hjic-493 143 19 ( ( PUNCT hjic-493 143 20 x+s)∩rn x+s)∩rn X hjic-493 143 21 ≥0 ≥0 NOUN hjic-493 143 22 . . PUNCT hjic-493 143 23 note note NOUN hjic-493 143 24 , , PUNCT hjic-493 143 25 that that SCONJ hjic-493 143 26 one one PRON hjic-493 143 27 should should AUX hjic-493 143 28 choose choose VERB hjic-493 143 29 the the DET hjic-493 143 30 initial initial ADJ hjic-493 143 31 value value NOUN hjic-493 143 32 of of ADP hjic-493 143 33 the the DET hjic-493 143 34 state state NOUN hjic-493 143 35 variables variable NOUN hjic-493 143 36 from from ADP hjic-493 143 37 s. s. PROPN hjic-493 143 38 fig.4 fig.4 PROPN hjic-493 143 39 shows show VERB hjic-493 143 40 the the DET hjic-493 143 41 time time NOUN hjic-493 143 42 dependent dependent ADJ hjic-493 143 43 behaviour behaviour NOUN hjic-493 143 44 of of ADP hjic-493 143 45 the the DET hjic-493 143 46 closed closed ADJ hjic-493 143 47 - - PUNCT hjic-493 143 48 loop loop NOUN hjic-493 143 49 solutions solution NOUN hjic-493 143 50 started start VERB hjic-493 143 51 from from ADP hjic-493 143 52 different different ADJ hjic-493 143 53 initial initial ADJ hjic-493 143 54 points point NOUN hjic-493 143 55 in in ADP hjic-493 143 56 s. s. PROPN hjic-493 143 57 107 107 NUM hjic-493 143 58 figure figure NOUN hjic-493 143 59 4 4 NUM hjic-493 143 60 : : PUNCT hjic-493 143 61 time time NOUN hjic-493 143 62 - - PUNCT hjic-493 143 63 domain domain NOUN hjic-493 143 64 simulation simulation NOUN hjic-493 143 65 of of ADP hjic-493 143 66 the the DET hjic-493 143 67 closed closed ADJ hjic-493 143 68 - - PUNCT hjic-493 143 69 loop loop NOUN hjic-493 143 70 system system NOUN hjic-493 143 71 conclusion conclusion NOUN hjic-493 143 72 it it PRON hjic-493 143 73 is be AUX hjic-493 143 74 shown show VERB hjic-493 143 75 in in ADP hjic-493 143 76 this this DET hjic-493 143 77 paper paper NOUN hjic-493 143 78 that that SCONJ hjic-493 143 79 the the DET hjic-493 143 80 domain domain NOUN hjic-493 143 81 of of ADP hjic-493 143 82 weakly weakly ADJ hjic-493 143 83 reversible reversible ADJ hjic-493 143 84 realizations realization NOUN hjic-493 143 85 is be AUX hjic-493 143 86 convex convex ADJ hjic-493 143 87 in in ADP hjic-493 143 88 the the DET hjic-493 143 89 parameter parameter NOUN hjic-493 143 90 space space NOUN hjic-493 143 91 . . PUNCT hjic-493 144 1 this this DET hjic-493 144 2 property property NOUN hjic-493 144 3 is be AUX hjic-493 144 4 utilized utilize VERB hjic-493 144 5 for for ADP hjic-493 144 6 developing develop VERB hjic-493 144 7 methods method NOUN hjic-493 144 8 in in ADP hjic-493 144 9 system system NOUN hjic-493 144 10 analysis analysis NOUN hjic-493 144 11 and and CCONJ hjic-493 144 12 robust robust ADJ hjic-493 144 13 control control NOUN hjic-493 144 14 design design NOUN hjic-493 144 15 . . PUNCT hjic-493 145 1 an an DET hjic-493 145 2 lp lp ADV hjic-493 145 3 - - PUNCT hjic-493 145 4 based base VERB hjic-493 145 5 optimization optimization NOUN hjic-493 145 6 method method NOUN hjic-493 145 7 is be AUX hjic-493 145 8 proposed propose VERB hjic-493 145 9 for for ADP hjic-493 145 10 testing testing NOUN hjic-493 145 11 if if SCONJ hjic-493 145 12 every every DET hjic-493 145 13 element element NOUN hjic-493 145 14 of of ADP hjic-493 145 15 a a DET hjic-493 145 16 convex convex ADJ hjic-493 145 17 domain domain NOUN hjic-493 145 18 given give VERB hjic-493 145 19 by by ADP hjic-493 145 20 its its PRON hjic-493 145 21 extremal extremal ADJ hjic-493 145 22 matrices matrix NOUN hjic-493 145 23 admits admit VERB hjic-493 145 24 a a DET hjic-493 145 25 weakly weakly ADJ hjic-493 145 26 reversible reversible ADJ hjic-493 145 27 realization realization NOUN hjic-493 145 28 . . PUNCT hjic-493 146 1 an an DET hjic-493 146 2 lp lp ADV hjic-493 146 3 - - PUNCT hjic-493 146 4 based base VERB hjic-493 146 5 feedback feedback NOUN hjic-493 146 6 design design NOUN hjic-493 146 7 method method NOUN hjic-493 146 8 is be AUX hjic-493 146 9 also also ADV hjic-493 146 10 proposed propose VERB hjic-493 146 11 that that SCONJ hjic-493 146 12 guarantees guarantee VERB hjic-493 146 13 stability stability NOUN hjic-493 146 14 with with ADP hjic-493 146 15 a a DET hjic-493 146 16 desired desire VERB hjic-493 146 17 equilibrium equilibrium NOUN hjic-493 146 18 point point NOUN hjic-493 146 19 . . PUNCT hjic-493 147 1 the the DET hjic-493 147 2 proposed propose VERB hjic-493 147 3 methods method NOUN hjic-493 147 4 are be AUX hjic-493 147 5 illustrated illustrate VERB hjic-493 147 6 with with ADP hjic-493 147 7 simple simple ADJ hjic-493 147 8 examples example NOUN hjic-493 147 9 . . PUNCT hjic-493 148 1 references reference NOUN hjic-493 148 2 [ [ X hjic-493 148 3 1 1 X hjic-493 148 4 ] ] PUNCT hjic-493 148 5 siljak siljak PROPN hjic-493 148 6 d. d. PROPN hjic-493 148 7 : : PUNCT hjic-493 148 8 parameter parameter NOUN hjic-493 148 9 space space NOUN hjic-493 148 10 methods method NOUN hjic-493 148 11 for for ADP hjic-493 148 12 robust robust ADJ hjic-493 148 13 control control NOUN hjic-493 148 14 design design NOUN hjic-493 148 15 : : PUNCT hjic-493 148 16 a a DET hjic-493 148 17 guided guide VERB hjic-493 148 18 tour tour NOUN hjic-493 148 19 , , PUNCT hjic-493 148 20 aut aut PROPN hjic-493 148 21 . . PUNCT hjic-493 148 22 contr contr PROPN hjic-493 148 23 . . PROPN hjic-493 148 24 , , PUNCT hjic-493 148 25 ieee ieee NOUN hjic-493 148 26 transactions transaction NOUN hjic-493 148 27 on on ADP hjic-493 148 28 , , PUNCT hjic-493 148 29 1989 1989 NUM hjic-493 148 30 , , PUNCT hjic-493 148 31 34(7 34(7 NUM hjic-493 148 32 ) ) PUNCT hjic-493 148 33 , , PUNCT hjic-493 149 1 674–688 674–688 NUM hjic-493 149 2 [ [ X hjic-493 149 3 2 2 X hjic-493 149 4 ] ] PUNCT hjic-493 149 5 angeli angeli PROPN hjic-493 149 6 d. d. PROPN hjic-493 149 7 : : PUNCT hjic-493 149 8 a a DET hjic-493 149 9 tutorial tutorial NOUN hjic-493 149 10 on on ADP hjic-493 149 11 chemical chemical ADJ hjic-493 149 12 network network NOUN hjic-493 149 13 dynamics dynamic NOUN hjic-493 149 14 , , PUNCT hjic-493 149 15 eur eur PROPN hjic-493 149 16 . . PUNCT hjic-493 150 1 j. j. PROPN hjic-493 150 2 contr contr PROPN hjic-493 150 3 . . PROPN hjic-493 150 4 , , PUNCT hjic-493 150 5 2009 2009 NUM hjic-493 150 6 , , PUNCT hjic-493 150 7 15 15 NUM hjic-493 150 8 , , PUNCT hjic-493 150 9 398–406 398–406 NUM hjic-493 150 10 [ [ X hjic-493 150 11 3 3 NUM hjic-493 150 12 ] ] PUNCT hjic-493 150 13 szederkényi szederkényi PROPN hjic-493 150 14 g. g. PROPN hjic-493 150 15 , , PUNCT hjic-493 150 16 hangos hangos PROPN hjic-493 150 17 k. k. PROPN hjic-493 150 18 m. m. PROPN hjic-493 150 19 , , PUNCT hjic-493 150 20 tuza tuza PROPN hjic-493 150 21 z. z. PROPN hjic-493 150 22 : : PUNCT hjic-493 150 23 finding find VERB hjic-493 150 24 weakly weakly ADJ hjic-493 150 25 reversible reversible ADJ hjic-493 150 26 realizations realization NOUN hjic-493 150 27 of of ADP hjic-493 150 28 chemical chemical ADJ hjic-493 150 29 reaction reaction NOUN hjic-493 150 30 networks network NOUN hjic-493 150 31 using use VERB hjic-493 150 32 optimization optimization NOUN hjic-493 150 33 , , PUNCT hjic-493 150 34 match match NOUN hjic-493 150 35 commun commun PROPN hjic-493 150 36 . . PUNCT hjic-493 151 1 math math PROPN hjic-493 151 2 . . PUNCT hjic-493 152 1 comp comp PROPN hjic-493 152 2 . . PUNCT hjic-493 153 1 chem chem PROPN hjic-493 153 2 . . PUNCT hjic-493 153 3 , , PUNCT hjic-493 153 4 2012 2012 NUM hjic-493 153 5 , , PUNCT hjic-493 153 6 67 67 NUM hjic-493 153 7 , , PUNCT hjic-493 153 8 193–212 193–212 NUM hjic-493 153 9 [ [ SYM hjic-493 153 10 4 4 NUM hjic-493 153 11 ] ] X hjic-493 153 12 feinberg feinberg PROPN hjic-493 153 13 m. m. PROPN hjic-493 153 14 , , PUNCT hjic-493 153 15 horn horn PROPN hjic-493 153 16 f. f. PROPN hjic-493 153 17 : : PUNCT hjic-493 153 18 chemical chemical ADJ hjic-493 153 19 mechanism mechanism NOUN hjic-493 153 20 structure structure NOUN hjic-493 153 21 and and CCONJ hjic-493 153 22 the the DET hjic-493 153 23 coincidence coincidence NOUN hjic-493 153 24 of of ADP hjic-493 153 25 the the DET hjic-493 153 26 stoichiometric stoichiometric ADJ hjic-493 153 27 and and CCONJ hjic-493 153 28 kinetic kinetic ADJ hjic-493 153 29 subspaces subspace NOUN hjic-493 153 30 , , PUNCT hjic-493 153 31 arch arch NOUN hjic-493 153 32 . . PUNCT hjic-493 154 1 rational rational ADJ hjic-493 154 2 mechanics mechanic NOUN hjic-493 154 3 and and CCONJ hjic-493 154 4 analysis analysis NOUN hjic-493 154 5 , , PUNCT hjic-493 154 6 1977 1977 NUM hjic-493 154 7 , , PUNCT hjic-493 154 8 66(1 66(1 NOUN hjic-493 154 9 ) ) PUNCT hjic-493 154 10 , , PUNCT hjic-493 154 11 83–97 83–97 NUM hjic-493 154 12 [ [ X hjic-493 154 13 5 5 NUM hjic-493 154 14 ] ] PUNCT hjic-493 154 15 rudan rudan PROPN hjic-493 154 16 j. j. PROPN hjic-493 154 17 , , PUNCT hjic-493 154 18 szederkényi szederkényi PROPN hjic-493 154 19 g. g. PROPN hjic-493 154 20 , , PUNCT hjic-493 154 21 hangos hangos PROPN hjic-493 154 22 k.m k.m PROPN hjic-493 154 23 . . PROPN hjic-493 154 24 , , PUNCT hjic-493 154 25 péni péni PROPN hjic-493 154 26 t. t. PROPN hjic-493 154 27 : : PUNCT hjic-493 154 28 polynomial polynomial ADJ hjic-493 154 29 time time NOUN hjic-493 154 30 algorithms algorithm NOUN hjic-493 154 31 to to PART hjic-493 154 32 determine determine VERB hjic-493 154 33 weakly weakly ADJ hjic-493 154 34 reversible reversible ADJ hjic-493 154 35 realizations realization NOUN hjic-493 154 36 of of ADP hjic-493 154 37 chemical chemical ADJ hjic-493 154 38 reaction reaction NOUN hjic-493 154 39 networks network NOUN hjic-493 154 40 , , PUNCT hjic-493 154 41 j. j. PROPN hjic-493 154 42 math math PROPN hjic-493 154 43 . . PUNCT hjic-493 155 1 chem chem PROPN hjic-493 155 2 . . PUNCT hjic-493 155 3 , , PUNCT hjic-493 155 4 2014 2014 NUM hjic-493 155 5 , , PUNCT hjic-493 155 6 52(5 52(5 NUM hjic-493 155 7 ) ) PUNCT hjic-493 155 8 , , PUNCT hjic-493 155 9 1386–1404 1386–1404 NUM hjic-493 155 10 [ [ X hjic-493 155 11 6 6 NUM hjic-493 155 12 ] ] PUNCT hjic-493 155 13 lipták lipták ADJ hjic-493 155 14 g. g. PROPN hjic-493 155 15 , , PUNCT hjic-493 155 16 szederkényi szederkényi PROPN hjic-493 155 17 g. g. PROPN hjic-493 155 18 , , PUNCT hjic-493 155 19 hangos hangos PROPN hjic-493 155 20 k.m k.m PROPN hjic-493 155 21 . . PROPN hjic-493 155 22 : : PUNCT hjic-493 156 1 kinetic kinetic ADJ hjic-493 156 2 feedback feedback NOUN hjic-493 156 3 computation computation NOUN hjic-493 156 4 for for ADP hjic-493 156 5 polynomial polynomial ADJ hjic-493 156 6 systems system NOUN hjic-493 156 7 to to PART hjic-493 156 8 achieve achieve VERB hjic-493 156 9 weak weak ADJ hjic-493 156 10 reversibility reversibility NOUN hjic-493 156 11 and and CCONJ hjic-493 156 12 minimal minimal ADJ hjic-493 156 13 deficiency deficiency NOUN hjic-493 156 14 , , PUNCT hjic-493 156 15 13th 13th ADJ hjic-493 156 16 eur eur ADJ hjic-493 156 17 . . PUNCT hjic-493 157 1 control control PROPN hjic-493 157 2 conf conf PROPN hjic-493 157 3 . . PUNCT hjic-493 158 1 ecc ecc PROPN hjic-493 158 2 , , PUNCT hjic-493 158 3 strasbourg strasbourg PROPN hjic-493 158 4 , , PUNCT hjic-493 158 5 france france PROPN hjic-493 158 6 , , PUNCT hjic-493 158 7 2014 2014 NUM hjic-493 158 8 , , PUNCT hjic-493 158 9 2691–2696 2691–2696 NUM hjic-493 158 10 [ [ X hjic-493 158 11 7 7 NUM hjic-493 158 12 ] ] X hjic-493 158 13 angeli angeli PROPN hjic-493 158 14 d. d. PROPN hjic-493 158 15 , , PUNCT hjic-493 158 16 lenhee lenhee PROPN hjic-493 158 17 , , PUNCT hjic-493 158 18 p.d p.d PROPN hjic-493 158 19 . . PROPN hjic-493 158 20 , , PUNCT hjic-493 158 21 sontag sontag PROPN hjic-493 158 22 e.d e.d PROPN hjic-493 158 23 . . PROPN hjic-493 158 24 : : PUNCT hjic-493 158 25 on on ADP hjic-493 158 26 the the DET hjic-493 158 27 structural structural ADJ hjic-493 158 28 monotonicity monotonicity NOUN hjic-493 158 29 of of ADP hjic-493 158 30 chemical chemical ADJ hjic-493 158 31 reaction reaction NOUN hjic-493 158 32 networks network NOUN hjic-493 158 33 , , PUNCT hjic-493 158 34 proc proc NOUN hjic-493 158 35 . . PUNCT hjic-493 159 1 45th 45th ADJ hjic-493 159 2 ieee ieee NOUN hjic-493 159 3 conf conf NOUN hjic-493 159 4 . . PUNCT hjic-493 160 1 decision decision NOUN hjic-493 160 2 and and CCONJ hjic-493 160 3 control control NOUN hjic-493 160 4 , , PUNCT hjic-493 160 5 2006 2006 NUM hjic-493 160 6 , , PUNCT hjic-493 160 7 7–12 7–12 PROPN