id	sid	tid	token	lemma	pos
hjic-704	1	1	microsoft	microsoft	PROPN
hjic-704	1	2	word	word	NOUN
hjic-704	1	3	16.14	16.14	NUM
hjic-704	1	4	polcz.docx	polcz.docx	NOUN
hjic-704	1	5	hungarian	hungarian	ADJ
hjic-704	1	6	journal	journal	NOUN
hjic-704	1	7	of	of	ADP
hjic-704	1	8	industry	industry	NOUN
hjic-704	1	9	and	and	CCONJ
hjic-704	1	10	chemistry	chemistry	NOUN
hjic-704	1	11	vol	vol	NOUN
hjic-704	1	12	.	.	PUNCT
hjic-704	2	1	44(2	44(2	NOUN
hjic-704	2	2	)	)	PUNCT
hjic-704	3	1	pp	pp	ADP
hjic-704	3	2	.	.	PUNCT
hjic-704	4	1	113–120	113–120	NUM
hjic-704	4	2	(	(	PUNCT
hjic-704	4	3	2016	2016	NUM
hjic-704	4	4	)	)	PUNCT
hjic-704	4	5	hjic.mk.uni-pannon.hu	hjic.mk.uni-pannon.hu	PROPN
hjic-704	4	6	doi	doi	PROPN
hjic-704	4	7	:	:	PUNCT
hjic-704	4	8	10.1515	10.1515	NUM
hjic-704	4	9	/	/	SYM
hjic-704	4	10	hjic-2016	hjic-2016	NOUN
hjic-704	4	11	-	-	PUNCT
hjic-704	4	12	0014	0014	NUM
hjic-704	4	13	computational	computational	ADJ
hjic-704	4	14	stability	stability	NOUN
hjic-704	4	15	analysis	analysis	NOUN
hjic-704	4	16	of	of	ADP
hjic-704	4	17	lotka	lotka	PROPN
hjic-704	4	18	-	-	PUNCT
hjic-704	4	19	volterra	volterra	PROPN
hjic-704	4	20	systems	system	NOUN
hjic-704	4	21	péter	péter	NOUN
hjic-704	4	22	polcz1,∗	polcz1,∗	NOUN
hjic-704	4	23	and	and	CCONJ
hjic-704	4	24	gábor	gábor	NOUN
hjic-704	4	25	szederkényi1,2	szederkényi1,2	PROPN
hjic-704	4	26	1	1	NUM
hjic-704	4	27	faculty	faculty	NOUN
hjic-704	4	28	of	of	ADP
hjic-704	4	29	information	information	NOUN
hjic-704	4	30	technology	technology	NOUN
hjic-704	4	31	and	and	CCONJ
hjic-704	4	32	bionics	bionic	NOUN
hjic-704	4	33	,	,	PUNCT
hjic-704	4	34	pázmány	pázmány	PROPN
hjic-704	4	35	péter	péter	PROPN
hjic-704	4	36	catholic	catholic	PROPN
hjic-704	4	37	university	university	PROPN
hjic-704	4	38	,	,	PUNCT
hjic-704	4	39	práter	práter	NOUN
hjic-704	4	40	u.	u.	PROPN
hjic-704	4	41	50	50	NUM
hjic-704	4	42	/	/	SYM
hjic-704	4	43	a	a	PRON
hjic-704	4	44	,	,	PUNCT
hjic-704	4	45	budapest	budapest	ADJ
hjic-704	4	46	,	,	PUNCT
hjic-704	4	47	1083	1083	NUM
hjic-704	4	48	,	,	PUNCT
hjic-704	4	49	hungary	hungary	NOUN
hjic-704	4	50	2	2	NUM
hjic-704	4	51	systems	system	NOUN
hjic-704	4	52	and	and	CCONJ
hjic-704	4	53	control	control	NOUN
hjic-704	4	54	lab	lab	PROPN
hjic-704	4	55	,	,	PUNCT
hjic-704	4	56	institute	institute	NOUN
hjic-704	4	57	for	for	ADP
hjic-704	4	58	computer	computer	NOUN
hjic-704	4	59	science	science	NOUN
hjic-704	4	60	and	and	CCONJ
hjic-704	4	61	control	control	NOUN
hjic-704	4	62	,	,	PUNCT
hjic-704	4	63	hungarian	hungarian	ADJ
hjic-704	4	64	academy	academy	NOUN
hjic-704	4	65	of	of	ADP
hjic-704	4	66	sciences	sciences	PROPN
hjic-704	4	67	,	,	PUNCT
hjic-704	4	68	práter	práter	NOUN
hjic-704	4	69	u.	u.	PROPN
hjic-704	4	70	50	50	NUM
hjic-704	4	71	/	/	SYM
hjic-704	4	72	a.	a.	NOUN
hjic-704	4	73	,	,	PUNCT
hjic-704	4	74	budapest	budapest	NOUN
hjic-704	4	75	,	,	PUNCT
hjic-704	4	76	1083	1083	NUM
hjic-704	4	77	,	,	PUNCT
hjic-704	4	78	hungary	hungary	VERB
hjic-704	4	79	this	this	DET
hjic-704	4	80	paper	paper	NOUN
hjic-704	4	81	concerns	concern	VERB
hjic-704	4	82	the	the	DET
hjic-704	4	83	computational	computational	ADJ
hjic-704	4	84	stability	stability	NOUN
hjic-704	4	85	analysis	analysis	NOUN
hjic-704	4	86	of	of	ADP
hjic-704	4	87	locally	locally	ADV
hjic-704	4	88	stable	stable	ADJ
hjic-704	4	89	lotka	lotka	PROPN
hjic-704	4	90	-	-	PUNCT
hjic-704	4	91	volterra	volterra	PROPN
hjic-704	4	92	(	(	PUNCT
hjic-704	4	93	lv	lv	PROPN
hjic-704	4	94	)	)	PUNCT
hjic-704	4	95	systems	system	NOUN
hjic-704	4	96	by	by	ADP
hjic-704	4	97	searching	search	VERB
hjic-704	4	98	for	for	ADP
hjic-704	4	99	appropriate	appropriate	ADJ
hjic-704	4	100	lyapunov	lyapunov	ADJ
hjic-704	4	101	functions	function	NOUN
hjic-704	4	102	in	in	ADP
hjic-704	4	103	a	a	DET
hjic-704	4	104	general	general	ADJ
hjic-704	4	105	quadratic	quadratic	ADJ
hjic-704	4	106	form	form	NOUN
hjic-704	4	107	composed	compose	VERB
hjic-704	4	108	of	of	ADP
hjic-704	4	109	higher	high	ADJ
hjic-704	4	110	order	order	NOUN
hjic-704	4	111	monomial	monomial	ADJ
hjic-704	4	112	terms	term	NOUN
hjic-704	4	113	.	.	PUNCT
hjic-704	5	1	the	the	DET
hjic-704	5	2	lyapunov	lyapunov	ADJ
hjic-704	5	3	conditions	condition	NOUN
hjic-704	5	4	are	be	AUX
hjic-704	5	5	ensured	ensure	VERB
hjic-704	5	6	through	through	ADP
hjic-704	5	7	the	the	DET
hjic-704	5	8	solution	solution	NOUN
hjic-704	5	9	of	of	ADP
hjic-704	5	10	linear	linear	ADJ
hjic-704	5	11	matrix	matrix	NOUN
hjic-704	5	12	inequalities	inequality	NOUN
hjic-704	5	13	.	.	PUNCT
hjic-704	6	1	the	the	DET
hjic-704	6	2	stability	stability	NOUN
hjic-704	6	3	region	region	NOUN
hjic-704	6	4	is	be	AUX
hjic-704	6	5	estimated	estimate	VERB
hjic-704	6	6	by	by	ADP
hjic-704	6	7	determining	determine	VERB
hjic-704	6	8	the	the	DET
hjic-704	6	9	level	level	NOUN
hjic-704	6	10	set	set	NOUN
hjic-704	6	11	of	of	ADP
hjic-704	6	12	the	the	DET
hjic-704	6	13	lyapunov	lyapunov	ADJ
hjic-704	6	14	function	function	NOUN
hjic-704	6	15	within	within	ADP
hjic-704	6	16	a	a	DET
hjic-704	6	17	suitable	suitable	ADJ
hjic-704	6	18	convex	convex	NOUN
hjic-704	6	19	domain	domain	NOUN
hjic-704	6	20	.	.	PUNCT
hjic-704	7	1	the	the	DET
hjic-704	7	2	paper	paper	NOUN
hjic-704	7	3	includes	include	VERB
hjic-704	7	4	interesting	interesting	ADJ
hjic-704	7	5	computational	computational	ADJ
hjic-704	7	6	results	result	NOUN
hjic-704	7	7	and	and	CCONJ
hjic-704	7	8	discussion	discussion	NOUN
hjic-704	7	9	on	on	ADP
hjic-704	7	10	the	the	DET
hjic-704	7	11	stability	stability	NOUN
hjic-704	7	12	regions	region	NOUN
hjic-704	7	13	of	of	ADP
hjic-704	7	14	higher	high	ADJ
hjic-704	7	15	(	(	PUNCT
hjic-704	7	16	3,4	3,4	NUM
hjic-704	7	17	)	)	PUNCT
hjic-704	7	18	dimensional	dimensional	ADJ
hjic-704	7	19	lv	lv	PROPN
hjic-704	7	20	models	model	NOUN
hjic-704	7	21	as	as	ADV
hjic-704	7	22	well	well	ADV
hjic-704	7	23	as	as	ADP
hjic-704	7	24	on	on	ADP
hjic-704	7	25	the	the	DET
hjic-704	7	26	monomial	monomial	ADJ
hjic-704	7	27	selection	selection	NOUN
hjic-704	7	28	for	for	ADP
hjic-704	7	29	constructing	construct	VERB
hjic-704	7	30	the	the	DET
hjic-704	7	31	lyapunov	lyapunov	ADJ
hjic-704	7	32	functions	function	NOUN
hjic-704	7	33	.	.	PUNCT
hjic-704	8	1	finally	finally	ADV
hjic-704	8	2	,	,	PUNCT
hjic-704	8	3	the	the	DET
hjic-704	8	4	stability	stability	NOUN
hjic-704	8	5	region	region	NOUN
hjic-704	8	6	is	be	AUX
hjic-704	8	7	estimated	estimate	VERB
hjic-704	8	8	of	of	ADP
hjic-704	8	9	an	an	DET
hjic-704	8	10	uncertain	uncertain	ADJ
hjic-704	8	11	2d	2d	NUM
hjic-704	8	12	lv	lv	PROPN
hjic-704	8	13	system	system	NOUN
hjic-704	8	14	with	with	ADP
hjic-704	8	15	an	an	DET
hjic-704	8	16	uncertain	uncertain	ADJ
hjic-704	8	17	interior	interior	ADJ
hjic-704	8	18	locally	locally	ADV
hjic-704	8	19	stable	stable	ADJ
hjic-704	8	20	equilibrium	equilibrium	NOUN
hjic-704	8	21	point	point	NOUN
hjic-704	8	22	.	.	PUNCT
hjic-704	9	1	keywords	keyword	NOUN
hjic-704	9	2	:	:	PUNCT
hjic-704	9	3	nonlinear	nonlinear	ADJ
hjic-704	9	4	systems	system	NOUN
hjic-704	9	5	,	,	PUNCT
hjic-704	9	6	lotka	lotka	PROPN
hjic-704	9	7	-	-	PUNCT
hjic-704	9	8	volterra	volterra	PROPN
hjic-704	9	9	models	model	NOUN
hjic-704	9	10	,	,	PUNCT
hjic-704	9	11	stability	stability	NOUN
hjic-704	9	12	analysis	analysis	NOUN
hjic-704	9	13	,	,	PUNCT
hjic-704	9	14	linear	linear	ADJ
hjic-704	9	15	matrix	matrix	NOUN
hjic-704	9	16	inequalities	inequality	NOUN
hjic-704	9	17	,	,	PUNCT
hjic-704	9	18	lyapunov	lyapunov	NOUN
hjic-704	9	19	function	function	VERB
hjic-704	9	20	1	1	NUM
hjic-704	9	21	.	.	PUNCT
hjic-704	10	1	introduction	introduction	NOUN
hjic-704	10	2	approximating	approximate	VERB
hjic-704	10	3	the	the	DET
hjic-704	10	4	domain	domain	NOUN
hjic-704	10	5	of	of	ADP
hjic-704	10	6	attraction	attraction	NOUN
hjic-704	10	7	(	(	PUNCT
hjic-704	10	8	doa	doa	NOUN
hjic-704	10	9	)	)	PUNCT
hjic-704	10	10	is	be	AUX
hjic-704	10	11	often	often	ADV
hjic-704	10	12	a	a	DET
hjic-704	10	13	fundamental	fundamental	ADJ
hjic-704	10	14	task	task	NOUN
hjic-704	10	15	in	in	ADP
hjic-704	10	16	the	the	DET
hjic-704	10	17	analysis	analysis	NOUN
hjic-704	10	18	and	and	CCONJ
hjic-704	10	19	control	control	NOUN
hjic-704	10	20	of	of	ADP
hjic-704	10	21	nonlinear	nonlinear	ADJ
hjic-704	10	22	systems	system	NOUN
hjic-704	10	23	.	.	PUNCT
hjic-704	11	1	the	the	DET
hjic-704	11	2	stability	stability	NOUN
hjic-704	11	3	properties	property	NOUN
hjic-704	11	4	of	of	ADP
hjic-704	11	5	dynamical	dynamical	ADJ
hjic-704	11	6	systems	system	NOUN
hjic-704	11	7	are	be	AUX
hjic-704	11	8	most	most	ADV
hjic-704	11	9	often	often	ADV
hjic-704	11	10	studied	study	VERB
hjic-704	11	11	using	use	VERB
hjic-704	11	12	lyapunov	lyapunov	ADJ
hjic-704	11	13	functions	function	NOUN
hjic-704	11	14	.	.	PUNCT
hjic-704	12	1	therefore	therefore	ADV
hjic-704	12	2	,	,	PUNCT
hjic-704	12	3	extensive	extensive	ADJ
hjic-704	12	4	literature	literature	NOUN
hjic-704	12	5	exists	exist	VERB
hjic-704	12	6	on	on	ADP
hjic-704	12	7	the	the	DET
hjic-704	12	8	computational	computational	ADJ
hjic-704	12	9	construction	construction	NOUN
hjic-704	12	10	of	of	ADP
hjic-704	12	11	lyapunov	lyapunov	ADJ
hjic-704	12	12	functions	function	NOUN
hjic-704	12	13	[	[	X
hjic-704	12	14	1	1	NUM
hjic-704	12	15	]	]	PUNCT
hjic-704	12	16	.	.	PUNCT
hjic-704	13	1	due	due	ADP
hjic-704	13	2	to	to	ADP
hjic-704	13	3	their	their	PRON
hjic-704	13	4	advantageous	advantageous	ADJ
hjic-704	13	5	properties	property	NOUN
hjic-704	13	6	and	and	CCONJ
hjic-704	13	7	the	the	DET
hjic-704	13	8	availability	availability	NOUN
hjic-704	13	9	of	of	ADP
hjic-704	13	10	efficient	efficient	ADJ
hjic-704	13	11	numerical	numerical	ADJ
hjic-704	13	12	solvers	solver	NOUN
hjic-704	13	13	,	,	PUNCT
hjic-704	13	14	the	the	DET
hjic-704	13	15	use	use	NOUN
hjic-704	13	16	of	of	ADP
hjic-704	13	17	linear	linear	ADJ
hjic-704	13	18	matrix	matrix	NOUN
hjic-704	13	19	inequalities	inequality	NOUN
hjic-704	13	20	(	(	PUNCT
hjic-704	13	21	lmi	lmi	PROPN
hjic-704	13	22	)	)	PUNCT
hjic-704	13	23	and	and	CCONJ
hjic-704	13	24	semi	semi	ADJ
hjic-704	13	25	-	-	ADJ
hjic-704	13	26	definite	definite	ADJ
hjic-704	13	27	programming	programming	NOUN
hjic-704	13	28	(	(	PUNCT
hjic-704	13	29	sdp	sdp	NOUN
hjic-704	13	30	)	)	PUNCT
hjic-704	13	31	techniques	technique	NOUN
hjic-704	13	32	has	have	AUX
hjic-704	13	33	become	become	VERB
hjic-704	13	34	popular	popular	ADJ
hjic-704	13	35	in	in	ADP
hjic-704	13	36	the	the	DET
hjic-704	13	37	field	field	NOUN
hjic-704	13	38	of	of	ADP
hjic-704	13	39	system	system	NOUN
hjic-704	13	40	and	and	CCONJ
hjic-704	13	41	control	control	NOUN
hjic-704	13	42	theory	theory	NOUN
hjic-704	13	43	.	.	PUNCT
hjic-704	14	1	important	important	ADJ
hjic-704	14	2	results	result	NOUN
hjic-704	14	3	were	be	AUX
hjic-704	14	4	announced	announce	VERB
hjic-704	14	5	[	[	PUNCT
hjic-704	14	6	2,3	2,3	NUM
hjic-704	14	7	]	]	PUNCT
hjic-704	14	8	in	in	ADP
hjic-704	14	9	the	the	DET
hjic-704	14	10	context	context	NOUN
hjic-704	14	11	of	of	ADP
hjic-704	14	12	linear	linear	ADJ
hjic-704	14	13	uncertain	uncertain	ADJ
hjic-704	14	14	systems	system	NOUN
hjic-704	14	15	,	,	PUNCT
hjic-704	14	16	their	their	PRON
hjic-704	14	17	stability	stability	NOUN
hjic-704	14	18	analysis	analysis	NOUN
hjic-704	14	19	and	and	CCONJ
hjic-704	14	20	control	control	NOUN
hjic-704	14	21	synthesis	synthesis	NOUN
hjic-704	14	22	.	.	PUNCT
hjic-704	15	1	recently	recently	ADV
hjic-704	15	2	,	,	PUNCT
hjic-704	15	3	an	an	DET
hjic-704	15	4	optimization	optimization	NOUN
hjic-704	15	5	-	-	PUNCT
hjic-704	15	6	based	base	VERB
hjic-704	15	7	method	method	NOUN
hjic-704	15	8	for	for	ADP
hjic-704	15	9	doa	doa	PROPN
hjic-704	15	10	estimation	estimation	NOUN
hjic-704	15	11	was	be	AUX
hjic-704	15	12	published	publish	VERB
hjic-704	15	13	[	[	PUNCT
hjic-704	15	14	4	4	NUM
hjic-704	15	15	]	]	PUNCT
hjic-704	15	16	,	,	PUNCT
hjic-704	15	17	where	where	SCONJ
hjic-704	15	18	the	the	DET
hjic-704	15	19	authors	author	NOUN
hjic-704	15	20	use	use	VERB
hjic-704	15	21	finsler	finsler	NOUN
hjic-704	15	22	’s	’s	PART
hjic-704	15	23	lemma	lemma	PROPN
hjic-704	15	24	and	and	CCONJ
hjic-704	15	25	affine	affine	VERB
hjic-704	15	26	parameter	parameter	NOUN
hjic-704	15	27	-	-	PUNCT
hjic-704	15	28	dependent	dependent	ADJ
hjic-704	15	29	lmis	lmis	ADV
hjic-704	15	30	to	to	PART
hjic-704	15	31	compute	compute	VERB
hjic-704	15	32	rational	rational	ADJ
hjic-704	15	33	lyapunov	lyapunov	ADJ
hjic-704	15	34	functions	function	NOUN
hjic-704	15	35	for	for	ADP
hjic-704	15	36	a	a	DET
hjic-704	15	37	wide	wide	ADJ
hjic-704	15	38	class	class	NOUN
hjic-704	15	39	of	of	ADP
hjic-704	15	40	locally	locally	ADV
hjic-704	15	41	asymptotically	asymptotically	ADV
hjic-704	15	42	stable	stable	ADJ
hjic-704	15	43	nonlinear	nonlinear	ADJ
hjic-704	15	44	systems	system	NOUN
hjic-704	15	45	.	.	PUNCT
hjic-704	16	1	based	base	VERB
hjic-704	16	2	on	on	ADP
hjic-704	16	3	these	these	DET
hjic-704	16	4	results	result	NOUN
hjic-704	16	5	an	an	DET
hjic-704	16	6	improved	improved	ADJ
hjic-704	16	7	method	method	NOUN
hjic-704	16	8	was	be	AUX
hjic-704	16	9	published	publish	VERB
hjic-704	16	10	[	[	PUNCT
hjic-704	16	11	5,6	5,6	NUM
hjic-704	16	12	]	]	PUNCT
hjic-704	16	13	,	,	PUNCT
hjic-704	16	14	where	where	SCONJ
hjic-704	16	15	the	the	DET
hjic-704	16	16	transformation	transformation	NOUN
hjic-704	16	17	of	of	ADP
hjic-704	16	18	the	the	DET
hjic-704	16	19	model	model	NOUN
hjic-704	16	20	to	to	ADP
hjic-704	16	21	the	the	DET
hjic-704	16	22	form	form	NOUN
hjic-704	16	23	required	require	VERB
hjic-704	16	24	for	for	ADP
hjic-704	16	25	optimization	optimization	NOUN
hjic-704	16	26	is	be	AUX
hjic-704	16	27	done	do	VERB
hjic-704	16	28	automatically	automatically	ADV
hjic-704	16	29	using	use	VERB
hjic-704	16	30	the	the	DET
hjic-704	16	31	linear	linear	ADJ
hjic-704	16	32	fraction	fraction	NOUN
hjic-704	16	33	transformation	transformation	NOUN
hjic-704	16	34	(	(	PUNCT
hjic-704	16	35	lft	lft	X
hjic-704	16	36	)	)	PUNCT
hjic-704	16	37	and	and	CCONJ
hjic-704	16	38	further	further	ADJ
hjic-704	16	39	automatic	automatic	ADJ
hjic-704	16	40	model	model	NOUN
hjic-704	16	41	simplification	simplification	NOUN
hjic-704	16	42	steps	step	NOUN
hjic-704	16	43	,	,	PUNCT
hjic-704	16	44	which	which	PRON
hjic-704	16	45	results	result	VERB
hjic-704	16	46	in	in	ADP
hjic-704	16	47	the	the	DET
hjic-704	16	48	dimension	dimension	NOUN
hjic-704	16	49	reduction	reduction	NOUN
hjic-704	16	50	of	of	ADP
hjic-704	16	51	the	the	DET
hjic-704	16	52	optimization	optimization	NOUN
hjic-704	16	53	task	task	NOUN
hjic-704	16	54	.	.	PUNCT
hjic-704	17	1	as	as	SCONJ
hjic-704	17	2	the	the	DET
hjic-704	17	3	dimensions	dimension	NOUN
hjic-704	17	4	of	of	ADP
hjic-704	17	5	the	the	DET
hjic-704	17	6	problem	problem	NOUN
hjic-704	17	7	are	be	AUX
hjic-704	17	8	*	*	PUNCT
hjic-704	17	9	correspondence	correspondence	NOUN
hjic-704	17	10	:	:	PUNCT
hjic-704	18	1	ppolcz@gmail.com	ppolcz@gmail.com	X
hjic-704	18	2	reduced	reduce	VERB
hjic-704	18	3	,	,	PUNCT
hjic-704	18	4	the	the	DET
hjic-704	18	5	method	method	NOUN
hjic-704	18	6	is	be	AUX
hjic-704	18	7	capable	capable	ADJ
hjic-704	18	8	of	of	ADP
hjic-704	18	9	handling	handle	VERB
hjic-704	18	10	more	more	ADJ
hjic-704	18	11	complex	complex	ADJ
hjic-704	18	12	models	model	NOUN
hjic-704	18	13	.	.	PUNCT
hjic-704	19	1	for	for	ADP
hjic-704	19	2	example	example	NOUN
hjic-704	19	3	,	,	PUNCT
hjic-704	19	4	the	the	DET
hjic-704	19	5	doa	doa	NOUN
hjic-704	19	6	is	be	AUX
hjic-704	19	7	successfully	successfully	ADV
hjic-704	19	8	estimated	estimate	VERB
hjic-704	19	9	for	for	ADP
hjic-704	19	10	a	a	DET
hjic-704	19	11	3	3	NUM
hjic-704	19	12	-	-	PUNCT
hjic-704	19	13	dimensional	dimensional	ADJ
hjic-704	19	14	rational	rational	ADJ
hjic-704	19	15	uncertain	uncertain	ADJ
hjic-704	19	16	system	system	NOUN
hjic-704	19	17	[	[	X
hjic-704	19	18	6	6	NUM
hjic-704	19	19	]	]	PUNCT
hjic-704	19	20	(	(	PUNCT
hjic-704	19	21	bioreactor	bioreactor	NOUN
hjic-704	19	22	model	model	NOUN
hjic-704	19	23	with	with	ADP
hjic-704	19	24	an	an	DET
hjic-704	19	25	applied	applied	ADJ
hjic-704	19	26	proportional	proportional	ADJ
hjic-704	19	27	and	and	CCONJ
hjic-704	19	28	integral	integral	ADJ
hjic-704	19	29	substrate	substrate	NOUN
hjic-704	19	30	feedback	feedback	NOUN
hjic-704	19	31	law	law	NOUN
hjic-704	19	32	)	)	PUNCT
hjic-704	19	33	.	.	PUNCT
hjic-704	20	1	the	the	DET
hjic-704	20	2	dynamical	dynamical	ADJ
hjic-704	20	3	descriptive	descriptive	ADJ
hjic-704	20	4	power	power	NOUN
hjic-704	20	5	of	of	ADP
hjic-704	20	6	lotkavolterra	lotkavolterra	ADJ
hjic-704	20	7	systems	system	NOUN
hjic-704	20	8	is	be	AUX
hjic-704	20	9	so	so	ADV
hjic-704	20	10	extensive	extensive	ADJ
hjic-704	20	11	that	that	SCONJ
hjic-704	20	12	lv	lv	PROPN
hjic-704	20	13	models	model	NOUN
hjic-704	20	14	“	"	PUNCT
hjic-704	20	15	have	have	VERB
hjic-704	20	16	the	the	DET
hjic-704	20	17	status	status	NOUN
hjic-704	20	18	of	of	ADP
hjic-704	20	19	canonical	canonical	ADJ
hjic-704	20	20	format	format	NOUN
hjic-704	20	21	”	"	PUNCT
hjic-704	20	22	within	within	ADP
hjic-704	20	23	the	the	DET
hjic-704	20	24	class	class	NOUN
hjic-704	20	25	of	of	ADP
hjic-704	20	26	smooth	smooth	ADJ
hjic-704	20	27	nonlinear	nonlinear	ADJ
hjic-704	20	28	dynamical	dynamical	ADJ
hjic-704	20	29	systems	system	NOUN
hjic-704	20	30	[	[	X
hjic-704	20	31	7	7	NUM
hjic-704	20	32	]	]	PUNCT
hjic-704	20	33	.	.	PUNCT
hjic-704	21	1	besides	besides	SCONJ
hjic-704	21	2	modelling	model	VERB
hjic-704	21	3	biological	biological	ADJ
hjic-704	21	4	/	/	SYM
hjic-704	21	5	ecological	ecological	ADJ
hjic-704	21	6	environments	environment	NOUN
hjic-704	21	7	,	,	PUNCT
hjic-704	21	8	they	they	PRON
hjic-704	21	9	are	be	AUX
hjic-704	21	10	widely	widely	ADV
hjic-704	21	11	used	use	VERB
hjic-704	21	12	in	in	ADP
hjic-704	21	13	other	other	ADJ
hjic-704	21	14	scientific	scientific	ADJ
hjic-704	21	15	fields	field	NOUN
hjic-704	21	16	like	like	ADP
hjic-704	21	17	neural	neural	ADJ
hjic-704	21	18	networks	network	NOUN
hjic-704	21	19	[	[	X
hjic-704	21	20	8	8	NUM
hjic-704	21	21	]	]	PUNCT
hjic-704	21	22	or	or	CCONJ
hjic-704	21	23	in	in	ADP
hjic-704	21	24	economics	economic	NOUN
hjic-704	21	25	,	,	PUNCT
hjic-704	21	26	where	where	SCONJ
hjic-704	21	27	the	the	DET
hjic-704	21	28	goodwinlotka	goodwinlotka	PROPN
hjic-704	21	29	-	-	PUNCT
hjic-704	21	30	volterra	volterra	NOUN
hjic-704	21	31	models	model	NOUN
hjic-704	21	32	are	be	AUX
hjic-704	21	33	applied	apply	VERB
hjic-704	21	34	for	for	ADP
hjic-704	21	35	modelling	model	VERB
hjic-704	21	36	the	the	DET
hjic-704	21	37	predator	predator	NOUN
hjic-704	21	38	-	-	PUNCT
hjic-704	21	39	prey	prey	NOUN
hjic-704	21	40	mechanism	mechanism	NOUN
hjic-704	21	41	of	of	ADP
hjic-704	21	42	the	the	DET
hjic-704	21	43	technological	technological	ADJ
hjic-704	21	44	substitution	substitution	NOUN
hjic-704	21	45	[	[	X
hjic-704	21	46	9,10	9,10	NUM
hjic-704	21	47	]	]	PUNCT
hjic-704	21	48	.	.	PUNCT
hjic-704	22	1	in	in	ADP
hjic-704	22	2	order	order	NOUN
hjic-704	22	3	to	to	PART
hjic-704	22	4	model	model	VERB
hjic-704	22	5	the	the	DET
hjic-704	22	6	correlation	correlation	NOUN
hjic-704	22	7	between	between	ADP
hjic-704	22	8	the	the	DET
hjic-704	22	9	employment	employment	NOUN
hjic-704	22	10	rate	rate	NOUN
hjic-704	22	11	and	and	CCONJ
hjic-704	22	12	the	the	DET
hjic-704	22	13	share	share	NOUN
hjic-704	22	14	of	of	ADP
hjic-704	22	15	wages	wage	NOUN
hjic-704	22	16	of	of	ADP
hjic-704	22	17	the	the	DET
hjic-704	22	18	working	work	VERB
hjic-704	22	19	population	population	NOUN
hjic-704	22	20	,	,	PUNCT
hjic-704	22	21	the	the	DET
hjic-704	22	22	authors	author	NOUN
hjic-704	22	23	of	of	ADP
hjic-704	22	24	ref	ref	NOUN
hjic-704	22	25	.	.	PUNCT
hjic-704	23	1	[	[	X
hjic-704	23	2	11	11	NUM
hjic-704	23	3	]	]	PUNCT
hjic-704	23	4	used	use	VERB
hjic-704	23	5	a	a	DET
hjic-704	23	6	stochastic	stochastic	ADJ
hjic-704	23	7	extension	extension	NOUN
hjic-704	23	8	of	of	ADP
hjic-704	23	9	the	the	DET
hjic-704	23	10	goodwin	goodwin	PROPN
hjic-704	23	11	model	model	NOUN
hjic-704	23	12	.	.	PUNCT
hjic-704	24	1	some	some	DET
hjic-704	24	2	important	important	ADJ
hjic-704	24	3	results	result	NOUN
hjic-704	24	4	that	that	PRON
hjic-704	24	5	make	make	VERB
hjic-704	24	6	lv	lv	PROPN
hjic-704	24	7	models	model	NOUN
hjic-704	24	8	even	even	ADV
hjic-704	24	9	more	more	ADV
hjic-704	24	10	attractive	attractive	ADJ
hjic-704	24	11	are	be	AUX
hjic-704	24	12	the	the	DET
hjic-704	24	13	existing	exist	VERB
hjic-704	24	14	techniques	technique	NOUN
hjic-704	24	15	used	use	VERB
hjic-704	24	16	to	to	PART
hjic-704	24	17	represent	represent	VERB
hjic-704	24	18	a	a	DET
hjic-704	24	19	general	general	ADJ
hjic-704	24	20	nonlinear	nonlinear	ADJ
hjic-704	24	21	system	system	NOUN
hjic-704	24	22	as	as	ADP
hjic-704	24	23	a	a	DET
hjic-704	24	24	multidimensional	multidimensional	ADJ
hjic-704	24	25	lv	lv	PROPN
hjic-704	24	26	model	model	NOUN
hjic-704	24	27	[	[	X
hjic-704	24	28	12	12	NUM
hjic-704	24	29	]	]	PUNCT
hjic-704	24	30	.	.	PUNCT
hjic-704	25	1	the	the	DET
hjic-704	25	2	analysis	analysis	NOUN
hjic-704	25	3	of	of	ADP
hjic-704	25	4	stability	stability	NOUN
hjic-704	25	5	and	and	CCONJ
hjic-704	25	6	behaviour	behaviour	NOUN
hjic-704	25	7	of	of	ADP
hjic-704	25	8	lv	lv	PROPN
hjic-704	25	9	systems	system	NOUN
hjic-704	25	10	is	be	AUX
hjic-704	25	11	extensive	extensive	ADJ
hjic-704	25	12	in	in	ADP
hjic-704	25	13	the	the	DET
hjic-704	25	14	literature	literature	NOUN
hjic-704	25	15	[	[	X
hjic-704	25	16	13	13	NUM
hjic-704	25	17	]	]	PUNCT
hjic-704	25	18	.	.	PUNCT
hjic-704	26	1	plank	plank	PROPN
hjic-704	26	2	has	have	AUX
hjic-704	26	3	shown	show	VERB
hjic-704	26	4	[	[	PUNCT
hjic-704	26	5	14	14	NUM
hjic-704	26	6	]	]	PUNCT
hjic-704	26	7	that	that	SCONJ
hjic-704	26	8	ndimensional	ndimensional	PROPN
hjic-704	26	9	lv	lv	PROPN
hjic-704	26	10	systems	system	NOUN
hjic-704	26	11	are	be	AUX
hjic-704	26	12	hamiltonian	hamiltonian	ADJ
hjic-704	26	13	if	if	SCONJ
hjic-704	26	14	they	they	PRON
hjic-704	26	15	fulfil	fulfil	VERB
hjic-704	26	16	certain	certain	ADJ
hjic-704	26	17	algebraic	algebraic	ADJ
hjic-704	26	18	properties	property	NOUN
hjic-704	26	19	(	(	PUNCT
hjic-704	26	20	theorem	theorem	VERB
hjic-704	26	21	3.1	3.1	NUM
hjic-704	26	22	in	in	ADP
hjic-704	26	23	ref	ref	NOUN
hjic-704	26	24	.	.	PUNCT
hjic-704	27	1	[	[	X
hjic-704	27	2	14	14	NUM
hjic-704	27	3	]	]	PUNCT
hjic-704	27	4	)	)	PUNCT
hjic-704	27	5	.	.	PUNCT
hjic-704	28	1	he	he	PRON
hjic-704	28	2	demonstrated	demonstrate	VERB
hjic-704	28	3	that	that	SCONJ
hjic-704	28	4	,	,	PUNCT
hjic-704	28	5	when	when	SCONJ
hjic-704	28	6	using	use	VERB
hjic-704	28	7	an	an	DET
hjic-704	28	8	appropriate	appropriate	ADJ
hjic-704	28	9	poisson	poisson	NOUN
hjic-704	28	10	structure	structure	NOUN
hjic-704	28	11	,	,	PUNCT
hjic-704	28	12	one	one	PRON
hjic-704	28	13	can	can	AUX
hjic-704	28	14	obtain	obtain	VERB
hjic-704	28	15	the	the	DET
hjic-704	28	16	hamiltonian	hamiltonian	ADJ
hjic-704	28	17	function	function	NOUN
hjic-704	28	18	of	of	ADP
hjic-704	28	19	the	the	DET
hjic-704	28	20	system	system	NOUN
hjic-704	28	21	,	,	PUNCT
hjic-704	28	22	which	which	PRON
hjic-704	28	23	is	be	AUX
hjic-704	28	24	a	a	DET
hjic-704	28	25	key	key	ADJ
hjic-704	28	26	object	object	NOUN
hjic-704	28	27	in	in	ADP
hjic-704	28	28	determining	determine	VERB
hjic-704	28	29	the	the	DET
hjic-704	28	30	system	system	NOUN
hjic-704	28	31	's	's	PART
hjic-704	28	32	doa	doa	NOUN
hjic-704	28	33	.	.	PUNCT
hjic-704	29	1	furthermore	furthermore	ADV
hjic-704	29	2	,	,	PUNCT
hjic-704	29	3	candidates	candidate	NOUN
hjic-704	29	4	of	of	ADP
hjic-704	29	5	hamiltonian	hamiltonian	ADJ
hjic-704	29	6	function	function	NOUN
hjic-704	29	7	were	be	AUX
hjic-704	29	8	defined	define	VERB
hjic-704	29	9	in	in	ADP
hjic-704	29	10	(	(	PUNCT
hjic-704	29	11	section	section	NOUN
hjic-704	29	12	iv	iv	NUM
hjic-704	29	13	in	in	ADP
hjic-704	29	14	ref	ref	NOUN
hjic-704	29	15	.	.	PUNCT
hjic-704	30	1	[	[	X
hjic-704	30	2	14	14	NUM
hjic-704	30	3	]	]	PUNCT
hjic-704	30	4	)	)	PUNCT
hjic-704	30	5	.	.	PUNCT
hjic-704	31	1	it	it	PRON
hjic-704	31	2	is	be	AUX
hjic-704	31	3	important	important	ADJ
hjic-704	31	4	to	to	PART
hjic-704	31	5	note	note	VERB
hjic-704	31	6	that	that	SCONJ
hjic-704	31	7	lv	lv	PROPN
hjic-704	31	8	systems	system	NOUN
hjic-704	31	9	are	be	AUX
hjic-704	31	10	polcz	polcz	ADJ
hjic-704	31	11	and	and	CCONJ
hjic-704	31	12	szederkényi	szederkényi	PROPN
hjic-704	31	13	hungarian	hungarian	ADJ
hjic-704	31	14	journal	journal	PROPN
hjic-704	31	15	of	of	ADP
hjic-704	31	16	industry	industry	NOUN
hjic-704	31	17	and	and	CCONJ
hjic-704	31	18	chemistry	chemistry	NOUN
hjic-704	31	19	114	114	NUM
hjic-704	31	20	kinetic	kinetic	NOUN
hjic-704	31	21	in	in	ADP
hjic-704	31	22	the	the	DET
hjic-704	31	23	sense	sense	NOUN
hjic-704	31	24	that	that	SCONJ
hjic-704	31	25	they	they	PRON
hjic-704	31	26	can	can	AUX
hjic-704	31	27	be	be	AUX
hjic-704	31	28	formally	formally	ADV
hjic-704	31	29	described	describe	VERB
hjic-704	31	30	as	as	ADP
hjic-704	31	31	chemical	chemical	NOUN
hjic-704	31	32	reaction	reaction	NOUN
hjic-704	31	33	networks	network	NOUN
hjic-704	31	34	with	with	ADP
hjic-704	31	35	mass	mass	ADJ
hjic-704	31	36	action	action	NOUN
hjic-704	31	37	kinetics	kinetic	NOUN
hjic-704	31	38	.	.	PUNCT
hjic-704	32	1	in	in	ADP
hjic-704	32	2	this	this	DET
hjic-704	32	3	paper	paper	NOUN
hjic-704	32	4	,	,	PUNCT
hjic-704	32	5	the	the	DET
hjic-704	32	6	local	local	ADJ
hjic-704	32	7	stability	stability	NOUN
hjic-704	32	8	properties	property	NOUN
hjic-704	32	9	of	of	ADP
hjic-704	32	10	lv	lv	PROPN
hjic-704	32	11	models	model	NOUN
hjic-704	32	12	are	be	AUX
hjic-704	32	13	analysed	analyse	VERB
hjic-704	32	14	by	by	ADP
hjic-704	32	15	applying	apply	VERB
hjic-704	32	16	the	the	DET
hjic-704	32	17	underlying	underlie	VERB
hjic-704	32	18	method	method	NOUN
hjic-704	32	19	presented	present	VERB
hjic-704	32	20	[	[	X
hjic-704	32	21	6	6	NUM
hjic-704	32	22	]	]	PUNCT
hjic-704	32	23	.	.	PUNCT
hjic-704	33	1	the	the	DET
hjic-704	33	2	stability	stability	NOUN
hjic-704	33	3	region	region	NOUN
hjic-704	33	4	is	be	AUX
hjic-704	33	5	estimated	estimate	VERB
hjic-704	33	6	on	on	ADP
hjic-704	33	7	a	a	DET
hjic-704	33	8	few	few	ADJ
hjic-704	33	9	locally	locally	ADV
hjic-704	33	10	stable	stable	ADJ
hjic-704	33	11	2-	2-	NUM
hjic-704	33	12	,	,	PUNCT
hjic-704	33	13	3-	3-	NOUN
hjic-704	33	14	,	,	PUNCT
hjic-704	33	15	and	and	CCONJ
hjic-704	33	16	4	4	NUM
hjic-704	33	17	-	-	PUNCT
hjic-704	33	18	dimensional	dimensional	ADJ
hjic-704	33	19	benchmark	benchmark	NOUN
hjic-704	33	20	lv	lv	PROPN
hjic-704	33	21	systems	system	NOUN
hjic-704	33	22	.	.	PUNCT
hjic-704	34	1	the	the	DET
hjic-704	34	2	doa	doa	NOUN
hjic-704	34	3	of	of	ADP
hjic-704	34	4	an	an	DET
hjic-704	34	5	uncertain	uncertain	ADJ
hjic-704	34	6	2d	2d	NOUN
hjic-704	34	7	system	system	NOUN
hjic-704	34	8	is	be	AUX
hjic-704	34	9	also	also	ADV
hjic-704	34	10	estimated	estimate	VERB
hjic-704	34	11	by	by	ADP
hjic-704	34	12	two	two	NUM
hjic-704	34	13	concentric	concentric	ADJ
hjic-704	34	14	regions	region	NOUN
hjic-704	34	15	.	.	PUNCT
hjic-704	35	1	the	the	DET
hjic-704	35	2	main	main	ADJ
hjic-704	35	3	motivation	motivation	NOUN
hjic-704	35	4	of	of	ADP
hjic-704	35	5	our	our	PRON
hjic-704	35	6	work	work	NOUN
hjic-704	35	7	was	be	AUX
hjic-704	35	8	to	to	PART
hjic-704	35	9	evaluate	evaluate	VERB
hjic-704	35	10	the	the	DET
hjic-704	35	11	applicability	applicability	NOUN
hjic-704	35	12	of	of	ADP
hjic-704	35	13	the	the	DET
hjic-704	35	14	approach	approach	NOUN
hjic-704	35	15	[	[	X
hjic-704	35	16	4	4	X
hjic-704	35	17	]	]	PUNCT
hjic-704	35	18	on	on	ADP
hjic-704	35	19	a	a	DET
hjic-704	35	20	general	general	ADJ
hjic-704	35	21	polynomial	polynomial	ADJ
hjic-704	35	22	system	system	NOUN
hjic-704	35	23	class	class	NOUN
hjic-704	35	24	consisting	consist	VERB
hjic-704	35	25	of	of	ADP
hjic-704	35	26	low	low	ADJ
hjic-704	35	27	-	-	PUNCT
hjic-704	35	28	degree	degree	NOUN
hjic-704	35	29	monomials	monomial	NOUN
hjic-704	35	30	,	,	PUNCT
hjic-704	35	31	and	and	CCONJ
hjic-704	35	32	to	to	PART
hjic-704	35	33	study	study	VERB
hjic-704	35	34	the	the	DET
hjic-704	35	35	limits	limit	NOUN
hjic-704	35	36	of	of	ADP
hjic-704	35	37	the	the	DET
hjic-704	35	38	method	method	NOUN
hjic-704	35	39	as	as	ADP
hjic-704	35	40	the	the	DET
hjic-704	35	41	number	number	NOUN
hjic-704	35	42	of	of	ADP
hjic-704	35	43	dimensions	dimension	NOUN
hjic-704	35	44	of	of	ADP
hjic-704	35	45	the	the	DET
hjic-704	35	46	state	state	NOUN
hjic-704	35	47	space	space	NOUN
hjic-704	35	48	increase	increase	NOUN
hjic-704	35	49	.	.	PUNCT
hjic-704	36	1	2	2	X
hjic-704	36	2	.	.	X
hjic-704	36	3	background	background	NOUN
hjic-704	36	4	in	in	ADP
hjic-704	36	5	this	this	DET
hjic-704	36	6	section	section	NOUN
hjic-704	36	7	,	,	PUNCT
hjic-704	36	8	the	the	DET
hjic-704	36	9	basic	basic	ADJ
hjic-704	36	10	notions	notion	NOUN
hjic-704	36	11	and	and	CCONJ
hjic-704	36	12	results	result	NOUN
hjic-704	36	13	on	on	ADP
hjic-704	36	14	which	which	PRON
hjic-704	36	15	our	our	PRON
hjic-704	36	16	computational	computational	ADJ
hjic-704	36	17	method	method	NOUN
hjic-704	36	18	is	be	AUX
hjic-704	36	19	based	base	VERB
hjic-704	36	20	are	be	AUX
hjic-704	36	21	presented	present	VERB
hjic-704	36	22	.	.	PUNCT
hjic-704	37	1	2.1	2.1	NUM
hjic-704	37	2	.	.	PUNCT
hjic-704	37	3	system	system	NOUN
hjic-704	37	4	class	class	NOUN
hjic-704	37	5	,	,	PUNCT
hjic-704	37	6	lyapunov	lyapunov	NOUN
hjic-704	37	7	functions	function	NOUN
hjic-704	37	8	,	,	PUNCT
hjic-704	37	9	and	and	CCONJ
hjic-704	37	10	the	the	DET
hjic-704	37	11	domain	domain	NOUN
hjic-704	37	12	of	of	ADP
hjic-704	37	13	attraction	attraction	NOUN
hjic-704	37	14	.	.	PUNCT
hjic-704	38	1	our	our	PRON
hjic-704	38	2	computational	computational	ADJ
hjic-704	38	3	method	method	NOUN
hjic-704	38	4	can	can	AUX
hjic-704	38	5	handle	handle	VERB
hjic-704	38	6	general	general	ADJ
hjic-704	38	7	nonlinear	nonlinear	ADJ
hjic-704	38	8	systems	system	NOUN
hjic-704	38	9	of	of	ADP
hjic-704	38	10	the	the	DET
hjic-704	38	11	form	form	NOUN
hjic-704	38	12	𝑥	𝑥	X
hjic-704	38	13	𝑡	𝑡	NOUN
hjic-704	38	14	=	=	SYM
hjic-704	38	15	𝑓(𝑥	𝑓(𝑥	NOUN
hjic-704	38	16	𝑡	𝑡	PROPN
hjic-704	38	17	,	,	PUNCT
hjic-704	38	18	δ	δ	PROPN
hjic-704	38	19	𝑡	𝑡	PROPN
hjic-704	38	20	)	)	PUNCT
hjic-704	38	21	𝑥	𝑥	PROPN
hjic-704	38	22	𝑡	𝑡	PROPN
hjic-704	38	23	∈	∈	PROPN
hjic-704	38	24	ℝ	ℝ	PROPN
hjic-704	38	25	!	!	PROPN
hjic-704	38	26	,	,	PUNCT
hjic-704	38	27	𝑥	𝑥	X
hjic-704	38	28	!	!	PUNCT
hjic-704	38	29	∈	∈	PROPN
hjic-704	38	30	𝒳	𝒳	PROPN
hjic-704	38	31	,	,	PUNCT
hjic-704	38	32	δ	δ	PROPN
hjic-704	38	33	𝑡	𝑡	PROPN
hjic-704	38	34	∈	∈	PROPN
hjic-704	38	35	𝒟	𝒟	PROPN
hjic-704	38	36	,	,	PUNCT
hjic-704	38	37	δ	δ	PROPN
hjic-704	38	38	𝑡	𝑡	PROPN
hjic-704	38	39	∈	∈	PROPN
hjic-704	38	40	𝒟	𝒟	PROPN
hjic-704	38	41	(	(	PUNCT
hjic-704	38	42	1	1	NUM
hjic-704	38	43	)	)	PUNCT
hjic-704	38	44	where	where	SCONJ
hjic-704	38	45	𝒳	𝒳	PROPN
hjic-704	38	46	⊂	⊂	PUNCT
hjic-704	38	47	ℝ	ℝ	PROPN
hjic-704	38	48	!	!	PUNCT
hjic-704	38	49	and	and	CCONJ
hjic-704	38	50	𝒟,𝒟	𝒟,𝒟	VERB
hjic-704	38	51	⊂	⊂	PROPN
hjic-704	38	52	ℝ	ℝ	PROPN
hjic-704	38	53	!	!	PROPN
hjic-704	38	54	are	be	AUX
hjic-704	38	55	given	give	VERB
hjic-704	38	56	polytopes	polytope	NOUN
hjic-704	38	57	,	,	PUNCT
hjic-704	38	58	x	x	X
hjic-704	38	59	is	be	AUX
hjic-704	38	60	the	the	DET
hjic-704	38	61	state	state	NOUN
hjic-704	38	62	vector	vector	NOUN
hjic-704	38	63	function	function	NOUN
hjic-704	38	64	with	with	ADP
hjic-704	38	65	its	its	PRON
hjic-704	38	66	initial	initial	ADJ
hjic-704	38	67	condition	condition	NOUN
hjic-704	38	68	x0	x0	PROPN
hjic-704	38	69	=	=	SYM
hjic-704	38	70	x(0	x(0	PROPN
hjic-704	38	71	)	)	PUNCT
hjic-704	38	72	,	,	PUNCT
hjic-704	38	73	and	and	CCONJ
hjic-704	38	74	δ	δ	PROPN
hjic-704	38	75	is	be	AUX
hjic-704	38	76	a	a	DET
hjic-704	38	77	smooth	smooth	ADJ
hjic-704	38	78	,	,	PUNCT
hjic-704	38	79	bounded	bound	VERB
hjic-704	38	80	vector	vector	NOUN
hjic-704	38	81	function	function	NOUN
hjic-704	38	82	of	of	ADP
hjic-704	38	83	uncertain	uncertain	ADJ
hjic-704	38	84	parameters	parameter	NOUN
hjic-704	38	85	with	with	ADP
hjic-704	38	86	a	a	DET
hjic-704	38	87	bounded	bounded	ADJ
hjic-704	38	88	time	time	NOUN
hjic-704	38	89	derivative	derivative	ADJ
hjic-704	38	90	.	.	PUNCT
hjic-704	39	1	the	the	DET
hjic-704	39	2	applied	apply	VERB
hjic-704	39	3	method	method	NOUN
hjic-704	39	4	is	be	AUX
hjic-704	39	5	presented	present	VERB
hjic-704	39	6	in	in	ADP
hjic-704	39	7	detail	detail	NOUN
hjic-704	39	8	elsewhere	elsewhere	ADV
hjic-704	39	9	[	[	X
hjic-704	39	10	15	15	NUM
hjic-704	39	11	]	]	PUNCT
hjic-704	39	12	.	.	PUNCT
hjic-704	40	1	from	from	ADP
hjic-704	40	2	now	now	ADV
hjic-704	40	3	on	on	ADV
hjic-704	40	4	,	,	PUNCT
hjic-704	40	5	the	the	DET
hjic-704	40	6	time	time	NOUN
hjic-704	40	7	arguments	argument	NOUN
hjic-704	40	8	of	of	ADP
hjic-704	40	9	x	x	PUNCT
hjic-704	40	10	and	and	CCONJ
hjic-704	40	11	δ	δ	PROPN
hjic-704	40	12	will	will	AUX
hjic-704	40	13	be	be	AUX
hjic-704	40	14	suppressed	suppress	VERB
hjic-704	40	15	as	as	SCONJ
hjic-704	40	16	is	be	AUX
hjic-704	40	17	commonly	commonly	ADV
hjic-704	40	18	done	do	VERB
hjic-704	40	19	in	in	ADP
hjic-704	40	20	the	the	DET
hjic-704	40	21	literature	literature	NOUN
hjic-704	40	22	.	.	PUNCT
hjic-704	41	1	it	it	PRON
hjic-704	41	2	is	be	AUX
hjic-704	41	3	assumed	assume	VERB
hjic-704	41	4	that	that	SCONJ
hjic-704	41	5	function	function	NOUN
hjic-704	41	6	𝑓:ℝ!×𝒟	𝑓:ℝ!×𝒟	PROPN
hjic-704	41	7	↦	↦	PROPN
hjic-704	41	8	ℝ	ℝ	PROPN
hjic-704	41	9	!	!	PUNCT
hjic-704	41	10	of	of	ADP
hjic-704	41	11	eq.(1	eq.(1	ADJ
hjic-704	41	12	)	)	PUNCT
hjic-704	41	13	is	be	AUX
hjic-704	41	14	a	a	DET
hjic-704	41	15	well	well	ADV
hjic-704	41	16	-	-	PUNCT
hjic-704	41	17	defined	define	VERB
hjic-704	41	18	smooth	smooth	ADJ
hjic-704	41	19	rational	rational	ADJ
hjic-704	41	20	mapping	mapping	NOUN
hjic-704	41	21	,	,	PUNCT
hjic-704	41	22	with	with	ADP
hjic-704	41	23	the	the	DET
hjic-704	41	24	property	property	NOUN
hjic-704	41	25	f(0	f(0	NOUN
hjic-704	41	26	,	,	PUNCT
hjic-704	41	27	δ	δ	PROPN
hjic-704	41	28	)	)	PUNCT
hjic-704	42	1	=	=	SYM
hjic-704	42	2	0	0	NUM
hjic-704	42	3	for	for	ADP
hjic-704	42	4	all	all	DET
hjic-704	42	5	𝛿	𝛿	DET
hjic-704	42	6	∈	∈	PROPN
hjic-704	42	7	𝒟.	𝒟.	NOUN
hjic-704	42	8	additionally	additionally	ADV
hjic-704	42	9	,	,	PUNCT
hjic-704	42	10	it	it	PRON
hjic-704	42	11	is	be	AUX
hjic-704	42	12	assumed	assume	VERB
hjic-704	42	13	that	that	SCONJ
hjic-704	42	14	x	x	NOUN
hjic-704	42	15	*	*	PUNCT
hjic-704	42	16	=	=	SYM
hjic-704	42	17	0	0	NUM
hjic-704	42	18	∈	∈	PROPN
hjic-704	42	19	ℝ	ℝ	PROPN
hjic-704	42	20	!	!	PROPN
hjic-704	42	21	is	be	AUX
hjic-704	42	22	a	a	DET
hjic-704	42	23	locally	locally	ADV
hjic-704	42	24	asymptotically	asymptotically	ADV
hjic-704	42	25	stable	stable	ADJ
hjic-704	42	26	equilibrium	equilibrium	NOUN
hjic-704	42	27	point	point	NOUN
hjic-704	42	28	of	of	ADP
hjic-704	42	29	eq.(1	eq.(1	ADJ
hjic-704	42	30	)	)	PUNCT
hjic-704	42	31	for	for	ADP
hjic-704	42	32	all	all	DET
hjic-704	42	33	δ	δ	PROPN
hjic-704	42	34	∈	∈	PROPN
hjic-704	42	35	𝒟.	𝒟.	PROPN
hjic-704	42	36	the	the	DET
hjic-704	42	37	set	set	NOUN
hjic-704	42	38	of	of	ADP
hjic-704	42	39	all	all	DET
hjic-704	42	40	initial	initial	ADJ
hjic-704	42	41	conditions	condition	NOUN
hjic-704	42	42	,	,	PUNCT
hjic-704	42	43	from	from	ADP
hjic-704	42	44	which	which	PRON
hjic-704	42	45	the	the	DET
hjic-704	42	46	solutions	solution	NOUN
hjic-704	42	47	converge	converge	VERB
hjic-704	42	48	to	to	ADP
hjic-704	42	49	x	x	X
hjic-704	42	50	*	*	PUNCT
hjic-704	42	51	,	,	PUNCT
hjic-704	42	52	is	be	AUX
hjic-704	42	53	called	call	VERB
hjic-704	42	54	the	the	DET
hjic-704	42	55	domain	domain	NOUN
hjic-704	42	56	of	of	ADP
hjic-704	42	57	attraction	attraction	NOUN
hjic-704	42	58	(	(	PUNCT
hjic-704	42	59	doa	doa	NOUN
hjic-704	42	60	)	)	PUNCT
hjic-704	42	61	.	.	PUNCT
hjic-704	43	1	furthermore	furthermore	ADV
hjic-704	43	2	,	,	PUNCT
hjic-704	43	3	it	it	PRON
hjic-704	43	4	is	be	AUX
hjic-704	43	5	assumed	assume	VERB
hjic-704	43	6	that	that	SCONJ
hjic-704	43	7	function	function	VERB
hjic-704	43	8	f(x	f(x	PROPN
hjic-704	43	9	,	,	PUNCT
hjic-704	43	10	δ	δ	PROPN
hjic-704	43	11	)	)	PUNCT
hjic-704	43	12	can	can	AUX
hjic-704	43	13	be	be	AUX
hjic-704	43	14	written	write	VERB
hjic-704	43	15	in	in	ADP
hjic-704	43	16	a	a	DET
hjic-704	43	17	so	so	ADV
hjic-704	43	18	-	-	PUNCT
hjic-704	43	19	called	call	VERB
hjic-704	43	20	quasi	quasi	ADJ
hjic-704	43	21	-	-	ADJ
hjic-704	43	22	lpv	lpv	ADJ
hjic-704	43	23	form	form	NOUN
hjic-704	43	24	f(x	f(x	PROPN
hjic-704	43	25	,	,	PUNCT
hjic-704	43	26	δ	δ	PROPN
hjic-704	43	27	)	)	PUNCT
hjic-704	43	28	=	=	PUNCT
hjic-704	43	29	function	function	NOUN
hjic-704	43	30	a(x	a(x	NOUN
hjic-704	43	31	,	,	PUNCT
hjic-704	43	32	δ	δ	PROPN
hjic-704	43	33	)	)	PUNCT
hjic-704	43	34	x	x	PUNCT
hjic-704	44	1	the	the	DET
hjic-704	44	2	aim	aim	NOUN
hjic-704	44	3	is	be	AUX
hjic-704	44	4	to	to	PART
hjic-704	44	5	identify	identify	VERB
hjic-704	44	6	an	an	DET
hjic-704	44	7	appropriate	appropriate	ADJ
hjic-704	44	8	rational	rational	ADJ
hjic-704	44	9	lyapunov	lyapunov	NOUN
hjic-704	44	10	function	function	NOUN
hjic-704	44	11	v(x	v(x	PROPN
hjic-704	44	12	,	,	PUNCT
hjic-704	44	13	δ	δ	PROPN
hjic-704	44	14	)	)	PUNCT
hjic-704	44	15	,	,	PUNCT
hjic-704	44	16	which	which	PRON
hjic-704	44	17	satisfies	satisfy	VERB
hjic-704	44	18	the	the	DET
hjic-704	44	19	following	follow	VERB
hjic-704	44	20	conditions	condition	NOUN
hjic-704	44	21	:	:	PUNCT
hjic-704	44	22	𝑣	𝑣	X
hjic-704	44	23	!	!	PUNCT
hjic-704	45	1	𝑥	𝑥	DET
hjic-704	45	2	≤	≤	NUM
hjic-704	45	3	𝑉	𝑉	PROPN
hjic-704	45	4	𝑥	𝑥	PROPN
hjic-704	45	5	,	,	PUNCT
hjic-704	45	6	δ	δ	PROPN
hjic-704	45	7	≤	≤	ADV
hjic-704	45	8	𝑢	𝑢	X
hjic-704	45	9	!	!	PUNCT
hjic-704	45	10	𝑥	𝑥	PROPN
hjic-704	45	11	,	,	PUNCT
hjic-704	45	12	∀(𝑥	∀(𝑥	PROPN
hjic-704	45	13	,	,	PUNCT
hjic-704	45	14	δ	δ	PROPN
hjic-704	45	15	)	)	PUNCT
hjic-704	45	16	∈	∈	PROPN
hjic-704	45	17	𝒳×𝒟	𝒳×𝒟	NOUN
hjic-704	45	18	𝑉	𝑉	PROPN
hjic-704	45	19	𝑥	𝑥	PROPN
hjic-704	45	20	,	,	PUNCT
hjic-704	45	21	δ	δ	PROPN
hjic-704	45	22	,	,	PUNCT
hjic-704	45	23	δ	δ	PROPN
hjic-704	45	24	≤	≤	ADJ
hjic-704	45	25	−𝑣	−𝑣	NOUN
hjic-704	45	26	!	!	PUNCT
hjic-704	46	1	𝑥	𝑥	PRON
hjic-704	46	2	∀(𝑥	∀(𝑥	PROPN
hjic-704	46	3	,	,	PUNCT
hjic-704	46	4	δ	δ	PROPN
hjic-704	46	5	,	,	PUNCT
hjic-704	46	6	δ	δ	PROPN
hjic-704	46	7	)	)	PUNCT
hjic-704	46	8	∈	∈	PROPN
hjic-704	46	9	𝒳×𝒟×𝒟	𝒳×𝒟×𝒟	PROPN
hjic-704	46	10	(	(	PUNCT
hjic-704	46	11	2	2	NUM
hjic-704	46	12	)	)	PUNCT
hjic-704	46	13	where	where	SCONJ
hjic-704	46	14	vl	vl	NOUN
hjic-704	46	15	,	,	PUNCT
hjic-704	46	16	ux	ux	PROPN
hjic-704	46	17	,	,	PUNCT
hjic-704	46	18	vd	vd	NOUN
hjic-704	46	19	are	be	AUX
hjic-704	46	20	continuous	continuous	ADJ
hjic-704	46	21	positive	positive	ADJ
hjic-704	46	22	functions	function	NOUN
hjic-704	46	23	on	on	ADP
hjic-704	46	24	𝒳.	𝒳.	PROPN
hjic-704	46	25	due	due	ADP
hjic-704	46	26	to	to	ADP
hjic-704	46	27	conditions	condition	NOUN
hjic-704	46	28	of	of	ADP
hjic-704	46	29	eq.(2	eq.(2	NOUN
hjic-704	46	30	)	)	PUNCT
hjic-704	46	31	any	any	DET
hjic-704	46	32	closed	closed	ADJ
hjic-704	46	33	level	level	NOUN
hjic-704	46	34	set	set	NOUN
hjic-704	46	35	of	of	ADP
hjic-704	46	36	the	the	DET
hjic-704	46	37	lyapunov	lyapunov	ADJ
hjic-704	46	38	function	function	NOUN
hjic-704	46	39	contained	contain	VERB
hjic-704	46	40	entirely	entirely	ADV
hjic-704	46	41	in	in	ADP
hjic-704	46	42	𝒳	𝒳	PROPN
hjic-704	46	43	bounds	bound	VERB
hjic-704	46	44	an	an	DET
hjic-704	46	45	invariant	invariant	ADJ
hjic-704	46	46	region	region	NOUN
hjic-704	46	47	of	of	ADP
hjic-704	46	48	the	the	DET
hjic-704	46	49	state	state	NOUN
hjic-704	46	50	space	space	NOUN
hjic-704	46	51	.	.	PUNCT
hjic-704	47	1	our	our	PRON
hjic-704	47	2	objective	objective	NOUN
hjic-704	47	3	is	be	AUX
hjic-704	47	4	to	to	PART
hjic-704	47	5	find	find	VERB
hjic-704	47	6	a	a	DET
hjic-704	47	7	lyapunov	lyapunov	ADJ
hjic-704	47	8	function	function	NOUN
hjic-704	47	9	,	,	PUNCT
hjic-704	47	10	which	which	PRON
hjic-704	47	11	fulfils	fulfil	VERB
hjic-704	47	12	the	the	DET
hjic-704	47	13	conditions	condition	NOUN
hjic-704	47	14	of	of	ADP
hjic-704	47	15	eq.(2	eq.(2	NOUN
hjic-704	47	16	)	)	PUNCT
hjic-704	47	17	and	and	CCONJ
hjic-704	47	18	to	to	PART
hjic-704	47	19	determine	determine	VERB
hjic-704	47	20	its	its	PRON
hjic-704	47	21	maximal	maximal	ADJ
hjic-704	47	22	invariant	invariant	ADJ
hjic-704	47	23	level	level	NOUN
hjic-704	47	24	set	set	VERB
hjic-704	47	25	completely	completely	ADV
hjic-704	47	26	inside	inside	ADP
hjic-704	47	27	𝒳.	𝒳.	PROPN
hjic-704	47	28	2.2	2.2	NUM
hjic-704	47	29	.	.	PUNCT
hjic-704	48	1	dynamical	dynamical	ADJ
hjic-704	48	2	system	system	NOUN
hjic-704	48	3	representation	representation	NOUN
hjic-704	48	4	a	a	DET
hjic-704	48	5	lyapunov	lyapunov	ADJ
hjic-704	48	6	function	function	NOUN
hjic-704	48	7	can	can	AUX
hjic-704	48	8	be	be	AUX
hjic-704	48	9	computed	compute	VERB
hjic-704	48	10	[	[	X
hjic-704	48	11	4	4	X
hjic-704	48	12	]	]	PUNCT
hjic-704	48	13	in	in	ADP
hjic-704	48	14	the	the	DET
hjic-704	48	15	form	form	NOUN
hjic-704	48	16	shown	show	VERB
hjic-704	48	17	in	in	ADP
hjic-704	48	18	eq.(3	eq.(3	NOUN
hjic-704	48	19	)	)	PUNCT
hjic-704	48	20	.	.	PUNCT
hjic-704	49	1	𝑉	𝑉	PROPN
hjic-704	49	2	𝑥	𝑥	PROPN
hjic-704	49	3	,	,	PUNCT
hjic-704	49	4	δ	δ	X
hjic-704	49	5	=	=	SYM
hjic-704	49	6	π	π	PROPN
hjic-704	49	7	!	!	PUNCT
hjic-704	49	8	!	!	PUNCT
hjic-704	50	1	𝑥	𝑥	INTJ
hjic-704	50	2	,	,	PUNCT
hjic-704	50	3	δ	δ	PROPN
hjic-704	50	4	𝑃π	𝑃π	PROPN
hjic-704	50	5	!	!	PUNCT
hjic-704	51	1	𝑥	𝑥	X
hjic-704	51	2	,	,	PUNCT
hjic-704	51	3	δ	δ	PROPN
hjic-704	51	4	,	,	PUNCT
hjic-704	51	5	π	π	X
hjic-704	51	6	!	!	PUNCT
hjic-704	51	7	=	=	PUNCT
hjic-704	52	1	𝑥	𝑥	X
hjic-704	52	2	π	π	X
hjic-704	52	3	(	(	PUNCT
hjic-704	52	4	3	3	NUM
hjic-704	52	5	)	)	PUNCT
hjic-704	52	6	where	where	SCONJ
hjic-704	52	7	𝑃	𝑃	NOUN
hjic-704	52	8	∈	∈	PROPN
hjic-704	52	9	ℝ!×	ℝ!×	PROPN
hjic-704	52	10	!	!	PROPN
hjic-704	52	11	is	be	AUX
hjic-704	52	12	a	a	DET
hjic-704	52	13	constant	constant	ADJ
hjic-704	52	14	symmetric	symmetric	ADJ
hjic-704	52	15	matrix	matrix	NOUN
hjic-704	52	16	,	,	PUNCT
hjic-704	52	17	not	not	PART
hjic-704	52	18	necessarily	necessarily	ADV
hjic-704	52	19	positive	positive	ADJ
hjic-704	52	20	definite	definite	ADJ
hjic-704	52	21	,	,	PUNCT
hjic-704	52	22	and	and	CCONJ
hjic-704	52	23	π:ℝ!×𝒟	π:ℝ!×𝒟	PROPN
hjic-704	52	24	↦	↦	PROPN
hjic-704	52	25	ℝ	ℝ	PROPN
hjic-704	52	26	!	!	PROPN
hjic-704	52	27	is	be	AUX
hjic-704	52	28	mapping	mapping	NOUN
hjic-704	52	29	,	,	PUNCT
hjic-704	52	30	in	in	ADP
hjic-704	52	31	which	which	PRON
hjic-704	52	32	each	each	DET
hjic-704	52	33	element	element	NOUN
hjic-704	52	34	is	be	AUX
hjic-704	52	35	a	a	DET
hjic-704	52	36	monomial	monomial	NOUN
hjic-704	52	37	in	in	ADP
hjic-704	52	38	(	(	PUNCT
hjic-704	52	39	x	x	NOUN
hjic-704	52	40	,	,	PUNCT
hjic-704	52	41	δ	δ	PROPN
hjic-704	52	42	)	)	PUNCT
hjic-704	52	43	,	,	PUNCT
hjic-704	52	44	or	or	CCONJ
hjic-704	52	45	a	a	DET
hjic-704	52	46	smooth	smooth	ADJ
hjic-704	52	47	rational	rational	ADJ
hjic-704	52	48	function	function	NOUN
hjic-704	52	49	with	with	ADP
hjic-704	52	50	a	a	DET
hjic-704	52	51	monomial	monomial	ADJ
hjic-704	52	52	numerator	numerator	NOUN
hjic-704	52	53	.	.	PUNCT
hjic-704	53	1	the	the	DET
hjic-704	53	2	arguments	argument	NOUN
hjic-704	53	3	of	of	ADP
hjic-704	53	4	π	π	PROPN
hjic-704	53	5	and	and	CCONJ
hjic-704	53	6	πb	πb	PRON
hjic-704	53	7	will	will	AUX
hjic-704	53	8	be	be	AUX
hjic-704	53	9	suppressed	suppress	VERB
hjic-704	53	10	below	below	ADV
hjic-704	53	11	.	.	PUNCT
hjic-704	54	1	applications	application	NOUN
hjic-704	54	2	of	of	ADP
hjic-704	54	3	the	the	DET
hjic-704	54	4	linear	linear	ADJ
hjic-704	54	5	fractional	fractional	ADJ
hjic-704	54	6	transformation	transformation	NOUN
hjic-704	54	7	(	(	PUNCT
hjic-704	54	8	lft	lft	X
hjic-704	54	9	)	)	PUNCT
hjic-704	54	10	and	and	CCONJ
hjic-704	54	11	further	far	ADV
hjic-704	54	12	algebraic	algebraic	ADJ
hjic-704	54	13	steps	step	NOUN
hjic-704	54	14	have	have	AUX
hjic-704	54	15	been	be	AUX
hjic-704	54	16	proposed	propose	VERB
hjic-704	54	17	[	[	X
hjic-704	54	18	5,6	5,6	NUM
hjic-704	54	19	]	]	PUNCT
hjic-704	54	20	to	to	PART
hjic-704	54	21	transform	transform	VERB
hjic-704	54	22	the	the	DET
hjic-704	54	23	system	system	NOUN
hjic-704	54	24	equation	equation	NOUN
hjic-704	55	1	𝑥	𝑥	NOUN
hjic-704	55	2	=	=	PUNCT
hjic-704	55	3	𝑓	𝑓	PRON
hjic-704	55	4	𝑥	𝑥	PROPN
hjic-704	55	5	,	,	PUNCT
hjic-704	55	6	δ	δ	PROPN
hjic-704	55	7	=	=	PUNCT
hjic-704	55	8	𝐴(𝑥	𝐴(𝑥	NOUN
hjic-704	55	9	,	,	PUNCT
hjic-704	55	10	δ)𝑥	δ)𝑥	NOUN
hjic-704	55	11	into	into	ADP
hjic-704	55	12	the	the	DET
hjic-704	55	13	desired	desire	VERB
hjic-704	55	14	differential	differential	ADJ
hjic-704	55	15	-	-	PUNCT
hjic-704	55	16	algebraic	algebraic	ADJ
hjic-704	55	17	representation	representation	NOUN
hjic-704	55	18	that	that	PRON
hjic-704	55	19	was	be	AUX
hjic-704	55	20	introduced	introduce	VERB
hjic-704	55	21	in	in	ADP
hjic-704	55	22	the	the	DET
hjic-704	55	23	same	same	ADJ
hjic-704	55	24	references	reference	NOUN
hjic-704	55	25	:	:	PUNCT
hjic-704	55	26	𝑥	𝑥	NOUN
hjic-704	55	27	=	=	SYM
hjic-704	55	28	𝐴	𝐴	PROPN
hjic-704	55	29	𝑥	𝑥	PROPN
hjic-704	55	30	,	,	PUNCT
hjic-704	55	31	δ	δ	NOUN
hjic-704	55	32	𝑥	𝑥	NOUN
hjic-704	55	33	=	=	PUNCT
hjic-704	55	34	𝐴𝑥	𝐴𝑥	NOUN
hjic-704	55	35	+	+	PUNCT
hjic-704	55	36	𝐵𝜋	𝐵𝜋	PROPN
hjic-704	55	37	𝑥	𝑥	NOUN
hjic-704	55	38	!	!	PUNCT
hjic-704	55	39	∈	∈	PROPN
hjic-704	55	40	𝒳	𝒳	PROPN
hjic-704	55	41	0	0	NUM
hjic-704	55	42	=	=	SYM
hjic-704	55	43	𝒩	𝒩	PROPN
hjic-704	55	44	!	!	PUNCT
hjic-704	55	45	!	!	PUNCT
hjic-704	56	1	𝑥	𝑥	INTJ
hjic-704	56	2	,	,	PUNCT
hjic-704	56	3	δ	δ	PROPN
hjic-704	56	4	π	π	PROPN
hjic-704	56	5	!	!	PUNCT
hjic-704	57	1	𝛿	𝛿	PROPN
hjic-704	57	2	∈	∈	PROPN
hjic-704	57	3	𝒟	𝒟	PROPN
hjic-704	57	4	,	,	PUNCT
hjic-704	57	5	𝛿	𝛿	PROPN
hjic-704	57	6	∈	∈	PROPN
hjic-704	57	7	𝒟	𝒟	NOUN
hjic-704	57	8	(	(	PUNCT
hjic-704	57	9	4	4	NUM
hjic-704	57	10	)	)	PUNCT
hjic-704	57	11	where	where	SCONJ
hjic-704	57	12	𝐴	𝐴	PROPN
hjic-704	57	13	∈	∈	PROPN
hjic-704	57	14	ℝ!×	ℝ!×	PROPN
hjic-704	57	15	!	!	PUNCT
hjic-704	57	16	and	and	CCONJ
hjic-704	57	17	𝐵	𝐵	PROPN
hjic-704	57	18	∈	∈	PROPN
hjic-704	57	19	ℝ!×	ℝ!×	PROPN
hjic-704	57	20	!	!	X
hjic-704	57	21	are	be	AUX
hjic-704	57	22	constant	constant	ADJ
hjic-704	57	23	matrices	matrix	NOUN
hjic-704	57	24	,	,	PUNCT
hjic-704	57	25	and	and	CCONJ
hjic-704	57	26	𝒩	𝒩	PROPN
hjic-704	57	27	!	!	PUNCT
hjic-704	57	28	!	!	PUNCT
hjic-704	58	1	𝑥	𝑥	X
hjic-704	58	2	,	,	PUNCT
hjic-704	58	3	δ	δ	PROPN
hjic-704	58	4	∈	∈	PROPN
hjic-704	58	5	ℝ!×	ℝ!×	PROPN
hjic-704	58	6	!	!	PROPN
hjic-704	58	7	is	be	AUX
hjic-704	58	8	an	an	DET
hjic-704	58	9	affine	affine	ADJ
hjic-704	58	10	matrix	matrix	NOUN
hjic-704	58	11	function	function	NOUN
hjic-704	58	12	in	in	ADP
hjic-704	58	13	(	(	PUNCT
hjic-704	58	14	x	x	NOUN
hjic-704	58	15	,	,	PUNCT
hjic-704	58	16	δ	δ	PROPN
hjic-704	58	17	)	)	PUNCT
hjic-704	58	18	also	also	ADV
hjic-704	58	19	known	know	VERB
hjic-704	58	20	as	as	ADP
hjic-704	58	21	an	an	DET
hjic-704	58	22	“	"	PUNCT
hjic-704	58	23	annihilator	annihilator	NOUN
hjic-704	58	24	”	"	PUNCT
hjic-704	58	25	.	.	PUNCT
hjic-704	59	1	these	these	DET
hjic-704	59	2	transformations	transformation	NOUN
hjic-704	59	3	also	also	ADV
hjic-704	59	4	result	result	VERB
hjic-704	59	5	in	in	ADP
hjic-704	59	6	the	the	DET
hjic-704	59	7	dimension	dimension	NOUN
hjic-704	59	8	reduction	reduction	NOUN
hjic-704	59	9	of	of	ADP
hjic-704	59	10	the	the	DET
hjic-704	59	11	optimization	optimization	NOUN
hjic-704	59	12	problem	problem	NOUN
hjic-704	59	13	compared	compare	VERB
hjic-704	59	14	to	to	ADP
hjic-704	59	15	the	the	DET
hjic-704	59	16	results	result	NOUN
hjic-704	59	17	presented	present	VERB
hjic-704	59	18	in	in	ADP
hjic-704	59	19	ref	ref	NOUN
hjic-704	59	20	.	.	PUNCT
hjic-704	60	1	[	[	X
hjic-704	60	2	4	4	NUM
hjic-704	60	3	]	]	PUNCT
hjic-704	60	4	.	.	PUNCT
hjic-704	61	1	the	the	DET
hjic-704	61	2	representation	representation	NOUN
hjic-704	61	3	in	in	ADP
hjic-704	61	4	eq.(4	eq.(4	ADJ
hjic-704	61	5	)	)	PUNCT
hjic-704	61	6	separates	separate	VERB
hjic-704	61	7	the	the	DET
hjic-704	61	8	linear	linear	ADJ
hjic-704	61	9	part	part	NOUN
hjic-704	61	10	of	of	ADP
hjic-704	61	11	the	the	DET
hjic-704	61	12	system	system	NOUN
hjic-704	61	13	(	(	PUNCT
hjic-704	61	14	x	x	X
hjic-704	61	15	)	)	PUNCT
hjic-704	61	16	from	from	ADP
hjic-704	61	17	its	its	PRON
hjic-704	61	18	nonlinear	nonlinear	ADJ
hjic-704	61	19	part	part	NOUN
hjic-704	61	20	(	(	PUNCT
hjic-704	61	21	π	π	PROPN
hjic-704	61	22	)	)	PUNCT
hjic-704	61	23	.	.	PUNCT
hjic-704	62	1	3	3	X
hjic-704	62	2	.	.	X
hjic-704	62	3	the	the	DET
hjic-704	62	4	sdp	sdp	NOUN
hjic-704	62	5	problem	problem	NOUN
hjic-704	62	6	for	for	ADP
hjic-704	62	7	estimating	estimate	VERB
hjic-704	62	8	the	the	DET
hjic-704	62	9	doa	doa	NOUN
hjic-704	62	10	in	in	ADP
hjic-704	62	11	this	this	DET
hjic-704	62	12	section	section	NOUN
hjic-704	62	13	,	,	PUNCT
hjic-704	62	14	how	how	SCONJ
hjic-704	62	15	to	to	PART
hjic-704	62	16	construct	construct	VERB
hjic-704	62	17	the	the	DET
hjic-704	62	18	semi	semi	ADJ
hjic-704	62	19	-	-	ADJ
hjic-704	62	20	definite	definite	ADJ
hjic-704	62	21	optimization	optimization	NOUN
hjic-704	62	22	task	task	NOUN
hjic-704	62	23	(	(	PUNCT
hjic-704	62	24	sdp	sdp	NOUN
hjic-704	62	25	)	)	PUNCT
hjic-704	62	26	is	be	AUX
hjic-704	62	27	presented	present	VERB
hjic-704	62	28	,	,	PUNCT
hjic-704	62	29	which	which	PRON
hjic-704	62	30	will	will	AUX
hjic-704	62	31	uniquely	uniquely	ADV
hjic-704	62	32	characterize	characterize	VERB
hjic-704	62	33	an	an	DET
hjic-704	62	34	appropriate	appropriate	ADJ
hjic-704	62	35	lyapunov	lyapunov	NOUN
hjic-704	62	36	function	function	NOUN
hjic-704	62	37	and	and	CCONJ
hjic-704	62	38	its	its	PRON
hjic-704	62	39	maximal	maximal	ADJ
hjic-704	62	40	invariant	invariant	ADJ
hjic-704	62	41	level	level	NOUN
hjic-704	62	42	set	set	VERB
hjic-704	62	43	εα	εα	ADV
hjic-704	62	44	as	as	ADP
hjic-704	62	45	an	an	DET
hjic-704	62	46	estimate	estimate	NOUN
hjic-704	62	47	of	of	ADP
hjic-704	62	48	the	the	DET
hjic-704	62	49	true	true	ADJ
hjic-704	62	50	domain	domain	NOUN
hjic-704	62	51	of	of	ADP
hjic-704	62	52	attraction	attraction	NOUN
hjic-704	62	53	.	.	PUNCT
hjic-704	63	1	it	it	PRON
hjic-704	63	2	is	be	AUX
hjic-704	63	3	assumed	assume	VERB
hjic-704	63	4	that	that	SCONJ
hjic-704	63	5	polytopes	polytope	NOUN
hjic-704	63	6	𝒳,𝒴	𝒳,𝒴	VERB
hjic-704	63	7	,	,	PUNCT
hjic-704	63	8	and	and	CCONJ
hjic-704	63	9	𝒟	𝒟	NOUN
hjic-704	63	10	are	be	AUX
hjic-704	63	11	already	already	ADV
hjic-704	63	12	given	give	VERB
hjic-704	63	13	.	.	PUNCT
hjic-704	64	1	using	use	VERB
hjic-704	64	2	the	the	DET
hjic-704	64	3	model	model	NOUN
hjic-704	64	4	representation	representation	NOUN
hjic-704	64	5	of	of	ADP
hjic-704	64	6	eq.(4	eq.(4	ADJ
hjic-704	64	7	)	)	PUNCT
hjic-704	64	8	and	and	CCONJ
hjic-704	64	9	a	a	DET
hjic-704	64	10	lyapunov	lyapunov	ADJ
hjic-704	64	11	function	function	NOUN
hjic-704	64	12	candidate	candidate	NOUN
hjic-704	64	13	of	of	ADP
hjic-704	64	14	the	the	DET
hjic-704	64	15	form	form	NOUN
hjic-704	64	16	in	in	ADP
hjic-704	64	17	eq.(3	eq.(3	NOUN
hjic-704	64	18	)	)	PUNCT
hjic-704	64	19	,	,	PUNCT
hjic-704	64	20	sufficient	sufficient	ADJ
hjic-704	64	21	lmis	lmis	ADV
hjic-704	64	22	for	for	ADP
hjic-704	64	23	the	the	DET
hjic-704	64	24	lyapunov	lyapunov	ADJ
hjic-704	64	25	conditions	condition	NOUN
hjic-704	64	26	in	in	ADP
hjic-704	64	27	eq.(2	eq.(2	ADJ
hjic-704	64	28	)	)	PUNCT
hjic-704	64	29	can	can	AUX
hjic-704	64	30	be	be	AUX
hjic-704	64	31	formulated	formulate	VERB
hjic-704	64	32	.	.	PUNCT
hjic-704	65	1	according	accord	VERB
hjic-704	65	2	to	to	ADP
hjic-704	65	3	finsler	finsler	NOUN
hjic-704	65	4	’s	’s	PART
hjic-704	65	5	lemma	lemma	PROPN
hjic-704	65	6	(	(	PUNCT
hjic-704	65	7	lemma	lemma	PROPN
hjic-704	65	8	2.1	2.1	NUM
hjic-704	65	9	in	in	ADP
hjic-704	65	10	ref	ref	NOUN
hjic-704	65	11	.	.	PUNCT
hjic-704	66	1	[	[	X
hjic-704	66	2	4	4	NUM
hjic-704	66	3	]	]	NUM
hjic-704	66	4	)	)	PUNCT
hjic-704	66	5	,	,	PUNCT
hjic-704	66	6	if	if	SCONJ
hjic-704	66	7	real	real	ADV
hjic-704	66	8	-	-	PUNCT
hjic-704	66	9	valued	value	VERB
hjic-704	66	10	matrices	matrix	NOUN
hjic-704	66	11	𝐿	𝐿	PROPN
hjic-704	66	12	!	!	PUNCT
hjic-704	66	13	∈	∈	PROPN
hjic-704	66	14	ℝ!×	ℝ!×	PROPN
hjic-704	66	15	!	!	PROPN
hjic-704	66	16	and	and	CCONJ
hjic-704	66	17	𝐿	𝐿	PROPN
hjic-704	66	18	!	!	PROPN
hjic-704	66	19	∈	∈	PROPN
hjic-704	66	20	ℝ(!!!"!!!!!")×	ℝ(!!!"!!!!!")×	ADJ
hjic-704	66	21	(	(	PUNCT
hjic-704	66	22	!	!	PUNCT
hjic-704	66	23	"	"	PUNCT
hjic-704	66	24	!	!	PUNCT
hjic-704	66	25	!	!	PUNCT
hjic-704	66	26	!	!	PUNCT
hjic-704	66	27	!	!	PUNCT
hjic-704	66	28	!	!	PUNCT
hjic-704	66	29	"	"	PUNCT
hjic-704	66	30	)	)	PUNCT
hjic-704	66	31	exist	exist	VERB
hjic-704	66	32	∀	∀	NOUN
hjic-704	66	33	𝑥	𝑥	NOUN
hjic-704	66	34	,	,	PUNCT
hjic-704	66	35	δ	δ	PROPN
hjic-704	66	36	∈	∈	PROPN
hjic-704	66	37	𝜗	𝜗	NOUN
hjic-704	66	38	𝒳×𝒟	𝒳×𝒟	NOUN
hjic-704	66	39	:	:	PUNCT
hjic-704	66	40	𝑃	𝑃	NOUN
hjic-704	66	41	+	+	CCONJ
hjic-704	66	42	𝐿!𝒩	𝐿!𝒩	ADJ
hjic-704	66	43	!	!	PUNCT
hjic-704	66	44	!	!	PUNCT
hjic-704	67	1	𝑥	𝑥	X
hjic-704	67	2	,	,	PUNCT
hjic-704	67	3	δ	δ	PROPN
hjic-704	67	4	+	+	PROPN
hjic-704	67	5	𝒩	𝒩	PROPN
hjic-704	67	6	!	!	PUNCT
hjic-704	67	7	!	!	PUNCT
hjic-704	67	8	!	!	PUNCT
hjic-704	68	1	𝑥	𝑥	X
hjic-704	68	2	,	,	PUNCT
hjic-704	68	3	δ	δ	PROPN
hjic-704	68	4	𝐿	𝐿	PROPN
hjic-704	68	5	!	!	PUNCT
hjic-704	68	6	!	!	PUNCT
hjic-704	69	1	>	>	X
hjic-704	69	2	0	0	PUNCT
hjic-704	70	1	(	(	PUNCT
hjic-704	70	2	5	5	NUM
hjic-704	70	3	)	)	PUNCT
hjic-704	70	4	∀	∀	PUNCT
hjic-704	71	1	𝑥	𝑥	NOUN
hjic-704	71	2	,	,	PUNCT
hjic-704	71	3	δ	δ	PROPN
hjic-704	71	4	,	,	PUNCT
hjic-704	71	5	δ	δ	PROPN
hjic-704	71	6	∈	∈	PROPN
hjic-704	71	7	𝜗	𝜗	X
hjic-704	71	8	𝒳×𝒟×𝒟	𝒳×𝒟×𝒟	X
hjic-704	71	9	:	:	PUNCT
hjic-704	71	10	𝑃	𝑃	X
hjic-704	71	11	!	!	PUNCT
hjic-704	72	1	+	+	PUNCT
hjic-704	72	2	𝑃	𝑃	NOUN
hjic-704	72	3	!	!	PUNCT
hjic-704	72	4	!	!	PUNCT
hjic-704	73	1	+	+	CCONJ
hjic-704	73	2	𝐿!𝒩	𝐿!𝒩	ADJ
hjic-704	73	3	!	!	PUNCT
hjic-704	73	4	!	!	PUNCT
hjic-704	74	1	𝑥	𝑥	X
hjic-704	74	2	,	,	PUNCT
hjic-704	74	3	δ	δ	PROPN
hjic-704	74	4	,	,	PUNCT
hjic-704	74	5	δ	δ	PROPN
hjic-704	74	6	+	+	PROPN
hjic-704	74	7	𝒩	𝒩	PROPN
hjic-704	74	8	!	!	PUNCT
hjic-704	74	9	!	!	PUNCT
hjic-704	74	10	!	!	PUNCT
hjic-704	75	1	𝑥	𝑥	X
hjic-704	75	2	,	,	PUNCT
hjic-704	75	3	δ	δ	PROPN
hjic-704	75	4	,	,	PUNCT
hjic-704	75	5	δ	δ	PROPN
hjic-704	75	6	<	<	X
hjic-704	75	7	0	0	NUM
hjic-704	75	8	(	(	PUNCT
hjic-704	75	9	6	6	NUM
hjic-704	75	10	)	)	PUNCT
hjic-704	75	11	then	then	ADV
hjic-704	75	12	the	the	DET
hjic-704	75	13	conditions	condition	NOUN
hjic-704	75	14	of	of	ADP
hjic-704	75	15	eq.(2	eq.(2	NOUN
hjic-704	75	16	)	)	PUNCT
hjic-704	75	17	are	be	AUX
hjic-704	75	18	satisfied	satisfied	ADJ
hjic-704	75	19	for	for	ADP
hjic-704	75	20	every	every	DET
hjic-704	75	21	(	(	PUNCT
hjic-704	75	22	𝑥	𝑥	PROPN
hjic-704	75	23	,	,	PUNCT
hjic-704	75	24	δ	δ	PROPN
hjic-704	75	25	,	,	PUNCT
hjic-704	75	26	δ	δ	PROPN
hjic-704	75	27	)	)	PUNCT
hjic-704	75	28	∈	∈	PROPN
hjic-704	75	29	𝒳×𝒟×𝒟.	𝒳×𝒟×𝒟.	PROPN
hjic-704	75	30	variables	variable	NOUN
hjic-704	75	31	pa	pa	PROPN
hjic-704	75	32	and	and	CCONJ
hjic-704	75	33	𝒩	𝒩	PROPN
hjic-704	75	34	!	!	PUNCT
hjic-704	75	35	!	!	PUNCT
hjic-704	76	1	𝑥	𝑥	X
hjic-704	76	2	,	,	PUNCT
hjic-704	76	3	δ	δ	PROPN
hjic-704	76	4	,	,	PUNCT
hjic-704	76	5	δ	δ	PROPN
hjic-704	76	6	are	be	AUX
hjic-704	76	7	computational	computational	ADJ
hjic-704	76	8	stability	stability	NOUN
hjic-704	76	9	analysis	analysis	NOUN
hjic-704	76	10	of	of	ADP
hjic-704	76	11	lotka	lotka	PROPN
hjic-704	76	12	-	-	PUNCT
hjic-704	76	13	volterra	volterra	PROPN
hjic-704	76	14	systems	system	NOUN
hjic-704	76	15	44(2	44(2	PROPN
hjic-704	76	16	)	)	PUNCT
hjic-704	76	17	pp	pp	ADV
hjic-704	76	18	.	.	PUNCT
hjic-704	77	1	113–120	113–120	NUM
hjic-704	77	2	(	(	PUNCT
hjic-704	77	3	2016	2016	NUM
hjic-704	77	4	)	)	PUNCT
hjic-704	77	5	doi	doi	NOUN
hjic-704	77	6	:	:	PUNCT
hjic-704	77	7	10.1515	10.1515	NUM
hjic-704	77	8	/	/	SYM
hjic-704	77	9	hjic-2016	hjic-2016	NOUN
hjic-704	77	10	-	-	PUNCT
hjic-704	77	11	0014	0014	NUM
hjic-704	77	12	115	115	NUM
hjic-704	77	13	defined	define	VERB
hjic-704	77	14	in	in	ADP
hjic-704	77	15	eqs.(3.16	eqs.(3.16	PROPN
hjic-704	77	16	)	)	PUNCT
hjic-704	77	17	and	and	CCONJ
hjic-704	77	18	(	(	PUNCT
hjic-704	77	19	3.22	3.22	NUM
hjic-704	77	20	)	)	PUNCT
hjic-704	77	21	of	of	ADP
hjic-704	77	22	ref	ref	NOUN
hjic-704	77	23	.	.	PUNCT
hjic-704	78	1	[	[	X
hjic-704	78	2	15	15	NUM
hjic-704	78	3	]	]	PUNCT
hjic-704	78	4	,	,	PUNCT
hjic-704	78	5	respectively	respectively	ADV
hjic-704	78	6	.	.	PUNCT
hjic-704	79	1	𝜗	𝜗	X
hjic-704	79	2	∙	∙	PROPN
hjic-704	79	3	denotes	denote	VERB
hjic-704	79	4	the	the	DET
hjic-704	79	5	corner	corner	NOUN
hjic-704	79	6	points	point	NOUN
hjic-704	79	7	(	(	PUNCT
hjic-704	79	8	vertices	vertex	NOUN
hjic-704	79	9	)	)	PUNCT
hjic-704	79	10	of	of	ADP
hjic-704	79	11	a	a	DET
hjic-704	79	12	given	give	VERB
hjic-704	79	13	polytope	polytope	NOUN
hjic-704	79	14	.	.	PUNCT
hjic-704	80	1	since	since	SCONJ
hjic-704	80	2	the	the	DET
hjic-704	80	3	lyapunov	lyapunov	ADJ
hjic-704	80	4	conditions	condition	NOUN
hjic-704	80	5	are	be	AUX
hjic-704	80	6	satisfied	satisfied	ADJ
hjic-704	80	7	within	within	ADP
hjic-704	80	8	𝒳	𝒳	PROPN
hjic-704	80	9	,	,	PUNCT
hjic-704	80	10	an	an	DET
hjic-704	80	11	attempt	attempt	NOUN
hjic-704	80	12	is	be	AUX
hjic-704	80	13	made	make	VERB
hjic-704	80	14	to	to	PART
hjic-704	80	15	identify	identify	VERB
hjic-704	80	16	the	the	DET
hjic-704	80	17	maximal	maximal	ADJ
hjic-704	80	18	α	α	NOUN
hjic-704	80	19	-	-	PUNCT
hjic-704	80	20	level	level	NOUN
hjic-704	80	21	set	set	NOUN
hjic-704	80	22	ε	ε	PROPN
hjic-704	80	23	!	!	PUNCT
hjic-704	80	24	=	=	PUNCT
hjic-704	81	1	𝑥	𝑥	DET
hjic-704	81	2	∈	∈	NOUN
hjic-704	81	3	𝒳|𝑉	𝒳|𝑉	NOUN
hjic-704	81	4	𝑥	𝑥	NOUN
hjic-704	81	5	=	=	SYM
hjic-704	81	6	𝛼	𝛼	NOUN
hjic-704	81	7	,	,	PUNCT
hjic-704	81	8	1	1	NUM
hjic-704	81	9	≤	≤	NUM
hjic-704	81	10	𝛼	𝛼	NOUN
hjic-704	81	11	,	,	PUNCT
hjic-704	81	12	which	which	PRON
hjic-704	81	13	lies	lie	VERB
hjic-704	81	14	inside	inside	ADP
hjic-704	81	15	𝒳.	𝒳.	PROPN
hjic-704	81	16	that	that	DET
hjic-704	81	17	level	level	NOUN
hjic-704	81	18	set	set	NOUN
hjic-704	81	19	will	will	AUX
hjic-704	81	20	be	be	AUX
hjic-704	81	21	invariant	invariant	ADJ
hjic-704	81	22	,	,	PUNCT
hjic-704	81	23	in	in	ADP
hjic-704	81	24	the	the	DET
hjic-704	81	25	sense	sense	NOUN
hjic-704	81	26	that	that	SCONJ
hjic-704	81	27	every	every	DET
hjic-704	81	28	trajectory	trajectory	NOUN
hjic-704	81	29	entering	enter	VERB
hjic-704	81	30	this	this	DET
hjic-704	81	31	region	region	NOUN
hjic-704	81	32	will	will	AUX
hjic-704	81	33	never	never	ADV
hjic-704	81	34	leave	leave	VERB
hjic-704	81	35	it	it	PRON
hjic-704	81	36	.	.	PUNCT
hjic-704	82	1	α	α	PRON
hjic-704	82	2	≥	≥	NUM
hjic-704	82	3	1is	1is	ADV
hjic-704	82	4	defined	define	VERB
hjic-704	82	5	,	,	PUNCT
hjic-704	82	6	as	as	ADP
hjic-704	82	7	a	a	DET
hjic-704	82	8	free	free	ADJ
hjic-704	82	9	variable	variable	NOUN
hjic-704	82	10	of	of	ADP
hjic-704	82	11	the	the	DET
hjic-704	82	12	optimization	optimization	NOUN
hjic-704	82	13	task	task	NOUN
hjic-704	82	14	,	,	PUNCT
hjic-704	82	15	and	and	CCONJ
hjic-704	82	16	𝜀	𝜀	AUX
hjic-704	82	17	!	!	PROPN
hjic-704	82	18	is	be	AUX
hjic-704	82	19	constrained	constrain	VERB
hjic-704	82	20	inside	inside	ADP
hjic-704	82	21	𝒳.	𝒳.	PROPN
hjic-704	82	22	one	one	NUM
hjic-704	82	23	can	can	AUX
hjic-704	82	24	observe	observe	VERB
hjic-704	82	25	that	that	SCONJ
hjic-704	82	26	by	by	ADP
hjic-704	82	27	maximizing	maximize	VERB
hjic-704	82	28	α	α	PRON
hjic-704	82	29	an	an	DET
hjic-704	82	30	unbounded	unbounded	ADJ
hjic-704	82	31	feasible	feasible	ADJ
hjic-704	82	32	solution	solution	NOUN
hjic-704	82	33	is	be	AUX
hjic-704	82	34	obtained	obtain	VERB
hjic-704	82	35	,	,	PUNCT
hjic-704	82	36	as	as	SCONJ
hjic-704	82	37	the	the	DET
hjic-704	82	38	function	function	NOUN
hjic-704	82	39	v(x	v(x	PROPN
hjic-704	82	40	,	,	PUNCT
hjic-704	82	41	δ	δ	PROPN
hjic-704	82	42	)	)	PUNCT
hjic-704	82	43	can	can	AUX
hjic-704	82	44	be	be	AUX
hjic-704	82	45	scaled	scale	VERB
hjic-704	82	46	arbitrarily	arbitrarily	ADV
hjic-704	82	47	.	.	PUNCT
hjic-704	83	1	therefore	therefore	ADV
hjic-704	83	2	,	,	PUNCT
hjic-704	83	3	as	as	ADP
hjic-704	83	4	fig.1	fig.1	ADJ
hjic-704	83	5	illustrates	illustrate	NOUN
hjic-704	83	6	,	,	PUNCT
hjic-704	83	7	an	an	DET
hjic-704	83	8	auxiliary	auxiliary	ADJ
hjic-704	83	9	polytope	polytope	NOUN
hjic-704	83	10	𝒴	𝒴	PROPN
hjic-704	83	11	is	be	AUX
hjic-704	83	12	defined	define	VERB
hjic-704	83	13	around	around	ADP
hjic-704	83	14	the	the	DET
hjic-704	83	15	locally	locally	ADV
hjic-704	83	16	stable	stable	ADJ
hjic-704	83	17	origin	origin	NOUN
hjic-704	83	18	inside	inside	ADP
hjic-704	83	19	𝒳	𝒳	PROPN
hjic-704	83	20	,	,	PUNCT
hjic-704	83	21	constraining	constrain	VERB
hjic-704	83	22	the	the	DET
hjic-704	83	23	1	1	NUM
hjic-704	83	24	-	-	PUNCT
hjic-704	83	25	level	level	NOUN
hjic-704	83	26	set	set	NOUN
hjic-704	83	27	𝜀	𝜀	NOUN
hjic-704	83	28	!	!	PUNCT
hjic-704	83	29	=	=	PUNCT
hjic-704	84	1	𝑥	𝑥	DET
hjic-704	84	2	∈	∈	NOUN
hjic-704	84	3	𝒳|𝑉	𝒳|𝑉	NOUN
hjic-704	84	4	𝑥	𝑥	NOUN
hjic-704	84	5	=	=	SYM
hjic-704	84	6	1	1	NUM
hjic-704	84	7	to	to	PART
hjic-704	84	8	be	be	AUX
hjic-704	84	9	around	around	ADP
hjic-704	84	10	𝒴.	𝒴.	NOUN
hjic-704	84	11	according	accord	VERB
hjic-704	84	12	to	to	ADP
hjic-704	84	13	finsler	finsler	NOUN
hjic-704	84	14	’s	’s	PART
hjic-704	84	15	lemma	lemma	PROPN
hjic-704	84	16	,	,	PUNCT
hjic-704	84	17	for	for	ADP
hjic-704	84	18	every	every	DET
hjic-704	84	19	𝑘	𝑘	PROPN
hjic-704	84	20	=	=	SYM
hjic-704	84	21	1,𝑀𝒳	1,𝑀𝒳	PROPN
hjic-704	84	22	and	and	CCONJ
hjic-704	84	23	𝑙	𝑙	NOUN
hjic-704	84	24	=	=	SYM
hjic-704	84	25	1,𝑀𝒴	1,𝑀𝒴	NOUN
hjic-704	84	26	,	,	PUNCT
hjic-704	84	27	if	if	SCONJ
hjic-704	84	28	real	real	ADV
hjic-704	84	29	-	-	PUNCT
hjic-704	84	30	valued	value	VERB
hjic-704	84	31	matrices	matrix	NOUN
hjic-704	84	32	𝐿	𝐿	PROPN
hjic-704	84	33	!	!	PROPN
hjic-704	84	34	!	!	PUNCT
hjic-704	84	35	,	,	PUNCT
hjic-704	85	1	𝐿	𝐿	PROPN
hjic-704	85	2	!	!	PUNCT
hjic-704	85	3	!	!	PUNCT
hjic-704	86	1	∈	∈	PROPN
hjic-704	86	2	ℝ	ℝ	NOUN
hjic-704	86	3	!	!	PUNCT
hjic-704	87	1	×	×	NOUN
hjic-704	87	2	!	!	PROPN
hjic-704	87	3	,	,	PUNCT
hjic-704	87	4	𝑀	𝑀	PROPN
hjic-704	87	5	!	!	PUNCT
hjic-704	87	6	!	!	PUNCT
hjic-704	88	1	,	,	PUNCT
hjic-704	88	2	𝑀	𝑀	PROPN
hjic-704	88	3	!	!	PUNCT
hjic-704	88	4	!	!	PUNCT
hjic-704	89	1	∈	∈	PROPN
hjic-704	89	2	ℝ	ℝ	PROPN
hjic-704	89	3	(	(	PUNCT
hjic-704	89	4	!	!	PUNCT
hjic-704	89	5	!	!	PUNCT
hjic-704	89	6	!	!	PUNCT
hjic-704	89	7	)	)	PUNCT
hjic-704	90	1	×	×	NOUN
hjic-704	90	2	!	!	PUNCT
hjic-704	90	3	exit	exit	NOUN
hjic-704	90	4	𝑄!!𝑃	𝑄!!𝑃	NOUN
hjic-704	90	5	!	!	PUNCT
hjic-704	90	6	!	!	PUNCT
hjic-704	91	1	(	(	PUNCT
hjic-704	91	2	!	!	PUNCT
hjic-704	91	3	)	)	PUNCT
hjic-704	92	1	𝑥	𝑥	X
hjic-704	92	2	,	,	PUNCT
hjic-704	92	3	δ	δ	PROPN
hjic-704	92	4	𝑄	𝑄	PROPN
hjic-704	92	5	!	!	PUNCT
hjic-704	93	1	≥	≥	NOUN
hjic-704	93	2	0	0	NUM
hjic-704	93	3	∀	∀	NOUN
hjic-704	94	1	𝑥	𝑥	NOUN
hjic-704	94	2	,	,	PUNCT
hjic-704	94	3	δ	δ	PROPN
hjic-704	94	4	∈	∈	PROPN
hjic-704	94	5	𝜗	𝜗	X
hjic-704	94	6	ℱ!𝒳×𝒟	ℱ!𝒳×𝒟	PUNCT
hjic-704	94	7	(	(	PUNCT
hjic-704	94	8	7	7	NUM
hjic-704	94	9	)	)	PUNCT
hjic-704	94	10	𝑄!!𝑃	𝑄!!𝑃	NOUN
hjic-704	94	11	!	!	PUNCT
hjic-704	94	12	!	!	PUNCT
hjic-704	95	1	(	(	PUNCT
hjic-704	95	2	!	!	PUNCT
hjic-704	95	3	)	)	PUNCT
hjic-704	96	1	𝑥	𝑥	X
hjic-704	96	2	,	,	PUNCT
hjic-704	96	3	δ	δ	PROPN
hjic-704	96	4	𝑄	𝑄	PROPN
hjic-704	96	5	!	!	PUNCT
hjic-704	97	1	≤	≤	ADV
hjic-704	97	2	0	0	NUM
hjic-704	97	3	∀	∀	NOUN
hjic-704	97	4	𝑥	𝑥	NOUN
hjic-704	97	5	,	,	PUNCT
hjic-704	97	6	δ	δ	PROPN
hjic-704	97	7	∈	∈	PROPN
hjic-704	97	8	𝜗	𝜗	X
hjic-704	97	9	ℱ	ℱ	PROPN
hjic-704	97	10	!	!	PUNCT
hjic-704	98	1	𝒴×𝒟	𝒴×𝒟	PROPN
hjic-704	98	2	(	(	PUNCT
hjic-704	98	3	8)	8)	NUM
hjic-704	98	4	then	then	ADV
hjic-704	98	5	𝜀	𝜀	PROPN
hjic-704	98	6	!	!	PROPN
hjic-704	98	7	is	be	AUX
hjic-704	98	8	inside	inside	ADP
hjic-704	98	9	𝒳	𝒳	PROPN
hjic-704	98	10	and	and	CCONJ
hjic-704	98	11	𝜀	𝜀	PROPN
hjic-704	98	12	!	!	PROPN
hjic-704	98	13	is	be	AUX
hjic-704	98	14	around	around	ADP
hjic-704	98	15	𝒴.	𝒴.	NOUN
hjic-704	98	16	variables	variable	NOUN
hjic-704	98	17	𝑄	𝑄	PROPN
hjic-704	98	18	!	!	PUNCT
hjic-704	98	19	,	,	PUNCT
hjic-704	99	1	𝑄	𝑄	PROPN
hjic-704	99	2	!	!	PUNCT
hjic-704	99	3	,	,	PUNCT
hjic-704	99	4	𝑃	𝑃	PROPN
hjic-704	99	5	!	!	PUNCT
hjic-704	99	6	!	!	PUNCT
hjic-704	100	1	(	(	PUNCT
hjic-704	100	2	!	!	PUNCT
hjic-704	100	3	)	)	PUNCT
hjic-704	100	4	,	,	PUNCT
hjic-704	100	5	and	and	CCONJ
hjic-704	100	6	𝑃	𝑃	NOUN
hjic-704	100	7	!	!	PUNCT
hjic-704	100	8	!	!	PUNCT
hjic-704	101	1	(	(	PUNCT
hjic-704	101	2	!	!	PUNCT
hjic-704	101	3	)	)	PUNCT
hjic-704	101	4	are	be	AUX
hjic-704	101	5	defined	define	VERB
hjic-704	101	6	in	in	ADP
hjic-704	101	7	eqs.(3.34	eqs.(3.34	NOUN
hjic-704	101	8	)	)	PUNCT
hjic-704	101	9	and	and	CCONJ
hjic-704	101	10	(	(	PUNCT
hjic-704	101	11	3.36	3.36	NUM
hjic-704	101	12	)	)	PUNCT
hjic-704	101	13	of	of	ADP
hjic-704	101	14	ref	ref	NOUN
hjic-704	101	15	.	.	PUNCT
hjic-704	102	1	[	[	X
hjic-704	102	2	15	15	NUM
hjic-704	102	3	]	]	PUNCT
hjic-704	102	4	,	,	PUNCT
hjic-704	102	5	ℱ!𝒳	ℱ!𝒳	PROPN
hjic-704	102	6	denotes	denote	VERB
hjic-704	102	7	the	the	DET
hjic-704	102	8	kth	kth	PROPN
hjic-704	102	9	facet	facet	PROPN
hjic-704	102	10	of	of	ADP
hjic-704	102	11	𝒳	𝒳	PROPN
hjic-704	102	12	,	,	PUNCT
hjic-704	102	13	furthermore	furthermore	ADV
hjic-704	102	14	,	,	PUNCT
hjic-704	102	15	𝑀𝒳	𝑀𝒳	PROPN
hjic-704	102	16	denotes	denote	VERB
hjic-704	102	17	the	the	DET
hjic-704	102	18	number	number	NOUN
hjic-704	102	19	of	of	ADP
hjic-704	102	20	facets	facet	NOUN
hjic-704	102	21	of	of	ADP
hjic-704	102	22	𝒳.	𝒳.	PROPN
hjic-704	102	23	the	the	DET
hjic-704	102	24	lmi	lmi	PROPN
hjic-704	102	25	conditions	condition	NOUN
hjic-704	102	26	of	of	ADP
hjic-704	102	27	eqs.(5)-(8	eqs.(5)-(8	X
hjic-704	102	28	)	)	PUNCT
hjic-704	102	29	are	be	AUX
hjic-704	102	30	affine	affine	NOUN
hjic-704	102	31	parameter	parameter	NOUN
hjic-704	102	32	-	-	PUNCT
hjic-704	102	33	dependent	dependent	ADJ
hjic-704	102	34	lmis	lmis	ADJ
hjic-704	102	35	,	,	PUNCT
hjic-704	102	36	which	which	PRON
hjic-704	102	37	can	can	AUX
hjic-704	102	38	be	be	AUX
hjic-704	102	39	computationally	computationally	ADV
hjic-704	102	40	handled	handle	VERB
hjic-704	102	41	by	by	ADP
hjic-704	102	42	checking	check	VERB
hjic-704	102	43	their	their	PRON
hjic-704	102	44	feasibility	feasibility	NOUN
hjic-704	102	45	at	at	ADP
hjic-704	102	46	the	the	DET
hjic-704	102	47	corner	corner	NOUN
hjic-704	102	48	points	point	NOUN
hjic-704	102	49	of	of	ADP
hjic-704	102	50	the	the	DET
hjic-704	102	51	polytopic	polytopic	NOUN
hjic-704	102	52	region	region	NOUN
hjic-704	102	53	,	,	PUNCT
hjic-704	102	54	on	on	ADP
hjic-704	102	55	which	which	PRON
hjic-704	102	56	the	the	DET
hjic-704	102	57	parameters	parameter	NOUN
hjic-704	102	58	𝑥	𝑥	PROPN
hjic-704	102	59	,	,	PUNCT
hjic-704	102	60	δ	δ	PROPN
hjic-704	102	61	,	,	PUNCT
hjic-704	102	62	δ	δ	PROPN
hjic-704	102	63	are	be	AUX
hjic-704	102	64	defined	define	VERB
hjic-704	102	65	.	.	PUNCT
hjic-704	103	1	depending	depend	VERB
hjic-704	103	2	on	on	ADP
hjic-704	103	3	the	the	DET
hjic-704	103	4	number	number	NOUN
hjic-704	103	5	of	of	ADP
hjic-704	103	6	the	the	DET
hjic-704	103	7	corner	corner	NOUN
hjic-704	103	8	points	point	NOUN
hjic-704	103	9	,	,	PUNCT
hjic-704	103	10	a	a	DET
hjic-704	103	11	given	give	VERB
hjic-704	103	12	number	number	NOUN
hjic-704	103	13	of	of	ADP
hjic-704	103	14	parameter	parameter	NOUN
hjic-704	103	15	independent	independent	PROPN
hjic-704	103	16	lmi	lmi	PROPN
hjic-704	103	17	conditions	condition	NOUN
hjic-704	103	18	(	(	PUNCT
hjic-704	103	19	table	table	NOUN
hjic-704	103	20	1	1	NUM
hjic-704	103	21	)	)	PUNCT
hjic-704	103	22	is	be	AUX
hjic-704	103	23	obtained	obtain	VERB
hjic-704	103	24	.	.	PUNCT
hjic-704	104	1	the	the	DET
hjic-704	104	2	sdp	sdp	NOUN
hjic-704	104	3	task	task	NOUN
hjic-704	104	4	can	can	AUX
hjic-704	104	5	be	be	AUX
hjic-704	104	6	summarized	summarize	VERB
hjic-704	104	7	as	as	SCONJ
hjic-704	104	8	follows	follow	VERB
hjic-704	104	9	.	.	PUNCT
hjic-704	105	1	in	in	ADP
hjic-704	105	2	order	order	NOUN
hjic-704	105	3	to	to	PART
hjic-704	105	4	find	find	VERB
hjic-704	105	5	the	the	DET
hjic-704	105	6	maximal	maximal	ADJ
hjic-704	105	7	invariant	invariant	ADJ
hjic-704	105	8	level	level	NOUN
hjic-704	105	9	set	set	VERB
hjic-704	105	10	𝜀	𝜀	PROPN
hjic-704	105	11	!	!	PROPN
hjic-704	105	12	of	of	ADP
hjic-704	105	13	the	the	DET
hjic-704	105	14	lyapunov	lyapunov	ADJ
hjic-704	105	15	function	function	NOUN
hjic-704	105	16	,	,	PUNCT
hjic-704	105	17	one	one	PRON
hjic-704	105	18	should	should	AUX
hjic-704	105	19	maximize	maximize	VERB
hjic-704	105	20	α	α	NOUN
hjic-704	105	21	,	,	PUNCT
hjic-704	105	22	under	under	ADP
hjic-704	105	23	the	the	DET
hjic-704	105	24	following	following	ADJ
hjic-704	105	25	conditions	condition	NOUN
hjic-704	105	26	:	:	PUNCT
hjic-704	105	27	eq.(5	eq.(5	NOUN
hjic-704	105	28	)	)	PUNCT
hjic-704	105	29	𝑉	𝑉	PROPN
hjic-704	105	30	𝑥	𝑥	PROPN
hjic-704	105	31	,	,	PUNCT
hjic-704	105	32	δ	δ	PROPN
hjic-704	105	33	is	be	AUX
hjic-704	105	34	positive	positive	ADJ
hjic-704	105	35	on	on	ADP
hjic-704	105	36	𝒳×𝒟	𝒳×𝒟	PROPN
hjic-704	105	37	eq.(6	eq.(6	X
hjic-704	105	38	)	)	PUNCT
hjic-704	105	39	𝑉	𝑉	PROPN
hjic-704	105	40	𝑥	𝑥	PROPN
hjic-704	105	41	,	,	PUNCT
hjic-704	105	42	δ	δ	PROPN
hjic-704	105	43	,	,	PUNCT
hjic-704	105	44	δ	δ	PROPN
hjic-704	105	45	is	be	AUX
hjic-704	105	46	negative	negative	ADJ
hjic-704	105	47	on	on	ADP
hjic-704	105	48	𝒳×𝒟×𝒟	𝒳×𝒟×𝒟	NOUN
hjic-704	105	49	eq.(7	eq.(7	NOUN
hjic-704	105	50	)	)	PUNCT
hjic-704	105	51	𝜀	𝜀	AUX
hjic-704	105	52	!	!	PROPN
hjic-704	105	53	lies	lie	NOUN
hjic-704	105	54	inside	inside	ADP
hjic-704	105	55	𝒳	𝒳	PROPN
hjic-704	105	56	eq.(8	eq.(8	ADV
hjic-704	105	57	)	)	PUNCT
hjic-704	106	1	𝒴	𝒴	PROPN
hjic-704	106	2	is	be	AUX
hjic-704	106	3	inside	inside	ADP
hjic-704	106	4	𝜀	𝜀	NOUN
hjic-704	106	5	!	!	PUNCT
hjic-704	107	1	the	the	DET
hjic-704	107	2	number	number	NOUN
hjic-704	107	3	of	of	ADP
hjic-704	107	4	lmis	lmis	ADJ
hjic-704	107	5	and	and	CCONJ
hjic-704	107	6	their	their	PRON
hjic-704	107	7	dimensions	dimension	NOUN
hjic-704	107	8	are	be	AUX
hjic-704	107	9	given	give	VERB
hjic-704	107	10	in	in	ADP
hjic-704	107	11	table	table	NOUN
hjic-704	107	12	1	1	NUM
hjic-704	107	13	,	,	PUNCT
hjic-704	107	14	furthermore	furthermore	ADV
hjic-704	107	15	,	,	PUNCT
hjic-704	107	16	the	the	DET
hjic-704	107	17	free	free	ADJ
hjic-704	107	18	variables	variable	NOUN
hjic-704	107	19	of	of	ADP
hjic-704	107	20	the	the	DET
hjic-704	107	21	optimization	optimization	NOUN
hjic-704	107	22	task	task	NOUN
hjic-704	107	23	are	be	AUX
hjic-704	107	24	listed	list	VERB
hjic-704	107	25	in	in	ADP
hjic-704	107	26	table	table	NOUN
hjic-704	107	27	2	2	NUM
hjic-704	107	28	.	.	PUNCT
hjic-704	107	29	figure	figure	NOUN
hjic-704	107	30	1	1	NUM
hjic-704	107	31	.	.	PUNCT
hjic-704	107	32	illustration	illustration	NOUN
hjic-704	107	33	of	of	ADP
hjic-704	107	34	the	the	DET
hjic-704	107	35	conditions	condition	NOUN
hjic-704	107	36	regarding	regard	VERB
hjic-704	107	37	𝒳	𝒳	PROPN
hjic-704	107	38	and	and	CCONJ
hjic-704	107	39	𝒴	𝒴	PROPN
hjic-704	107	40	.	.	PUNCT
hjic-704	108	1	inside	inside	ADP
hjic-704	108	2	polytope	polytope	NOUN
hjic-704	108	3	𝒳	𝒳	PROPN
hjic-704	108	4	of	of	ADP
hjic-704	108	5	the	the	DET
hjic-704	108	6	lyapunov	lyapunov	ADJ
hjic-704	108	7	conditions	condition	NOUN
hjic-704	108	8	in	in	ADP
hjic-704	108	9	eq.(2	eq.(2	ADJ
hjic-704	108	10	)	)	PUNCT
hjic-704	108	11	are	be	AUX
hjic-704	108	12	required	require	VERB
hjic-704	108	13	.	.	PUNCT
hjic-704	109	1	the	the	DET
hjic-704	109	2	α	α	NOUN
hjic-704	109	3	-	-	PUNCT
hjic-704	109	4	level	level	NOUN
hjic-704	109	5	set	set	VERB
hjic-704	109	6	ε	ε	PROPN
hjic-704	109	7	!	!	PROPN
hjic-704	109	8	of	of	ADP
hjic-704	109	9	the	the	DET
hjic-704	109	10	lyapunov	lyapunov	ADJ
hjic-704	109	11	function	function	NOUN
hjic-704	109	12	should	should	AUX
hjic-704	109	13	lie	lie	VERB
hjic-704	109	14	inside	inside	ADP
hjic-704	109	15	polytope	polytope	NOUN
hjic-704	109	16	𝒳	𝒳	PROPN
hjic-704	109	17	(	(	PUNCT
hjic-704	109	18	hence	hence	ADV
hjic-704	109	19	it	it	PRON
hjic-704	109	20	is	be	AUX
hjic-704	109	21	invariant	invariant	ADJ
hjic-704	109	22	)	)	PUNCT
hjic-704	109	23	.	.	PUNCT
hjic-704	110	1	the	the	DET
hjic-704	110	2	1	1	NUM
hjic-704	110	3	-	-	PUNCT
hjic-704	110	4	level	level	NOUN
hjic-704	110	5	set	set	NOUN
hjic-704	110	6	ε1	ε1	NOUN
hjic-704	110	7	should	should	AUX
hjic-704	110	8	be	be	AUX
hjic-704	110	9	around	around	ADP
hjic-704	110	10	polytope	polytope	NOUN
hjic-704	110	11	𝒴.	𝒴.	PROPN
hjic-704	110	12	this	this	DET
hjic-704	110	13	condition	condition	NOUN
hjic-704	110	14	ensures	ensure	VERB
hjic-704	110	15	that	that	SCONJ
hjic-704	110	16	the	the	DET
hjic-704	110	17	problem	problem	NOUN
hjic-704	110	18	has	have	VERB
hjic-704	110	19	a	a	DET
hjic-704	110	20	bounded	bounded	ADJ
hjic-704	110	21	solution	solution	NOUN
hjic-704	110	22	.	.	PUNCT
hjic-704	111	1	table	table	NOUN
hjic-704	111	2	2	2	NUM
hjic-704	111	3	.	.	PUNCT
hjic-704	111	4	free	free	ADJ
hjic-704	111	5	variables	variable	NOUN
hjic-704	111	6	of	of	ADP
hjic-704	111	7	the	the	DET
hjic-704	111	8	optimization	optimization	NOUN
hjic-704	111	9	task	task	NOUN
hjic-704	111	10	and	and	CCONJ
hjic-704	111	11	the	the	DET
hjic-704	111	12	number	number	NOUN
hjic-704	111	13	of	of	ADP
hjic-704	111	14	(	(	PUNCT
hjic-704	111	15	scalar	scalar	ADJ
hjic-704	111	16	)	)	PUNCT
hjic-704	111	17	symbolic	symbolic	ADJ
hjic-704	111	18	decision	decision	NOUN
hjic-704	111	19	variables	variable	NOUN
hjic-704	111	20	they	they	PRON
hjic-704	111	21	introduce	introduce	VERB
hjic-704	111	22	into	into	ADP
hjic-704	111	23	the	the	DET
hjic-704	111	24	optimization	optimization	NOUN
hjic-704	111	25	task	task	NOUN
hjic-704	111	26	.	.	PUNCT
hjic-704	112	1	matrix	matrix	NOUN
hjic-704	112	2	variable	variable	ADJ
hjic-704	112	3	number	number	NOUN
hjic-704	112	4	of	of	ADP
hjic-704	112	5	(	(	PUNCT
hjic-704	112	6	scalar	scalar	ADJ
hjic-704	112	7	)	)	PUNCT
hjic-704	112	8	independent	independent	ADJ
hjic-704	112	9	decision	decision	NOUN
hjic-704	112	10	variables	variable	NOUN
hjic-704	112	11	appearing	appear	VERB
hjic-704	112	12	in	in	ADP
hjic-704	112	13	the	the	DET
hjic-704	112	14	sdp	sdp	NOUN
hjic-704	112	15	α	α	NOUN
hjic-704	112	16	1	1	NUM
hjic-704	112	17	p	p	NOUN
hjic-704	112	18	½	½	NOUN
hjic-704	112	19	m(m+1	m(m+1	X
hjic-704	112	20	)	)	PUNCT
hjic-704	112	21	lb	lb	NUM
hjic-704	112	22	mq	mq	PROPN
hjic-704	112	23	la	la	PROPN
hjic-704	112	24	(	(	PUNCT
hjic-704	112	25	n	n	PROPN
hjic-704	112	26	+	+	CCONJ
hjic-704	112	27	2p	2p	NUM
hjic-704	112	28	+	+	CCONJ
hjic-704	112	29	n2	n2	ADJ
hjic-704	112	30	+	+	CCONJ
hjic-704	112	31	np)(2q	np)(2q	ADJ
hjic-704	112	32	+	+	CCONJ
hjic-704	112	33	n2	n2	ADJ
hjic-704	112	34	+	+	CCONJ
hjic-704	112	35	nq	nq	PROPN
hjic-704	112	36	)	)	PUNCT
hjic-704	112	37	𝐿!!and	𝐿!!and	PRON
hjic-704	112	38	𝐿	𝐿	PROPN
hjic-704	112	39	!	!	PUNCT
hjic-704	112	40	!	!	PUNCT
hjic-704	112	41	!	!	PUNCT
hjic-704	112	42	!	!	PUNCT
hjic-704	113	1	𝑀𝒳	𝑀𝒳	PROPN
hjic-704	114	1	+	+	NOUN
hjic-704	114	2	𝑀𝒴!×𝑚𝑞	𝑀𝒴!×𝑚𝑞	PROPN
hjic-704	114	3	𝑀!!and	𝑀!!and	PROPN
hjic-704	114	4	𝑀	𝑀	PROPN
hjic-704	114	5	!	!	PUNCT
hjic-704	114	6	!	!	PUNCT
hjic-704	114	7	!	!	PUNCT
hjic-704	115	1	!	!	PUNCT
hjic-704	116	1	𝑀𝒳	𝑀𝒳	PROPN
hjic-704	117	1	+	+	NOUN
hjic-704	117	2	𝑀𝒴!×(𝑚	𝑀𝒴!×(𝑚	PROPN
hjic-704	117	3	+	+	CCONJ
hjic-704	117	4	1)𝑛	1)𝑛	NUM
hjic-704	117	5	the	the	DET
hjic-704	117	6	dimensional	dimensional	ADJ
hjic-704	117	7	parameters	parameter	NOUN
hjic-704	117	8	are	be	AUX
hjic-704	117	9	the	the	DET
hjic-704	117	10	following	following	NOUN
hjic-704	117	11	:	:	PUNCT
hjic-704	117	12	n	n	DET
hjic-704	117	13	number	number	NOUN
hjic-704	117	14	of	of	ADP
hjic-704	117	15	state	state	NOUN
hjic-704	117	16	variables	variable	NOUN
hjic-704	117	17	(	(	PUNCT
hjic-704	117	18	size	size	NOUN
hjic-704	117	19	of	of	ADP
hjic-704	117	20	x	x	NOUN
hjic-704	117	21	)	)	PUNCT
hjic-704	117	22	p	p	ADJ
hjic-704	117	23	number	number	NOUN
hjic-704	117	24	of	of	ADP
hjic-704	117	25	elements	element	NOUN
hjic-704	117	26	in	in	ADP
hjic-704	117	27	π	π	PROPN
hjic-704	117	28	m	m	NOUN
hjic-704	117	29	number	number	NOUN
hjic-704	117	30	of	of	ADP
hjic-704	117	31	elements	element	NOUN
hjic-704	117	32	in	in	ADP
hjic-704	117	33	πb	πb	PRON
hjic-704	117	34	(	(	PUNCT
hjic-704	117	35	n	n	PROPN
hjic-704	117	36	+	+	X
hjic-704	117	37	p	p	X
hjic-704	117	38	)	)	PUNCT
hjic-704	117	39	q	q	NOUN
hjic-704	117	40	number	number	NOUN
hjic-704	117	41	of	of	ADP
hjic-704	117	42	rows	row	NOUN
hjic-704	117	43	in	in	ADP
hjic-704	117	44	annihilator	annihilator	PROPN
hjic-704	117	45	𝒩!!(𝑥	𝒩!!(𝑥	PROPN
hjic-704	117	46	,	,	PUNCT
hjic-704	117	47	δ	δ	PROPN
hjic-704	117	48	)	)	PUNCT
hjic-704	117	49	𝑀𝒳	𝑀𝒳	PROPN
hjic-704	117	50	number	number	NOUN
hjic-704	117	51	of	of	ADP
hjic-704	117	52	corner	corner	NOUN
hjic-704	117	53	points	point	NOUN
hjic-704	117	54	of	of	ADP
hjic-704	117	55	𝒳	𝒳	PRON
hjic-704	117	56	𝑀𝒴	𝑀𝒴	NOUN
hjic-704	117	57	number	number	NOUN
hjic-704	117	58	of	of	ADP
hjic-704	117	59	corner	corner	NOUN
hjic-704	117	60	points	point	NOUN
hjic-704	117	61	of	of	ADP
hjic-704	117	62	𝒴	𝒴	NOUN
hjic-704	117	63	𝑀𝒟	𝑀𝒟	ADJ
hjic-704	117	64	number	number	NOUN
hjic-704	117	65	of	of	ADP
hjic-704	117	66	corner	corner	NOUN
hjic-704	117	67	points	point	NOUN
hjic-704	117	68	of	of	ADP
hjic-704	117	69	𝒟	𝒟	NOUN
hjic-704	117	70	𝑀𝒟	𝑀𝒟	PROPN
hjic-704	117	71	!	!	PUNCT
hjic-704	117	72	number	number	NOUN
hjic-704	117	73	of	of	ADP
hjic-704	117	74	corner	corner	NOUN
hjic-704	117	75	points	point	NOUN
hjic-704	117	76	of	of	ADP
hjic-704	117	77	𝒟	𝒟	NOUN
hjic-704	117	78	!	!	PUNCT
hjic-704	117	79	table	table	NOUN
hjic-704	117	80	1	1	NUM
hjic-704	117	81	.	.	X
hjic-704	117	82	number	number	NOUN
hjic-704	117	83	and	and	CCONJ
hjic-704	117	84	dimensions	dimension	NOUN
hjic-704	117	85	of	of	ADP
hjic-704	117	86	parameter	parameter	NOUN
hjic-704	117	87	independent	independent	ADJ
hjic-704	117	88	lmis	lmis	NOUN
hjic-704	117	89	of	of	ADP
hjic-704	117	90	the	the	DET
hjic-704	117	91	optimization	optimization	NOUN
hjic-704	117	92	task	task	NOUN
hjic-704	117	93	.	.	PUNCT
hjic-704	118	1	dimension	dimension	NOUN
hjic-704	118	2	of	of	ADP
hjic-704	118	3	the	the	DET
hjic-704	118	4	lmis	lmis	ADJ
hjic-704	118	5	no	no	PROPN
hjic-704	118	6	.	.	PUNCT
hjic-704	118	7	of	of	ADP
hjic-704	118	8	lmis	lmis	ADJ
hjic-704	118	9	eq.(5	eq.(5	NOUN
hjic-704	118	10	)	)	PUNCT
hjic-704	118	11	m	m	PROPN
hjic-704	118	12	𝑀𝒳	𝑀𝒳	NOUN
hjic-704	118	13	∙𝑀𝒟	∙𝑀𝒟	PUNCT
hjic-704	118	14	eq.(6	eq.(6	NOUN
hjic-704	118	15	)	)	PUNCT
hjic-704	118	16	n	n	PROPN
hjic-704	118	17	+	+	CCONJ
hjic-704	118	18	2p	2p	NUM
hjic-704	118	19	+	+	CCONJ
hjic-704	118	20	n2	n2	ADJ
hjic-704	118	21	+	+	CCONJ
hjic-704	118	22	np	np	INTJ
hjic-704	118	23	𝑀𝒳	𝑀𝒳	NOUN
hjic-704	118	24	∙𝑀𝒟	∙𝑀𝒟	PUNCT
hjic-704	118	25	∙𝑀𝒟	∙𝑀𝒟	PROPN
hjic-704	118	26	!	!	PUNCT
hjic-704	119	1	eq.(7	eq.(7	NOUN
hjic-704	119	2	)	)	PUNCT
hjic-704	120	1	m	m	VERB
hjic-704	120	2	+	+	ADJ
hjic-704	120	3	1	1	NUM
hjic-704	120	4	2𝑀𝒳	2𝑀𝒳	NUM
hjic-704	120	5	∙𝑀𝒟	∙𝑀𝒟	PROPN
hjic-704	120	6	eq.(8	eq.(8	X
hjic-704	120	7	)	)	PUNCT
hjic-704	121	1	m	m	VERB
hjic-704	121	2	+	+	ADJ
hjic-704	121	3	1	1	NUM
hjic-704	121	4	2𝑀𝒴	2𝑀𝒴	NUM
hjic-704	121	5	∙𝑀𝒟	∙𝑀𝒟	PUNCT
hjic-704	121	6	figure	figure	NOUN
hjic-704	121	7	2	2	NUM
hjic-704	121	8	.	.	PUNCT
hjic-704	122	1	polytope	polytope	PROPN
hjic-704	122	2	𝒳	𝒳	PROPN
hjic-704	122	3	is	be	AUX
hjic-704	122	4	evaluated	evaluate	VERB
hjic-704	122	5	through	through	ADP
hjic-704	122	6	iterations	iteration	NOUN
hjic-704	122	7	considering	consider	VERB
hjic-704	122	8	the	the	DET
hjic-704	122	9	bounding	bounding	NOUN
hjic-704	122	10	box	box	NOUN
hjic-704	122	11	of	of	ADP
hjic-704	122	12	the	the	DET
hjic-704	122	13	obtained	obtain	VERB
hjic-704	122	14	α	α	NOUN
hjic-704	122	15	-	-	PUNCT
hjic-704	122	16	level	level	NOUN
hjic-704	122	17	set	set	NOUN
hjic-704	122	18	.	.	PUNCT
hjic-704	123	1	polcz	polcz	PROPN
hjic-704	123	2	and	and	CCONJ
hjic-704	123	3	szederkényi	szederkényi	PROPN
hjic-704	123	4	hungarian	hungarian	ADJ
hjic-704	123	5	journal	journal	PROPN
hjic-704	123	6	of	of	ADP
hjic-704	123	7	industry	industry	NOUN
hjic-704	123	8	and	and	CCONJ
hjic-704	123	9	chemistry	chemistry	NOUN
hjic-704	123	10	116	116	NUM
hjic-704	123	11	3.1	3.1	NUM
hjic-704	123	12	.	.	PUNCT
hjic-704	124	1	finding	find	VERB
hjic-704	124	2	the	the	DET
hjic-704	124	3	most	most	ADV
hjic-704	124	4	appropriate	appropriate	ADJ
hjic-704	124	5	outer	outer	ADJ
hjic-704	124	6	polytope	polytope	NOUN
hjic-704	124	7	in	in	ADP
hjic-704	124	8	the	the	DET
hjic-704	124	9	case	case	NOUN
hjic-704	124	10	of	of	ADP
hjic-704	124	11	2d	2d	PROPN
hjic-704	124	12	systems	system	NOUN
hjic-704	124	13	,	,	PUNCT
hjic-704	124	14	polytope	polytope	PROPN
hjic-704	124	15	𝒳	𝒳	PROPN
hjic-704	124	16	is	be	AUX
hjic-704	124	17	evaluated	evaluate	VERB
hjic-704	124	18	manually	manually	ADV
hjic-704	124	19	through	through	ADP
hjic-704	124	20	iterations	iteration	NOUN
hjic-704	124	21	.	.	PUNCT
hjic-704	125	1	when	when	SCONJ
hjic-704	125	2	having	have	VERB
hjic-704	125	3	a	a	DET
hjic-704	125	4	higherdimensional	higherdimensional	ADJ
hjic-704	125	5	system	system	NOUN
hjic-704	125	6	(	(	PUNCT
hjic-704	125	7	n	n	CCONJ
hjic-704	125	8	≥	≥	NOUN
hjic-704	125	9	3	3	NUM
hjic-704	125	10	)	)	PUNCT
hjic-704	125	11	,	,	PUNCT
hjic-704	125	12	the	the	DET
hjic-704	125	13	iterative	iterative	NOUN
hjic-704	125	14	procedure	procedure	NOUN
hjic-704	125	15	[	[	X
hjic-704	125	16	6	6	NUM
hjic-704	125	17	]	]	PUNCT
hjic-704	125	18	is	be	AUX
hjic-704	125	19	applied	apply	VERB
hjic-704	125	20	that	that	SCONJ
hjic-704	125	21	starts	start	VERB
hjic-704	125	22	from	from	ADP
hjic-704	125	23	an	an	DET
hjic-704	125	24	initial	initial	ADJ
hjic-704	125	25	polytope	polytope	NOUN
hjic-704	125	26	𝒳	𝒳	PROPN
hjic-704	125	27	(	(	PUNCT
hjic-704	125	28	!	!	PUNCT
hjic-704	125	29	)	)	PUNCT
hjic-704	125	30	,	,	PUNCT
hjic-704	125	31	then	then	ADV
hjic-704	125	32	a	a	DET
hjic-704	125	33	new	new	ADJ
hjic-704	125	34	polytope	polytope	NOUN
hjic-704	125	35	𝒳	𝒳	PROPN
hjic-704	125	36	(	(	PUNCT
hjic-704	125	37	!	!	PUNCT
hjic-704	125	38	)	)	PUNCT
hjic-704	125	39	is	be	AUX
hjic-704	125	40	defined	define	VERB
hjic-704	125	41	by	by	ADP
hjic-704	125	42	enlarging	enlarge	VERB
hjic-704	125	43	the	the	DET
hjic-704	125	44	axis	axis	NOUN
hjic-704	125	45	aligned	aligned	ADJ
hjic-704	125	46	bounding	bounding	NOUN
hjic-704	125	47	box	box	NOUN
hjic-704	125	48	of	of	ADP
hjic-704	125	49	the	the	DET
hjic-704	125	50	obtained	obtain	VERB
hjic-704	125	51	α	α	NOUN
hjic-704	125	52	-	-	PUNCT
hjic-704	125	53	level	level	NOUN
hjic-704	125	54	set	set	NOUN
hjic-704	125	55	ε	ε	PROPN
hjic-704	125	56	!	!	PUNCT
hjic-704	125	57	(	(	PUNCT
hjic-704	125	58	!	!	PUNCT
hjic-704	125	59	)	)	PUNCT
hjic-704	125	60	.	.	PUNCT
hjic-704	126	1	during	during	ADP
hjic-704	126	2	the	the	DET
hjic-704	126	3	iterations	iteration	NOUN
hjic-704	126	4	,	,	PUNCT
hjic-704	126	5	𝒳	𝒳	PROPN
hjic-704	126	6	(	(	PUNCT
hjic-704	126	7	!	!	PUNCT
hjic-704	126	8	)	)	PUNCT
hjic-704	126	9	is	be	AUX
hjic-704	126	10	constrained	constrain	VERB
hjic-704	126	11	to	to	PART
hjic-704	126	12	be	be	AUX
hjic-704	126	13	a	a	DET
hjic-704	126	14	rectangular	rectangular	ADJ
hjic-704	126	15	polytope	polytope	NOUN
hjic-704	126	16	.	.	PUNCT
hjic-704	127	1	fig.2	fig.2	PROPN
hjic-704	127	2	illustrates	illustrate	VERB
hjic-704	127	3	the	the	DET
hjic-704	127	4	operation	operation	NOUN
hjic-704	127	5	of	of	ADP
hjic-704	127	6	a	a	DET
hjic-704	127	7	single	single	ADJ
hjic-704	127	8	iteration	iteration	NOUN
hjic-704	127	9	step	step	NOUN
hjic-704	127	10	.	.	PUNCT
hjic-704	128	1	4	4	X
hjic-704	128	2	.	.	X
hjic-704	128	3	lotka	lotka	PROPN
hjic-704	128	4	-	-	PUNCT
hjic-704	128	5	volterra	volterra	PROPN
hjic-704	128	6	systems	systems	PROPN
hjic-704	128	7	the	the	DET
hjic-704	128	8	n	n	ADV
hjic-704	128	9	-	-	PUNCT
hjic-704	128	10	dimensional	dimensional	ADJ
hjic-704	128	11	lv	lv	PROPN
hjic-704	128	12	equation	equation	NOUN
hjic-704	128	13	has	have	VERB
hjic-704	128	14	the	the	DET
hjic-704	128	15	form	form	NOUN
hjic-704	128	16	𝑥	𝑥	X
hjic-704	128	17	=	=	PUNCT
hjic-704	128	18	𝑑𝑖𝑎𝑔	𝑑𝑖𝑎𝑔	NOUN
hjic-704	128	19	𝑥	𝑥	NOUN
hjic-704	128	20	+	+	NUM
hjic-704	128	21	𝑏	𝑏	NOUN
hjic-704	128	22	,	,	PUNCT
hjic-704	128	23	𝐴	𝐴	PROPN
hjic-704	128	24	∈	∈	PROPN
hjic-704	128	25	ℝ!×	ℝ!×	PROPN
hjic-704	128	26	!	!	PROPN
hjic-704	128	27	,	,	PUNCT
hjic-704	128	28	𝑏	𝑏	PROPN
hjic-704	128	29	∈	∈	PROPN
hjic-704	128	30	ℝ	ℝ	PROPN
hjic-704	128	31	!	!	PROPN
hjic-704	128	32	,	,	PUNCT
hjic-704	128	33	(	(	PUNCT
hjic-704	128	34	9	9	X
hjic-704	128	35	)	)	PUNCT
hjic-704	128	36	where	where	SCONJ
hjic-704	128	37	diag(a	diag(a	NOUN
hjic-704	128	38	)	)	PUNCT
hjic-704	128	39	,	,	PUNCT
hjic-704	129	1	𝑎	𝑎	PROPN
hjic-704	129	2	∈	∈	PROPN
hjic-704	129	3	ℝ	ℝ	PROPN
hjic-704	129	4	!	!	PROPN
hjic-704	129	5	denotes	denote	VERB
hjic-704	129	6	an	an	DET
hjic-704	129	7	n	n	NUM
hjic-704	129	8	×	×	NOUN
hjic-704	129	9	n	n	CCONJ
hjic-704	129	10	square	square	ADJ
hjic-704	129	11	diagonal	diagonal	ADJ
hjic-704	129	12	matrix	matrix	NOUN
hjic-704	129	13	with	with	ADP
hjic-704	129	14	the	the	DET
hjic-704	129	15	x1	x1	PROPN
hjic-704	129	16	,	,	PUNCT
hjic-704	129	17	…	…	PUNCT
hjic-704	129	18	,	,	PUNCT
hjic-704	129	19	xn	xn	PROPN
hjic-704	129	20	on	on	ADP
hjic-704	129	21	the	the	DET
hjic-704	129	22	main	main	ADJ
hjic-704	129	23	diagonal	diagonal	NOUN
hjic-704	129	24	.	.	PUNCT
hjic-704	130	1	the	the	DET
hjic-704	130	2	system	system	NOUN
hjic-704	130	3	is	be	AUX
hjic-704	130	4	translated	translate	VERB
hjic-704	130	5	into	into	ADP
hjic-704	130	6	its	its	PRON
hjic-704	130	7	,	,	PUNCT
hjic-704	130	8	by	by	ADP
hjic-704	130	9	assumption	assumption	NOUN
hjic-704	130	10	,	,	PUNCT
hjic-704	130	11	unique	unique	ADJ
hjic-704	130	12	interior	interior	ADJ
hjic-704	130	13	equilibrium	equilibrium	NOUN
hjic-704	130	14	point	point	NOUN
hjic-704	130	15	𝑥∗	𝑥∗	PROPN
hjic-704	130	16	=	=	PUNCT
hjic-704	131	1	−𝐴!!𝑏	−𝐴!!𝑏	ADV
hjic-704	131	2	by	by	ADP
hjic-704	131	3	introducing	introduce	VERB
hjic-704	131	4	the	the	DET
hjic-704	131	5	centred	centred	ADJ
hjic-704	131	6	state	state	NOUN
hjic-704	131	7	vector	vector	NOUN
hjic-704	131	8	𝑥	𝑥	NOUN
hjic-704	131	9	=	=	SYM
hjic-704	131	10	𝑥	𝑥	PROPN
hjic-704	131	11	−	−	PROPN
hjic-704	132	1	𝑥∗	𝑥∗	PROPN
hjic-704	132	2	.	.	PUNCT
hjic-704	133	1	then	then	ADV
hjic-704	133	2	,	,	PUNCT
hjic-704	133	3	an	an	DET
hjic-704	133	4	autonomous	autonomous	ADJ
hjic-704	133	5	nonlinear	nonlinear	ADJ
hjic-704	133	6	system	system	NOUN
hjic-704	133	7	of	of	ADP
hjic-704	133	8	the	the	DET
hjic-704	133	9	form	form	NOUN
hjic-704	133	10	𝑥	𝑥	X
hjic-704	133	11	=	=	SYM
hjic-704	133	12	𝒜	𝒜	NOUN
hjic-704	133	13	𝑥	𝑥	NOUN
hjic-704	133	14	𝑥	𝑥	NOUN
hjic-704	133	15	is	be	AUX
hjic-704	133	16	obtained	obtain	VERB
hjic-704	133	17	,	,	PUNCT
hjic-704	133	18	where	where	SCONJ
hjic-704	133	19	the	the	DET
hjic-704	133	20	matrix	matrix	NOUN
hjic-704	133	21	function	function	NOUN
hjic-704	133	22	𝒜	𝒜	NOUN
hjic-704	133	23	can	can	AUX
hjic-704	133	24	be	be	AUX
hjic-704	133	25	expressed	express	VERB
hjic-704	133	26	as	as	ADP
hjic-704	133	27	:	:	PUNCT
hjic-704	133	28	𝒜	𝒜	NOUN
hjic-704	133	29	𝑥	𝑥	NOUN
hjic-704	133	30	=	=	PUNCT
hjic-704	133	31	𝑑𝑖𝑎𝑔	𝑑𝑖𝑎𝑔	NOUN
hjic-704	134	1	𝑥	𝑥	X
hjic-704	134	2	+	+	CCONJ
hjic-704	134	3	𝑥∗	𝑥∗	PROPN
hjic-704	134	4	𝐴.	𝐴.	PROPN
hjic-704	134	5	by	by	ADP
hjic-704	134	6	applying	apply	VERB
hjic-704	134	7	the	the	DET
hjic-704	134	8	lft	lft	NOUN
hjic-704	134	9	and	and	CCONJ
hjic-704	134	10	the	the	DET
hjic-704	134	11	further	further	ADJ
hjic-704	134	12	algebraic	algebraic	ADJ
hjic-704	134	13	model	model	NOUN
hjic-704	134	14	transformation	transformation	NOUN
hjic-704	134	15	steps	step	NOUN
hjic-704	134	16	,	,	PUNCT
hjic-704	134	17	a	a	DET
hjic-704	134	18	model	model	NOUN
hjic-704	134	19	is	be	AUX
hjic-704	134	20	obtained	obtain	VERB
hjic-704	134	21	in	in	ADP
hjic-704	134	22	the	the	DET
hjic-704	134	23	representation	representation	NOUN
hjic-704	134	24	of	of	ADP
hjic-704	134	25	eq.(4	eq.(4	ADJ
hjic-704	134	26	)	)	PUNCT
hjic-704	134	27	,	,	PUNCT
hjic-704	134	28	where	where	SCONJ
hjic-704	134	29	the	the	DET
hjic-704	134	30	entries	entry	NOUN
hjic-704	134	31	of	of	ADP
hjic-704	134	32	π(x	π(x	NOUN
hjic-704	134	33	)	)	PUNCT
hjic-704	134	34	are	be	AUX
hjic-704	134	35	second	second	ADJ
hjic-704	134	36	order	order	NOUN
hjic-704	134	37	monomials	monomial	NOUN
hjic-704	134	38	of	of	ADP
hjic-704	134	39	the	the	DET
hjic-704	134	40	state	state	NOUN
hjic-704	134	41	variables	variable	NOUN
hjic-704	134	42	.	.	PUNCT
hjic-704	135	1	5	5	X
hjic-704	135	2	.	.	X
hjic-704	135	3	numerical	numerical	ADJ
hjic-704	135	4	results	result	NOUN
hjic-704	135	5	in	in	ADP
hjic-704	135	6	this	this	DET
hjic-704	135	7	section	section	NOUN
hjic-704	135	8	,	,	PUNCT
hjic-704	135	9	the	the	DET
hjic-704	135	10	applicability	applicability	NOUN
hjic-704	135	11	of	of	ADP
hjic-704	135	12	the	the	DET
hjic-704	135	13	approach	approach	NOUN
hjic-704	135	14	presented	present	VERB
hjic-704	135	15	above	above	ADV
hjic-704	135	16	is	be	AUX
hjic-704	135	17	illustrated	illustrate	VERB
hjic-704	135	18	through	through	ADP
hjic-704	135	19	different	different	ADJ
hjic-704	135	20	locally	locally	ADV
hjic-704	135	21	stable	stable	ADJ
hjic-704	135	22	lotkavolterra	lotkavolterra	NOUN
hjic-704	135	23	models	model	NOUN
hjic-704	135	24	.	.	PUNCT
hjic-704	136	1	the	the	DET
hjic-704	136	2	results	result	NOUN
hjic-704	136	3	presented	present	VERB
hjic-704	136	4	here	here	ADV
hjic-704	136	5	have	have	AUX
hjic-704	136	6	been	be	AUX
hjic-704	136	7	computed	compute	VERB
hjic-704	136	8	in	in	ADP
hjic-704	136	9	a	a	DET
hjic-704	136	10	matlab	matlab	PROPN
hjic-704	136	11	environment	environment	NOUN
hjic-704	136	12	.	.	PUNCT
hjic-704	137	1	for	for	ADP
hjic-704	137	2	symbolic	symbolic	ADJ
hjic-704	137	3	computations	computation	NOUN
hjic-704	137	4	,	,	PUNCT
hjic-704	137	5	matlab	matlab	PROPN
hjic-704	137	6	’s	’s	PART
hjic-704	137	7	built	build	VERB
hjic-704	137	8	-	-	PUNCT
hjic-704	137	9	in	in	ADP
hjic-704	137	10	symbolic	symbolic	ADJ
hjic-704	137	11	math	math	NOUN
hjic-704	137	12	toolbox	toolbox	NOUN
hjic-704	137	13	was	be	AUX
hjic-704	137	14	used	use	VERB
hjic-704	137	15	based	base	VERB
hjic-704	137	16	on	on	ADP
hjic-704	137	17	mupad	mupad	PROPN
hjic-704	137	18	.	.	PUNCT
hjic-704	138	1	for	for	ADP
hjic-704	138	2	linear	linear	ADJ
hjic-704	138	3	fractional	fractional	ADJ
hjic-704	138	4	transformations	transformation	NOUN
hjic-704	138	5	(	(	PUNCT
hjic-704	138	6	lft	lft	X
hjic-704	138	7	)	)	PUNCT
hjic-704	138	8	,	,	PUNCT
hjic-704	138	9	the	the	DET
hjic-704	138	10	enhanced	enhance	VERB
hjic-704	138	11	lfr	lfr	NOUN
hjic-704	138	12	-	-	PUNCT
hjic-704	138	13	toolbox	toolbox	NOUN
hjic-704	138	14	is	be	AUX
hjic-704	138	15	used	use	VERB
hjic-704	138	16	[	[	PUNCT
hjic-704	138	17	16	16	NUM
hjic-704	138	18	,	,	PUNCT
hjic-704	138	19	17	17	NUM
hjic-704	138	20	]	]	PUNCT
hjic-704	138	21	.	.	PUNCT
hjic-704	139	1	to	to	PART
hjic-704	139	2	model	model	VERB
hjic-704	139	3	and	and	CCONJ
hjic-704	139	4	solve	solve	VERB
hjic-704	139	5	semi	semi	ADJ
hjic-704	139	6	-	-	ADJ
hjic-704	139	7	definite	definite	ADJ
hjic-704	139	8	optimization	optimization	NOUN
hjic-704	139	9	(	(	PUNCT
hjic-704	139	10	sdp	sdp	NOUN
hjic-704	139	11	)	)	PUNCT
hjic-704	139	12	problems	problem	NOUN
hjic-704	139	13	,	,	PUNCT
hjic-704	139	14	mosek	mosek	PROPN
hjic-704	139	15	solver	solver	PROPN
hjic-704	139	16	with	with	ADP
hjic-704	139	17	yalmip	yalmip	NOUN
hjic-704	139	18	was	be	AUX
hjic-704	139	19	used	use	VERB
hjic-704	139	20	[	[	PUNCT
hjic-704	139	21	18	18	NUM
hjic-704	139	22	]	]	PUNCT
hjic-704	139	23	.	.	PUNCT
hjic-704	140	1	5.1	5.1	NUM
hjic-704	140	2	.	.	PUNCT
hjic-704	141	1	2d	2d	PROPN
hjic-704	141	2	lotka	lotka	PROPN
hjic-704	141	3	-	-	PUNCT
hjic-704	141	4	volterra	volterra	PROPN
hjic-704	141	5	system	system	NOUN
hjic-704	141	6	a	a	DET
hjic-704	141	7	locally	locally	ADV
hjic-704	141	8	stable	stable	ADJ
hjic-704	141	9	lv	lv	PROPN
hjic-704	141	10	system	system	NOUN
hjic-704	141	11	is	be	AUX
hjic-704	141	12	considered	consider	VERB
hjic-704	141	13	with	with	ADP
hjic-704	141	14	the	the	DET
hjic-704	141	15	model	model	NOUN
hjic-704	141	16	matrix	matrix	NOUN
hjic-704	141	17	:	:	PUNCT
hjic-704	141	18	𝐴	𝐴	PROPN
hjic-704	141	19	=	=	PUNCT
hjic-704	142	1	-2	-2	INTJ
hjic-704	142	2	-3	-3	INTJ
hjic-704	142	3	1.4	1.4	NUM
hjic-704	142	4	1	1	NUM
hjic-704	142	5	,	,	PUNCT
hjic-704	142	6	with	with	ADP
hjic-704	142	7	a	a	DET
hjic-704	142	8	unique	unique	ADJ
hjic-704	142	9	interior	interior	ADJ
hjic-704	142	10	equilibrium	equilibrium	NOUN
hjic-704	142	11	point	point	NOUN
hjic-704	142	12	x	x	X
hjic-704	142	13	*	*	PUNCT
hjic-704	142	14	=	=	PUNCT
hjic-704	143	1	[	[	X
hjic-704	143	2	1	1	NUM
hjic-704	143	3	1]t	1]t	NUM
hjic-704	143	4	.	.	PUNCT
hjic-704	144	1	in	in	ADP
hjic-704	144	2	fig.3	fig.3	PROPN
hjic-704	144	3	,	,	PUNCT
hjic-704	144	4	some	some	DET
hjic-704	144	5	trajectories	trajectory	NOUN
hjic-704	144	6	of	of	ADP
hjic-704	144	7	the	the	DET
hjic-704	144	8	centred	centre	VERB
hjic-704	144	9	system	system	NOUN
hjic-704	144	10	can	can	AUX
hjic-704	144	11	be	be	AUX
hjic-704	144	12	observed	observe	VERB
hjic-704	144	13	from	from	ADP
hjic-704	144	14	different	different	ADJ
hjic-704	144	15	initial	initial	ADJ
hjic-704	144	16	conditions	condition	NOUN
hjic-704	144	17	.	.	PUNCT
hjic-704	145	1	the	the	DET
hjic-704	145	2	red	red	ADJ
hjic-704	145	3	trajectories	trajectory	NOUN
hjic-704	145	4	converge	converge	VERB
hjic-704	145	5	at	at	ADP
hjic-704	145	6	the	the	DET
hjic-704	145	7	equilibrium	equilibrium	NOUN
hjic-704	145	8	point	point	NOUN
hjic-704	145	9	,	,	PUNCT
hjic-704	145	10	the	the	DET
hjic-704	145	11	blue	blue	ADJ
hjic-704	145	12	ones	one	NOUN
hjic-704	145	13	do	do	AUX
hjic-704	145	14	not	not	PART
hjic-704	145	15	tend	tend	VERB
hjic-704	145	16	to	to	ADP
hjic-704	145	17	the	the	DET
hjic-704	145	18	equilibrium	equilibrium	NOUN
hjic-704	145	19	point	point	NOUN
hjic-704	145	20	.	.	PUNCT
hjic-704	146	1	after	after	ADP
hjic-704	146	2	solving	solve	VERB
hjic-704	146	3	the	the	DET
hjic-704	146	4	corresponding	corresponding	ADJ
hjic-704	146	5	sdp	sdp	NOUN
hjic-704	146	6	,	,	PUNCT
hjic-704	146	7	the	the	DET
hjic-704	146	8	obtained	obtain	VERB
hjic-704	146	9	lyapunov	lyapunov	NOUN
hjic-704	146	10	function	function	NOUN
hjic-704	146	11	is	be	AUX
hjic-704	146	12	𝑉	𝑉	PROPN
hjic-704	146	13	𝑥	𝑥	NOUN
hjic-704	146	14	=	=	PUNCT
hjic-704	146	15	π!!𝑃π	π!!𝑃π	NOUN
hjic-704	146	16	!	!	PUNCT
hjic-704	147	1	(	(	PUNCT
hjic-704	147	2	fig.4	fig.4	PROPN
hjic-704	147	3	)	)	PUNCT
hjic-704	147	4	,	,	PUNCT
hjic-704	147	5	where	where	SCONJ
hjic-704	147	6	π	π	NOUN
hjic-704	147	7	=	=	SYM
hjic-704	147	8	𝑥	𝑥	PROPN
hjic-704	147	9	!	!	PUNCT
hjic-704	147	10	!	!	PUNCT
hjic-704	148	1	𝑥!𝑥	𝑥!𝑥	PROPN
hjic-704	148	2	!	!	PUNCT
hjic-704	149	1	𝑥	𝑥	X
hjic-704	149	2	!	!	PUNCT
hjic-704	149	3	!	!	PUNCT
hjic-704	149	4	!	!	PUNCT
hjic-704	150	1	,	,	PUNCT
hjic-704	150	2	π	π	X
hjic-704	150	3	!	!	PUNCT
hjic-704	150	4	=	=	PUNCT
hjic-704	151	1	𝑥	𝑥	X
hjic-704	151	2	π	π	X
hjic-704	151	3	(	(	PUNCT
hjic-704	151	4	10	10	NUM
hjic-704	151	5	)	)	PUNCT
hjic-704	151	6	𝑃	𝑃	NOUN
hjic-704	151	7	=	=	SYM
hjic-704	151	8	87.39	87.39	NUM
hjic-704	151	9	63.83	63.83	NUM
hjic-704	151	10	-3.45	-3.45	NUM
hjic-704	151	11	0	0	NUM
hjic-704	151	12	0	0	NUM
hjic-704	151	13	63.83	63.83	NUM
hjic-704	151	14	165.26	165.26	NUM
hjic-704	151	15	67.24	67.24	NUM
hjic-704	151	16	100.85	100.85	NUM
hjic-704	151	17	28.76	28.76	NUM
hjic-704	151	18	-3.45	-3.45	NUM
hjic-704	151	19	67.24	67.24	NUM
hjic-704	151	20	7.63	7.63	NUM
hjic-704	151	21	0.15	0.15	NUM
hjic-704	151	22	0	0	NUM
hjic-704	151	23	0	0	NUM
hjic-704	151	24	100.85	100.85	NUM
hjic-704	151	25	0.15	0.15	NUM
hjic-704	151	26	38.78	38.78	NUM
hjic-704	151	27	39.97	39.97	NUM
hjic-704	151	28	0	0	NUM
hjic-704	151	29	28.76	28.76	NUM
hjic-704	151	30	0	0	NUM
hjic-704	151	31	39.97	39.97	NUM
hjic-704	151	32	15.53	15.53	NUM
hjic-704	151	33	in	in	ADP
hjic-704	151	34	fig.3	fig.3	PROPN
hjic-704	151	35	,	,	PUNCT
hjic-704	151	36	the	the	DET
hjic-704	151	37	shape	shape	NOUN
hjic-704	151	38	of	of	ADP
hjic-704	151	39	the	the	DET
hjic-704	151	40	manually	manually	ADV
hjic-704	151	41	chosen	choose	VERB
hjic-704	151	42	polytope	polytope	PROPN
hjic-704	151	43	𝒳	𝒳	PROPN
hjic-704	151	44	,	,	PUNCT
hjic-704	151	45	and	and	CCONJ
hjic-704	151	46	the	the	DET
hjic-704	151	47	obtained	obtain	VERB
hjic-704	151	48	invariant	invariant	ADJ
hjic-704	151	49	α	α	NOUN
hjic-704	151	50	-	-	PUNCT
hjic-704	151	51	level	level	NOUN
hjic-704	151	52	set	set	NOUN
hjic-704	151	53	of	of	ADP
hjic-704	151	54	the	the	DET
hjic-704	151	55	lyapunov	lyapunov	ADJ
hjic-704	151	56	function	function	NOUN
hjic-704	151	57	can	can	AUX
hjic-704	151	58	be	be	AUX
hjic-704	151	59	seen	see	VERB
hjic-704	151	60	,	,	PUNCT
hjic-704	151	61	which	which	PRON
hjic-704	151	62	is	be	AUX
hjic-704	151	63	considered	consider	VERB
hjic-704	151	64	as	as	ADP
hjic-704	151	65	the	the	DET
hjic-704	151	66	estimated	estimate	VERB
hjic-704	151	67	doa	doa	NOUN
hjic-704	151	68	(	(	PUNCT
hjic-704	151	69	filled	fill	VERB
hjic-704	151	70	orange	orange	PROPN
hjic-704	151	71	region	region	PROPN
hjic-704	151	72	)	)	PUNCT
hjic-704	151	73	.	.	PUNCT
hjic-704	152	1	areas	area	NOUN
hjic-704	152	2	can	can	AUX
hjic-704	152	3	be	be	AUX
hjic-704	152	4	observed	observe	VERB
hjic-704	152	5	,	,	PUNCT
hjic-704	152	6	where	where	SCONJ
hjic-704	152	7	the	the	DET
hjic-704	152	8	lyapunov	lyapunov	ADJ
hjic-704	152	9	function	function	NOUN
hjic-704	152	10	's	's	PART
hjic-704	152	11	time	time	NOUN
hjic-704	152	12	derivative	derivative	NOUN
hjic-704	152	13	is	be	AUX
hjic-704	152	14	positive	positive	ADJ
hjic-704	152	15	(	(	PUNCT
hjic-704	152	16	green	green	ADJ
hjic-704	152	17	region	region	NOUN
hjic-704	152	18	)	)	PUNCT
hjic-704	152	19	can	can	AUX
hjic-704	152	20	also	also	ADV
hjic-704	152	21	be	be	AUX
hjic-704	152	22	observed	observe	VERB
hjic-704	152	23	to	to	PART
hjic-704	152	24	be	be	AUX
hjic-704	152	25	completely	completely	ADV
hjic-704	152	26	outside	outside	ADV
hjic-704	152	27	of	of	ADP
hjic-704	152	28	𝒳.	𝒳.	PROPN
hjic-704	152	29	fig.5	fig.5	PROPN
hjic-704	152	30	illustrates	illustrate	VERB
hjic-704	152	31	how	how	SCONJ
hjic-704	152	32	the	the	DET
hjic-704	152	33	value	value	NOUN
hjic-704	152	34	of	of	ADP
hjic-704	152	35	the	the	DET
hjic-704	152	36	lyapunov	lyapunov	NOUN
hjic-704	152	37	function	function	NOUN
hjic-704	152	38	decreases	decrease	VERB
hjic-704	152	39	along	along	ADP
hjic-704	152	40	the	the	DET
hjic-704	152	41	trajectories	trajectory	NOUN
hjic-704	152	42	.	.	PUNCT
hjic-704	153	1	figure	figure	VERB
hjic-704	153	2	3	3	NUM
hjic-704	153	3	.	.	NOUN
hjic-704	153	4	phase	phase	NOUN
hjic-704	153	5	diagram	diagram	NOUN
hjic-704	153	6	of	of	ADP
hjic-704	153	7	the	the	DET
hjic-704	153	8	2d	2d	NUM
hjic-704	153	9	locally	locally	ADV
hjic-704	153	10	stable	stable	ADJ
hjic-704	153	11	system	system	NOUN
hjic-704	153	12	.	.	PUNCT
hjic-704	154	1	red	red	ADJ
hjic-704	154	2	trajectories	trajectory	NOUN
hjic-704	154	3	converge	converge	VERB
hjic-704	154	4	at	at	ADP
hjic-704	154	5	the	the	DET
hjic-704	154	6	origin	origin	NOUN
hjic-704	154	7	,	,	PUNCT
hjic-704	154	8	the	the	DET
hjic-704	154	9	blue	blue	ADJ
hjic-704	154	10	ones	one	NOUN
hjic-704	154	11	do	do	AUX
hjic-704	154	12	not	not	PART
hjic-704	154	13	converge	converge	VERB
hjic-704	154	14	at	at	ADP
hjic-704	154	15	the	the	DET
hjic-704	154	16	origin	origin	NOUN
hjic-704	154	17	.	.	PUNCT
hjic-704	155	1	the	the	DET
hjic-704	155	2	estimated	estimate	VERB
hjic-704	155	3	doa	doa	NOUN
hjic-704	155	4	and	and	CCONJ
hjic-704	155	5	the	the	DET
hjic-704	155	6	used	use	VERB
hjic-704	155	7	polytope	polytope	NOUN
hjic-704	155	8	𝒳	𝒳	PRON
hjic-704	155	9	are	be	AUX
hjic-704	155	10	illustrated	illustrate	VERB
hjic-704	155	11	by	by	ADP
hjic-704	155	12	the	the	DET
hjic-704	155	13	orange	orange	NOUN
hjic-704	155	14	-	-	PUNCT
hjic-704	155	15	filled	fill	VERB
hjic-704	155	16	region	region	NOUN
hjic-704	155	17	and	and	CCONJ
hjic-704	155	18	by	by	ADP
hjic-704	155	19	the	the	DET
hjic-704	155	20	grey	grey	PROPN
hjic-704	155	21	-	-	PUNCT
hjic-704	155	22	dashed	dash	VERB
hjic-704	155	23	polytope	polytope	NOUN
hjic-704	155	24	,	,	PUNCT
hjic-704	155	25	respectively	respectively	ADV
hjic-704	155	26	.	.	PUNCT
hjic-704	156	1	the	the	DET
hjic-704	156	2	green	green	PROPN
hjic-704	156	3	area	area	NOUN
hjic-704	156	4	highlights	highlight	VERB
hjic-704	156	5	the	the	DET
hjic-704	156	6	subset	subset	NOUN
hjic-704	156	7	of	of	ADP
hjic-704	156	8	the	the	DET
hjic-704	156	9	state	state	NOUN
hjic-704	156	10	space	space	NOUN
hjic-704	156	11	where	where	SCONJ
hjic-704	156	12	the	the	DET
hjic-704	156	13	lyapunov	lyapunov	NOUN
hjic-704	156	14	function	function	NOUN
hjic-704	156	15	features	feature	VERB
hjic-704	156	16	a	a	DET
hjic-704	156	17	positive	positive	ADJ
hjic-704	156	18	time	time	NOUN
hjic-704	156	19	-	-	PUNCT
hjic-704	156	20	derivative	derivative	ADJ
hjic-704	156	21	.	.	PUNCT
hjic-704	157	1	figure	figure	NOUN
hjic-704	157	2	4	4	NUM
hjic-704	157	3	.	.	PUNCT
hjic-704	158	1	the	the	DET
hjic-704	158	2	obtained	obtain	VERB
hjic-704	158	3	lyapunov	lyapunov	NOUN
hjic-704	158	4	function	function	NOUN
hjic-704	158	5	in	in	ADP
hjic-704	158	6	the	the	DET
hjic-704	158	7	case	case	NOUN
hjic-704	158	8	of	of	ADP
hjic-704	158	9	the	the	DET
hjic-704	158	10	2d	2d	NUM
hjic-704	158	11	lv	lv	PROPN
hjic-704	158	12	system	system	NOUN
hjic-704	158	13	.	.	PUNCT
hjic-704	159	1	computational	computational	ADJ
hjic-704	159	2	stability	stability	NOUN
hjic-704	159	3	analysis	analysis	NOUN
hjic-704	159	4	of	of	ADP
hjic-704	159	5	lotka	lotka	PROPN
hjic-704	159	6	-	-	PUNCT
hjic-704	159	7	volterra	volterra	PROPN
hjic-704	159	8	systems	system	NOUN
hjic-704	159	9	44(2	44(2	PROPN
hjic-704	159	10	)	)	PUNCT
hjic-704	160	1	pp	pp	ADV
hjic-704	160	2	.	.	PUNCT
hjic-704	161	1	113–120	113–120	NUM
hjic-704	161	2	(	(	PUNCT
hjic-704	161	3	2016	2016	NUM
hjic-704	161	4	)	)	PUNCT
hjic-704	161	5	doi	doi	NOUN
hjic-704	161	6	:	:	PUNCT
hjic-704	161	7	10.1515	10.1515	NUM
hjic-704	161	8	/	/	SYM
hjic-704	161	9	hjic-2016	hjic-2016	NOUN
hjic-704	161	10	-	-	PUNCT
hjic-704	161	11	0014	0014	NUM
hjic-704	161	12	117	117	NUM
hjic-704	161	13	5.2	5.2	NUM
hjic-704	161	14	.	.	PUNCT
hjic-704	162	1	3d	3d	PROPN
hjic-704	162	2	lotka	lotka	PROPN
hjic-704	162	3	-	-	PUNCT
hjic-704	162	4	volterra	volterra	PROPN
hjic-704	162	5	system	system	NOUN
hjic-704	162	6	a	a	DET
hjic-704	162	7	locally	locally	ADV
hjic-704	162	8	stable	stable	ADJ
hjic-704	162	9	3d	3d	PROPN
hjic-704	162	10	lv	lv	PROPN
hjic-704	162	11	system	system	NOUN
hjic-704	162	12	has	have	AUX
hjic-704	162	13	been	be	AUX
hjic-704	162	14	chosen	choose	VERB
hjic-704	162	15	with	with	ADP
hjic-704	162	16	the	the	DET
hjic-704	162	17	model	model	NOUN
hjic-704	162	18	matrix	matrix	NOUN
hjic-704	162	19	𝐴	𝐴	NOUN
hjic-704	162	20	=	=	SYM
hjic-704	162	21	0.06	0.06	NUM
hjic-704	162	22	0.21	0.21	NUM
hjic-704	162	23	0.83	0.83	NUM
hjic-704	162	24	−2.47	−2.47	NOUN
hjic-704	162	25	−2.10	−2.10	VERB
hjic-704	162	26	−3.64	−3.64	PROPN
hjic-704	162	27	0.06	0.06	NUM
hjic-704	162	28	0.47	0.47	NUM
hjic-704	162	29	−0.45	−0.45	NOUN
hjic-704	162	30	.	.	PUNCT
hjic-704	163	1	similarly	similarly	ADV
hjic-704	163	2	to	to	ADP
hjic-704	163	3	the	the	DET
hjic-704	163	4	2d	2d	NUM
hjic-704	163	5	example	example	NOUN
hjic-704	163	6	,	,	PUNCT
hjic-704	163	7	the	the	DET
hjic-704	163	8	equilibrium	equilibrium	NOUN
hjic-704	163	9	point	point	NOUN
hjic-704	163	10	is	be	AUX
hjic-704	163	11	set	set	VERB
hjic-704	163	12	to	to	ADP
hjic-704	163	13	x	x	X
hjic-704	163	14	*	*	PUNCT
hjic-704	164	1	=	=	PUNCT
hjic-704	164	2	[	[	PUNCT
hjic-704	164	3	1	1	NUM
hjic-704	164	4	1	1	NUM
hjic-704	164	5	1	1	NUM
hjic-704	164	6	]	]	PUNCT
hjic-704	164	7	t.	t.	X
hjic-704	164	8	the	the	DET
hjic-704	164	9	monomial	monomial	ADJ
hjic-704	164	10	set	set	NOUN
hjic-704	164	11	appearing	appear	VERB
hjic-704	164	12	in	in	ADP
hjic-704	164	13	πb	πb	NOUN
hjic-704	164	14	contains	contain	VERB
hjic-704	164	15	the	the	DET
hjic-704	164	16	state	state	NOUN
hjic-704	164	17	variables	variable	NOUN
hjic-704	164	18	and	and	CCONJ
hjic-704	164	19	every	every	DET
hjic-704	164	20	possible	possible	ADJ
hjic-704	164	21	2nd	2nd	ADJ
hjic-704	164	22	order	order	NOUN
hjic-704	164	23	monomial	monomial	ADJ
hjic-704	164	24	:	:	PUNCT
hjic-704	164	25	π	π	X
hjic-704	164	26	!	!	PUNCT
hjic-704	165	1	=	=	PUNCT
hjic-704	165	2	𝑥	𝑥	NOUN
hjic-704	165	3	!	!	PUNCT
hjic-704	165	4	!	!	PUNCT
hjic-704	166	1	𝑥!𝑥	𝑥!𝑥	PROPN
hjic-704	166	2	!	!	PUNCT
hjic-704	167	1	𝑥!𝑥	𝑥!𝑥	PROPN
hjic-704	167	2	!	!	PUNCT
hjic-704	168	1	𝑥	𝑥	X
hjic-704	168	2	!	!	PUNCT
hjic-704	168	3	!	!	PUNCT
hjic-704	169	1	𝑥!𝑥	𝑥!𝑥	PROPN
hjic-704	169	2	!	!	PUNCT
hjic-704	170	1	𝑥	𝑥	X
hjic-704	170	2	!	!	PUNCT
hjic-704	170	3	!	!	PUNCT
hjic-704	171	1	(	(	PUNCT
hjic-704	171	2	12	12	NUM
hjic-704	171	3	)	)	PUNCT
hjic-704	171	4	matrix	matrix	NOUN
hjic-704	171	5	p	p	NOUN
hjic-704	171	6	is	be	AUX
hjic-704	171	7	a	a	DET
hjic-704	171	8	9×9	9×9	NUM
hjic-704	171	9	symmetric	symmetric	ADJ
hjic-704	171	10	matrix	matrix	NOUN
hjic-704	171	11	.	.	PUNCT
hjic-704	172	1	fig.6	fig.6	PROPN
hjic-704	172	2	illustrates	illustrate	VERB
hjic-704	172	3	the	the	DET
hjic-704	172	4	invariant	invariant	ADJ
hjic-704	172	5	α	α	NOUN
hjic-704	172	6	-	-	PUNCT
hjic-704	172	7	level	level	NOUN
hjic-704	172	8	set	set	NOUN
hjic-704	172	9	of	of	ADP
hjic-704	172	10	the	the	DET
hjic-704	172	11	obtained	obtain	VERB
hjic-704	172	12	lyapunov	lyapunov	NOUN
hjic-704	172	13	function	function	NOUN
hjic-704	172	14	(	(	PUNCT
hjic-704	172	15	3d	3d	PROPN
hjic-704	172	16	red	red	ADJ
hjic-704	172	17	volume	volume	NOUN
hjic-704	172	18	)	)	PUNCT
hjic-704	172	19	.	.	PUNCT
hjic-704	173	1	in	in	ADP
hjic-704	173	2	fig.7	fig.7	ADJ
hjic-704	173	3	,	,	PUNCT
hjic-704	173	4	one	one	PRON
hjic-704	173	5	can	can	AUX
hjic-704	173	6	see	see	VERB
hjic-704	173	7	the	the	DET
hjic-704	173	8	cross	cros	NOUN
hjic-704	173	9	-	-	NOUN
hjic-704	173	10	sections	section	NOUN
hjic-704	173	11	of	of	ADP
hjic-704	173	12	the	the	DET
hjic-704	173	13	3d	3d	NUM
hjic-704	173	14	invariant	invariant	ADJ
hjic-704	173	15	region	region	NOUN
hjic-704	173	16	from	from	ADP
hjic-704	173	17	three	three	NUM
hjic-704	173	18	different	different	ADJ
hjic-704	173	19	viewpoints	viewpoint	NOUN
hjic-704	173	20	.	.	PUNCT
hjic-704	174	1	some	some	DET
hjic-704	174	2	trajectories	trajectory	NOUN
hjic-704	174	3	of	of	ADP
hjic-704	174	4	the	the	DET
hjic-704	174	5	system	system	NOUN
hjic-704	174	6	are	be	AUX
hjic-704	174	7	shown	show	VERB
hjic-704	174	8	in	in	ADP
hjic-704	174	9	red	red	ADJ
hjic-704	174	10	(	(	PUNCT
hjic-704	174	11	stable	stable	ADJ
hjic-704	174	12	)	)	PUNCT
hjic-704	174	13	and	and	CCONJ
hjic-704	174	14	blue	blue	ADJ
hjic-704	174	15	(	(	PUNCT
hjic-704	174	16	unstable	unstable	ADJ
hjic-704	174	17	)	)	PUNCT
hjic-704	174	18	.	.	PUNCT
hjic-704	175	1	figure	figure	NOUN
hjic-704	175	2	5	5	NUM
hjic-704	175	3	.	.	PUNCT
hjic-704	176	1	in	in	ADP
hjic-704	176	2	panel	panel	NOUN
hjic-704	176	3	a	a	PRON
hjic-704	176	4	,	,	PUNCT
hjic-704	176	5	the	the	DET
hjic-704	176	6	obtained	obtain	VERB
hjic-704	176	7	invariant	invariant	ADJ
hjic-704	176	8	level	level	NOUN
hjic-704	176	9	set	set	NOUN
hjic-704	176	10	is	be	AUX
hjic-704	176	11	shown	show	VERB
hjic-704	176	12	,	,	PUNCT
hjic-704	176	13	furthermore	furthermore	ADV
hjic-704	176	14	some	some	DET
hjic-704	176	15	trajectories	trajectory	NOUN
hjic-704	176	16	x(i)(t	x(i)(t	NUM
hjic-704	176	17	)	)	PUNCT
hjic-704	176	18	of	of	ADP
hjic-704	176	19	the	the	DET
hjic-704	176	20	system	system	NOUN
hjic-704	176	21	can	can	AUX
hjic-704	176	22	be	be	AUX
hjic-704	176	23	seen	see	VERB
hjic-704	176	24	in	in	ADP
hjic-704	176	25	different	different	ADJ
hjic-704	176	26	colors	color	NOUN
hjic-704	176	27	with	with	ADP
hjic-704	176	28	initial	initial	ADJ
hjic-704	176	29	conditions	condition	NOUN
hjic-704	176	30	𝑥	𝑥	NOUN
hjic-704	176	31	!	!	PUNCT
hjic-704	176	32	(	(	PUNCT
hjic-704	176	33	!	!	PUNCT
hjic-704	176	34	)	)	PUNCT
hjic-704	177	1	close	close	ADV
hjic-704	177	2	to	to	ADP
hjic-704	177	3	the	the	DET
hjic-704	177	4	boundary	boundary	NOUN
hjic-704	177	5	of	of	ADP
hjic-704	177	6	the	the	DET
hjic-704	177	7	estimated	estimate	VERB
hjic-704	177	8	doa	doa	NOUN
hjic-704	177	9	.	.	PUNCT
hjic-704	178	1	the	the	DET
hjic-704	178	2	values	value	NOUN
hjic-704	178	3	of	of	ADP
hjic-704	178	4	the	the	DET
hjic-704	178	5	lyapunov	lyapunov	ADJ
hjic-704	178	6	function	function	NOUN
hjic-704	178	7	along	along	ADP
hjic-704	178	8	the	the	DET
hjic-704	178	9	trajectories	trajectory	NOUN
hjic-704	178	10	(	(	PUNCT
hjic-704	178	11	v(i)(t	v(i)(t	ADJ
hjic-704	178	12	)	)	PUNCT
hjic-704	178	13	)	)	PUNCT
hjic-704	178	14	are	be	AUX
hjic-704	178	15	presented	present	VERB
hjic-704	178	16	in	in	ADP
hjic-704	178	17	panel	panel	NOUN
hjic-704	178	18	b	b	NOUN
hjic-704	178	19	,	,	PUNCT
hjic-704	178	20	respectively	respectively	ADV
hjic-704	178	21	.	.	PUNCT
hjic-704	179	1	figure	figure	NOUN
hjic-704	179	2	7	7	NUM
hjic-704	179	3	.	.	PUNCT
hjic-704	180	1	cross	cross	ADJ
hjic-704	180	2	-	-	ADJ
hjic-704	180	3	sectional	sectional	ADJ
hjic-704	180	4	view	view	NOUN
hjic-704	180	5	of	of	ADP
hjic-704	180	6	the	the	DET
hjic-704	180	7	3d	3d	NUM
hjic-704	180	8	estimate	estimate	NOUN
hjic-704	180	9	along	along	ADP
hjic-704	180	10	the	the	DET
hjic-704	180	11	major	major	ADJ
hjic-704	180	12	planes	plane	NOUN
hjic-704	180	13	xi	xi	PROPN
hjic-704	180	14	,	,	PUNCT
hjic-704	180	15	xj	xj	PROPN
hjic-704	180	16	and	and	CCONJ
hjic-704	180	17	using	use	VERB
hjic-704	180	18	different	different	ADJ
hjic-704	180	19	values	value	NOUN
hjic-704	180	20	for	for	ADP
hjic-704	180	21	xk	xk	PROPN
hjic-704	180	22	,	,	PUNCT
hjic-704	180	23	where	where	SCONJ
hjic-704	180	24	(	(	PUNCT
hjic-704	180	25	i	i	PROPN
hjic-704	180	26	,	,	PUNCT
hjic-704	180	27	j	j	PROPN
hjic-704	180	28	,	,	PUNCT
hjic-704	180	29	k	k	NOUN
hjic-704	180	30	)	)	PUNCT
hjic-704	180	31	is	be	AUX
hjic-704	180	32	a	a	DET
hjic-704	180	33	permutation	permutation	NOUN
hjic-704	180	34	of	of	ADP
hjic-704	180	35	(	(	PUNCT
hjic-704	180	36	1	1	NUM
hjic-704	180	37	,	,	PUNCT
hjic-704	180	38	2	2	NUM
hjic-704	180	39	,	,	PUNCT
hjic-704	180	40	3	3	NUM
hjic-704	180	41	)	)	PUNCT
hjic-704	180	42	.	.	PUNCT
hjic-704	181	1	figure	figure	VERB
hjic-704	181	2	6	6	NUM
hjic-704	181	3	.	.	PUNCT
hjic-704	181	4	estimated	estimate	VERB
hjic-704	181	5	doa	doa	NOUN
hjic-704	181	6	of	of	ADP
hjic-704	181	7	the	the	DET
hjic-704	181	8	locally	locally	ADV
hjic-704	181	9	stable	stable	ADJ
hjic-704	181	10	3d	3d	PROPN
hjic-704	181	11	lotka	lotka	PROPN
hjic-704	181	12	-	-	PUNCT
hjic-704	181	13	volterra	volterra	NOUN
hjic-704	181	14	system	system	NOUN
hjic-704	181	15	(	(	PUNCT
hjic-704	181	16	red	red	ADJ
hjic-704	181	17	mesh	mesh	NOUN
hjic-704	181	18	)	)	PUNCT
hjic-704	181	19	and	and	CCONJ
hjic-704	181	20	the	the	DET
hjic-704	181	21	corresponding	corresponding	ADJ
hjic-704	181	22	final	final	ADJ
hjic-704	181	23	polytope	polytope	NOUN
hjic-704	181	24	𝒳.	𝒳.	PROPN
hjic-704	181	25	polcz	polcz	PROPN
hjic-704	181	26	and	and	CCONJ
hjic-704	181	27	szederkényi	szederkényi	PROPN
hjic-704	181	28	hungarian	hungarian	ADJ
hjic-704	181	29	journal	journal	PROPN
hjic-704	181	30	of	of	ADP
hjic-704	181	31	industry	industry	NOUN
hjic-704	181	32	and	and	CCONJ
hjic-704	181	33	chemistry	chemistry	NOUN
hjic-704	181	34	118	118	NUM
hjic-704	181	35	5.3	5.3	NUM
hjic-704	181	36	.	.	PUNCT
hjic-704	182	1	4d	4d	PROPN
hjic-704	182	2	lotka	lotka	PROPN
hjic-704	182	3	-	-	PUNCT
hjic-704	182	4	volterra	volterra	PROPN
hjic-704	182	5	system	system	NOUN
hjic-704	182	6	the	the	DET
hjic-704	182	7	method	method	NOUN
hjic-704	182	8	was	be	AUX
hjic-704	182	9	applied	apply	VERB
hjic-704	182	10	to	to	ADP
hjic-704	182	11	a	a	DET
hjic-704	182	12	locally	locally	ADV
hjic-704	182	13	stable	stable	ADJ
hjic-704	182	14	4d	4d	ADJ
hjic-704	182	15	lv	lv	PROPN
hjic-704	182	16	system	system	NOUN
hjic-704	182	17	with	with	ADP
hjic-704	182	18	a	a	DET
hjic-704	182	19	unique	unique	ADJ
hjic-704	182	20	interior	interior	ADJ
hjic-704	182	21	equilibrium	equilibrium	NOUN
hjic-704	182	22	point	point	NOUN
hjic-704	182	23	:	:	PUNCT
hjic-704	183	1	x	x	X
hjic-704	183	2	*	*	PUNCT
hjic-704	183	3	=	=	PUNCT
hjic-704	183	4	[	[	PUNCT
hjic-704	183	5	1	1	NUM
hjic-704	183	6	1	1	NUM
hjic-704	183	7	1	1	NUM
hjic-704	183	8	1	1	NUM
hjic-704	183	9	]	]	PUNCT
hjic-704	183	10	t	t	NOUN
hjic-704	183	11	.	.	PUNCT
hjic-704	184	1	(	(	PUNCT
hjic-704	184	2	13	13	NUM
hjic-704	184	3	)	)	PUNCT
hjic-704	184	4	the	the	DET
hjic-704	184	5	model	model	NOUN
hjic-704	184	6	matrix	matrix	NOUN
hjic-704	184	7	of	of	ADP
hjic-704	184	8	the	the	DET
hjic-704	184	9	lv	lv	PROPN
hjic-704	184	10	system	system	NOUN
hjic-704	184	11	was	be	AUX
hjic-704	184	12	chosen	choose	VERB
hjic-704	184	13	to	to	PART
hjic-704	184	14	be	be	AUX
hjic-704	184	15	:	:	PUNCT
hjic-704	184	16	𝐴	𝐴	PROPN
hjic-704	184	17	=	=	SYM
hjic-704	184	18	-4.7126	-4.7126	X
hjic-704	184	19	-1.5833	-1.5833	X
hjic-704	185	1	1.5346	1.5346	NUM
hjic-704	185	2	2.3230	2.3230	NUM
hjic-704	185	3	-9.2461	-9.2461	NOUN
hjic-704	185	4	-3.1634	-3.1634	NOUN
hjic-704	185	5	2.8648	2.8648	NUM
hjic-704	185	6	2.7796	2.7796	NUM
hjic-704	185	7	-14.258	-14.258	NOUN
hjic-704	185	8	-4.5477	-4.5477	NOUN
hjic-704	185	9	3.6104	3.6104	NUM
hjic-704	185	10	4.6238	4.6238	NUM
hjic-704	185	11	-3.1687	-3.1687	NOUN
hjic-704	185	12	-0.8016	-0.8016	PROPN
hjic-704	186	1	1.2287	1.2287	NUM
hjic-704	186	2	1.2656	1.2656	NUM
hjic-704	186	3	.	.	PUNCT
hjic-704	187	1	due	due	ADP
hjic-704	187	2	to	to	ADP
hjic-704	187	3	the	the	DET
hjic-704	187	4	fact	fact	NOUN
hjic-704	187	5	that	that	SCONJ
hjic-704	187	6	model	model	NOUN
hjic-704	187	7	matrix	matrix	NOUN
hjic-704	187	8	a	a	PRON
hjic-704	187	9	is	be	AUX
hjic-704	187	10	a	a	DET
hjic-704	187	11	“	"	PUNCT
hjic-704	187	12	full	full	ADJ
hjic-704	187	13	”	"	PUNCT
hjic-704	187	14	matrix	matrix	NOUN
hjic-704	187	15	,	,	PUNCT
hjic-704	187	16	i.e.	i.e.	X
hjic-704	187	17	there	there	PRON
hjic-704	187	18	are	be	VERB
hjic-704	187	19	no	no	DET
hjic-704	187	20	zero	zero	NUM
hjic-704	187	21	entries	entry	NOUN
hjic-704	187	22	in	in	ADP
hjic-704	187	23	it	it	PRON
hjic-704	187	24	,	,	PUNCT
hjic-704	187	25	every	every	DET
hjic-704	187	26	secondorder	secondorder	NOUN
hjic-704	187	27	monomial	monomial	NOUN
hjic-704	187	28	will	will	AUX
hjic-704	187	29	appear	appear	VERB
hjic-704	187	30	in	in	ADP
hjic-704	187	31	the	the	DET
hjic-704	187	32	equation	equation	NOUN
hjic-704	187	33	of	of	ADP
hjic-704	187	34	the	the	DET
hjic-704	187	35	system	system	NOUN
hjic-704	187	36	.	.	PUNCT
hjic-704	188	1	as	as	ADP
hjic-704	188	2	a	a	DET
hjic-704	188	3	consequence	consequence	NOUN
hjic-704	188	4	,	,	PUNCT
hjic-704	188	5	the	the	DET
hjic-704	188	6	lft	lft	X
hjic-704	188	7	will	will	AUX
hjic-704	188	8	produce	produce	VERB
hjic-704	188	9	a	a	DET
hjic-704	188	10	model	model	NOUN
hjic-704	188	11	eq.(4	eq.(4	VERB
hjic-704	188	12	)	)	PUNCT
hjic-704	188	13	,	,	PUNCT
hjic-704	188	14	in	in	ADP
hjic-704	188	15	which	which	PRON
hjic-704	188	16	π	π	NOUN
hjic-704	188	17	will	will	AUX
hjic-704	188	18	contain	contain	VERB
hjic-704	188	19	every	every	DET
hjic-704	188	20	possible	possible	ADJ
hjic-704	188	21	second	second	ADJ
hjic-704	188	22	-	-	PUNCT
hjic-704	188	23	order	order	NOUN
hjic-704	188	24	monomial	monomial	NOUN
hjic-704	188	25	.	.	PUNCT
hjic-704	189	1	this	this	PRON
hjic-704	189	2	means	mean	VERB
hjic-704	189	3	that	that	SCONJ
hjic-704	189	4	the	the	DET
hjic-704	189	5	number	number	NOUN
hjic-704	189	6	of	of	ADP
hjic-704	189	7	monomials	monomial	NOUN
hjic-704	189	8	(	(	PUNCT
hjic-704	189	9	including	include	VERB
hjic-704	189	10	the	the	DET
hjic-704	189	11	state	state	NOUN
hjic-704	189	12	variables	variable	NOUN
hjic-704	189	13	)	)	PUNCT
hjic-704	189	14	is	be	AUX
hjic-704	189	15	mb	mb	NOUN
hjic-704	189	16	=	=	PUNCT
hjic-704	189	17	(	(	PUNCT
hjic-704	189	18	n2	n2	NOUN
hjic-704	189	19	+	+	NUM
hjic-704	189	20	3n	3n	NUM
hjic-704	189	21	)	)	PUNCT
hjic-704	189	22	/	/	SYM
hjic-704	189	23	2	2	NUM
hjic-704	189	24	in	in	ADP
hjic-704	189	25	the	the	DET
hjic-704	189	26	case	case	NOUN
hjic-704	189	27	of	of	ADP
hjic-704	189	28	a	a	DET
hjic-704	189	29	“	"	PUNCT
hjic-704	189	30	full	full	ADJ
hjic-704	189	31	”	"	PUNCT
hjic-704	189	32	model	model	NOUN
hjic-704	189	33	matrix	matrix	NOUN
hjic-704	189	34	.	.	PUNCT
hjic-704	190	1	in	in	ADP
hjic-704	190	2	table	table	NOUN
hjic-704	190	3	3	3	NUM
hjic-704	190	4	,	,	PUNCT
hjic-704	190	5	the	the	DET
hjic-704	190	6	number	number	NOUN
hjic-704	190	7	and	and	CCONJ
hjic-704	190	8	sizes	size	NOUN
hjic-704	190	9	of	of	ADP
hjic-704	190	10	the	the	DET
hjic-704	190	11	lmis	lmis	ADJ
hjic-704	190	12	have	have	AUX
hjic-704	190	13	been	be	AUX
hjic-704	190	14	summarised	summarise	VERB
hjic-704	190	15	in	in	ADP
hjic-704	190	16	the	the	DET
hjic-704	190	17	case	case	NOUN
hjic-704	190	18	of	of	ADP
hjic-704	190	19	n	n	CCONJ
hjic-704	190	20	-	-	PUNCT
hjic-704	190	21	dimensional	dimensional	ADJ
hjic-704	190	22	lv	lv	PROPN
hjic-704	190	23	systems	system	NOUN
hjic-704	190	24	with	with	ADP
hjic-704	190	25	a	a	DET
hjic-704	190	26	“	"	PUNCT
hjic-704	190	27	full	full	ADJ
hjic-704	190	28	”	"	PUNCT
hjic-704	190	29	model	model	NOUN
hjic-704	190	30	matrix	matrix	NOUN
hjic-704	190	31	.	.	PUNCT
hjic-704	191	1	the	the	DET
hjic-704	191	2	exponential	exponential	ADJ
hjic-704	191	3	factor	factor	NOUN
hjic-704	191	4	2n	2n	NUM
hjic-704	191	5	in	in	ADP
hjic-704	191	6	table	table	NOUN
hjic-704	191	7	3	3	NUM
hjic-704	191	8	originates	originate	NOUN
hjic-704	191	9	from	from	ADP
hjic-704	191	10	the	the	DET
hjic-704	191	11	rectangular	rectangular	ADJ
hjic-704	191	12	shape	shape	NOUN
hjic-704	191	13	of	of	ADP
hjic-704	191	14	polytope	polytope	NOUN
hjic-704	191	15	𝒳	𝒳	PROPN
hjic-704	191	16	possessing	possess	VERB
hjic-704	191	17	2n	2n	NUM
hjic-704	191	18	corner	corner	NOUN
hjic-704	191	19	points	point	NOUN
hjic-704	191	20	.	.	PUNCT
hjic-704	192	1	on	on	ADP
hjic-704	192	2	the	the	DET
hjic-704	192	3	other	other	ADJ
hjic-704	192	4	hand	hand	NOUN
hjic-704	192	5	,	,	PUNCT
hjic-704	192	6	the	the	DET
hjic-704	192	7	feasibility	feasibility	NOUN
hjic-704	192	8	of	of	ADP
hjic-704	192	9	lmi	lmi	PROPN
hjic-704	192	10	conditions	condition	NOUN
hjic-704	192	11	in	in	ADP
hjic-704	192	12	eqs.(7	eqs.(7	PROPN
hjic-704	192	13	)	)	PUNCT
hjic-704	192	14	and	and	CCONJ
hjic-704	192	15	(	(	PUNCT
hjic-704	192	16	8)	8)	NUM
hjic-704	192	17	should	should	AUX
hjic-704	192	18	be	be	AUX
hjic-704	192	19	checked	check	VERB
hjic-704	192	20	at	at	ADP
hjic-704	192	21	each	each	DET
hjic-704	192	22	corner	corner	NOUN
hjic-704	192	23	point	point	NOUN
hjic-704	192	24	of	of	ADP
hjic-704	192	25	every	every	DET
hjic-704	192	26	facet	facet	NOUN
hjic-704	192	27	of	of	ADP
hjic-704	192	28	the	the	DET
hjic-704	192	29	polytope	polytope	NOUN
hjic-704	192	30	.	.	PUNCT
hjic-704	193	1	furthermore	furthermore	ADV
hjic-704	193	2	,	,	PUNCT
hjic-704	193	3	an	an	DET
hjic-704	193	4	n	n	ADV
hjic-704	193	5	-	-	PUNCT
hjic-704	193	6	dimensional	dimensional	ADJ
hjic-704	193	7	rectangular	rectangular	ADJ
hjic-704	193	8	polytope	polytope	NOUN
hjic-704	193	9	has	have	VERB
hjic-704	193	10	2n	2n	NUM
hjic-704	193	11	facets	facet	NOUN
hjic-704	193	12	with	with	ADP
hjic-704	193	13	2n-1	2n-1	NOUN
hjic-704	193	14	corner	corner	NOUN
hjic-704	193	15	points	point	NOUN
hjic-704	193	16	.	.	PUNCT
hjic-704	194	1	as	as	SCONJ
hjic-704	194	2	can	can	AUX
hjic-704	194	3	be	be	AUX
hjic-704	194	4	seen	see	VERB
hjic-704	194	5	,	,	PUNCT
hjic-704	194	6	a	a	DET
hjic-704	194	7	rectangular	rectangular	ADJ
hjic-704	194	8	polytope	polytope	NOUN
hjic-704	194	9	introduces	introduce	VERB
hjic-704	194	10	an	an	DET
hjic-704	194	11	exponential	exponential	ADJ
hjic-704	194	12	increase	increase	NOUN
hjic-704	194	13	in	in	ADP
hjic-704	194	14	the	the	DET
hjic-704	194	15	dimension	dimension	NOUN
hjic-704	194	16	of	of	ADP
hjic-704	194	17	the	the	DET
hjic-704	194	18	given	give	VERB
hjic-704	194	19	problem	problem	NOUN
hjic-704	194	20	.	.	PUNCT
hjic-704	195	1	however	however	ADV
hjic-704	195	2	,	,	PUNCT
hjic-704	195	3	n	n	CCONJ
hjic-704	195	4	-	-	PUNCT
hjic-704	195	5	dimensional	dimensional	ADJ
hjic-704	195	6	intervals	interval	NOUN
hjic-704	195	7	can	can	AUX
hjic-704	195	8	be	be	AUX
hjic-704	195	9	easily	easily	ADV
hjic-704	195	10	handled	handle	VERB
hjic-704	195	11	compared	compare	VERB
hjic-704	195	12	to	to	ADP
hjic-704	195	13	arbitrarily	arbitrarily	ADV
hjic-704	195	14	shaped	shape	VERB
hjic-704	195	15	polytopes	polytope	NOUN
hjic-704	195	16	defined	define	VERB
hjic-704	195	17	by	by	ADP
hjic-704	195	18	(	(	PUNCT
hjic-704	195	19	hyper)-triangle	hyper)-triangle	PROPN
hjic-704	195	20	meshes	mesh	NOUN
hjic-704	195	21	.	.	PUNCT
hjic-704	196	1	fig.8	fig.8	PROPN
hjic-704	196	2	illustrates	illustrate	VERB
hjic-704	196	3	the	the	DET
hjic-704	196	4	cross	cross	NOUN
hjic-704	196	5	sections	section	NOUN
hjic-704	196	6	of	of	ADP
hjic-704	196	7	the	the	DET
hjic-704	196	8	invariant	invariant	ADJ
hjic-704	196	9	domain	domain	NOUN
hjic-704	196	10	along	along	ADP
hjic-704	196	11	the	the	DET
hjic-704	196	12	different	different	ADJ
hjic-704	196	13	pair	pair	NOUN
hjic-704	196	14	of	of	ADP
hjic-704	196	15	axes	axis	NOUN
hjic-704	196	16	.	.	PUNCT
hjic-704	197	1	5.4	5.4	NUM
hjic-704	197	2	.	.	PUNCT
hjic-704	197	3	2d	2d	PROPN
hjic-704	197	4	uncertain	uncertain	ADJ
hjic-704	197	5	lv	lv	PROPN
hjic-704	197	6	system	system	NOUN
hjic-704	197	7	with	with	ADP
hjic-704	197	8	an	an	DET
hjic-704	197	9	uncertain	uncertain	ADJ
hjic-704	197	10	equilibrium	equilibrium	NOUN
hjic-704	197	11	point	point	NOUN
hjic-704	197	12	in	in	ADP
hjic-704	197	13	this	this	DET
hjic-704	197	14	section	section	NOUN
hjic-704	197	15	,	,	PUNCT
hjic-704	197	16	the	the	DET
hjic-704	197	17	same	same	ADJ
hjic-704	197	18	2	2	NUM
hjic-704	197	19	-	-	PUNCT
hjic-704	197	20	dimensional	dimensional	ADJ
hjic-704	197	21	system	system	NOUN
hjic-704	197	22	is	be	AUX
hjic-704	197	23	presented	present	VERB
hjic-704	197	24	that	that	PRON
hjic-704	197	25	appeared	appear	VERB
hjic-704	197	26	in	in	ADP
hjic-704	197	27	section	section	NOUN
hjic-704	197	28	5.1	5.1	NUM
hjic-704	197	29	with	with	ADP
hjic-704	197	30	the	the	DET
hjic-704	197	31	same	same	ADJ
hjic-704	197	32	model	model	NOUN
hjic-704	197	33	parameters	parameter	NOUN
hjic-704	197	34	but	but	CCONJ
hjic-704	197	35	with	with	ADP
hjic-704	197	36	an	an	DET
hjic-704	197	37	additional	additional	ADJ
hjic-704	197	38	uncertain	uncertain	ADJ
hjic-704	197	39	term	term	NOUN
hjic-704	197	40	kδ	kδ	NOUN
hjic-704	197	41	,	,	PUNCT
hjic-704	197	42	where	where	SCONJ
hjic-704	197	43	k	k	NOUN
hjic-704	198	1	=	=	PUNCT
hjic-704	199	1	[	[	X
hjic-704	199	2	1	1	NUM
hjic-704	199	3	1]t	1]t	NUM
hjic-704	199	4	.	.	PUNCT
hjic-704	200	1	it	it	PRON
hjic-704	200	2	is	be	AUX
hjic-704	200	3	assumes	assume	NOUN
hjic-704	200	4	,	,	PUNCT
hjic-704	200	5	that	that	SCONJ
hjic-704	200	6	δ	δ	PROPN
hjic-704	200	7	∈	∈	PROPN
hjic-704	200	8	𝒟	𝒟	PROPN
hjic-704	200	9	=	=	SYM
hjic-704	200	10	-0.1	-0.1	PROPN
hjic-704	200	11	,	,	PUNCT
hjic-704	200	12	0.1	0.1	NUM
hjic-704	200	13	is	be	AUX
hjic-704	200	14	an	an	DET
hjic-704	200	15	unknown	unknown	ADJ
hjic-704	200	16	constant	constant	ADJ
hjic-704	200	17	parameter	parameter	NOUN
hjic-704	200	18	(	(	PUNCT
hjic-704	200	19	δ	δ	NOUN
hjic-704	200	20	=	=	PROPN
hjic-704	200	21	0	0	NUM
hjic-704	200	22	)	)	PUNCT
hjic-704	200	23	.	.	PUNCT
hjic-704	201	1	the	the	DET
hjic-704	201	2	equation	equation	NOUN
hjic-704	201	3	of	of	ADP
hjic-704	201	4	the	the	DET
hjic-704	201	5	uncertain	uncertain	ADJ
hjic-704	201	6	model	model	NOUN
hjic-704	201	7	is	be	AUX
hjic-704	201	8	the	the	DET
hjic-704	201	9	following	following	NOUN
hjic-704	201	10	:	:	PUNCT
hjic-704	201	11	𝑥	𝑥	X
hjic-704	201	12	=	=	SYM
hjic-704	201	13	𝑑𝑖𝑎𝑔(𝑥	𝑑𝑖𝑎𝑔(𝑥	PROPN
hjic-704	201	14	)	)	PUNCT
hjic-704	202	1	𝐴𝑥	𝐴𝑥	NOUN
hjic-704	202	2	+	+	PUNCT
hjic-704	203	1	𝐾δ	𝐾δ	PROPN
hjic-704	203	2	+	+	NUM
hjic-704	203	3	𝑏	𝑏	PROPN
hjic-704	203	4	(	(	PUNCT
hjic-704	203	5	15	15	NUM
hjic-704	203	6	)	)	PUNCT
hjic-704	203	7	table	table	NOUN
hjic-704	203	8	3	3	NUM
hjic-704	203	9	.	.	X
hjic-704	203	10	number	number	NOUN
hjic-704	203	11	and	and	CCONJ
hjic-704	203	12	sizes	size	NOUN
hjic-704	203	13	of	of	ADP
hjic-704	203	14	the	the	DET
hjic-704	203	15	lmis	lmis	ADJ
hjic-704	203	16	in	in	ADP
hjic-704	203	17	the	the	DET
hjic-704	203	18	case	case	NOUN
hjic-704	203	19	of	of	ADP
hjic-704	203	20	n	n	CCONJ
hjic-704	203	21	-	-	PUNCT
hjic-704	203	22	dimensional	dimensional	ADJ
hjic-704	203	23	lv	lv	PROPN
hjic-704	203	24	systems	system	NOUN
hjic-704	203	25	.	.	PUNCT
hjic-704	204	1	size	size	NOUN
hjic-704	204	2	number	number	NOUN
hjic-704	204	3	description	description	NOUN
hjic-704	204	4	mb	mb	ADP
hjic-704	204	5	×	×	PROPN
hjic-704	204	6	mb	mb	PROPN
hjic-704	204	7	2n	2n	NUM
hjic-704	204	8	positivity	positivity	NOUN
hjic-704	204	9	of	of	ADP
hjic-704	204	10	𝑉(𝑥	𝑉(𝑥	PROPN
hjic-704	204	11	)	)	PUNCT
hjic-704	204	12	ma	ma	PROPN
hjic-704	204	13	×	×	PROPN
hjic-704	204	14	ma	ma	PROPN
hjic-704	204	15	2n	2n	NUM
hjic-704	204	16	negativity	negativity	NOUN
hjic-704	204	17	of	of	ADP
hjic-704	204	18	�	�	PROPN
hjic-704	204	19	̇	̇	PROPN
hjic-704	204	20	�	�	PROPN
hjic-704	204	21	(𝑥	(𝑥	NOUN
hjic-704	204	22	)	)	PUNCT
hjic-704	204	23	mb	mb	ADP
hjic-704	204	24	×	×	NOUN
hjic-704	204	25	mb	mb	ADP
hjic-704	204	26	n	n	CCONJ
hjic-704	204	27	⋅	⋅	PROPN
hjic-704	204	28	2n	2n	NUM
hjic-704	204	29	ε	ε	PROPN
hjic-704	204	30	!	!	PUNCT
hjic-704	204	31	∈	∈	PROPN
hjic-704	204	32	𝔗𝔫𝔱(𝒳	𝔗𝔫𝔱(𝒳	X
hjic-704	204	33	)	)	PUNCT
hjic-704	204	34	mb	mb	ADP
hjic-704	204	35	×	×	NOUN
hjic-704	204	36	mb	mb	ADP
hjic-704	204	37	n	n	CCONJ
hjic-704	204	38	⋅	⋅	PROPN
hjic-704	204	39	2n	2n	NUM
hjic-704	204	40	𝒴	𝒴	PROPN
hjic-704	204	41	∈	∈	PROPN
hjic-704	204	42	𝔗𝔫𝔱(ε	𝔗𝔫𝔱(ε	NOUN
hjic-704	204	43	!	!	PUNCT
hjic-704	204	44	)	)	PUNCT
hjic-704	205	1	mb	mb	ADP
hjic-704	205	2	is	be	AUX
hjic-704	205	3	the	the	DET
hjic-704	205	4	size	size	NOUN
hjic-704	205	5	of	of	ADP
hjic-704	205	6	the	the	DET
hjic-704	205	7	lyapunov	lyapunov	ADJ
hjic-704	205	8	matrix	matrix	NOUN
hjic-704	205	9	p	p	X
hjic-704	205	10	,	,	PUNCT
hjic-704	205	11	ma	ma	PROPN
hjic-704	205	12	=	=	PROPN
hjic-704	205	13	½	½	PROPN
hjic-704	205	14	(	(	PUNCT
hjic-704	205	15	n3	n3	NOUN
hjic-704	205	16	+	+	CCONJ
hjic-704	205	17	5n2	5n2	NUM
hjic-704	205	18	+	+	CCONJ
hjic-704	205	19	4n	4n	NOUN
hjic-704	205	20	)	)	PUNCT
hjic-704	205	21	is	be	AUX
hjic-704	205	22	the	the	DET
hjic-704	205	23	size	size	NOUN
hjic-704	205	24	of	of	ADP
hjic-704	205	25	the	the	DET
hjic-704	205	26	matrix	matrix	NOUN
hjic-704	205	27	pa(p	pa(p	NUM
hjic-704	205	28	)	)	PUNCT
hjic-704	205	29	,	,	PUNCT
hjic-704	205	30	which	which	PRON
hjic-704	205	31	appears	appear	VERB
hjic-704	205	32	in	in	ADP
hjic-704	205	33	the	the	DET
hjic-704	205	34	lmi	lmi	PROPN
hjic-704	205	35	ensuring	ensure	VERB
hjic-704	205	36	the	the	DET
hjic-704	205	37	negativity	negativity	NOUN
hjic-704	205	38	of	of	ADP
hjic-704	205	39	the	the	DET
hjic-704	205	40	time	time	NOUN
hjic-704	205	41	derivative	derivative	NOUN
hjic-704	205	42	of	of	ADP
hjic-704	205	43	the	the	DET
hjic-704	205	44	lyapunov	lyapunov	ADJ
hjic-704	205	45	function	function	NOUN
hjic-704	205	46	.	.	PUNCT
hjic-704	206	1	figure	figure	VERB
hjic-704	206	2	8	8	NUM
hjic-704	206	3	.	.	PUNCT
hjic-704	207	1	cross	cross	ADJ
hjic-704	207	2	-	-	ADJ
hjic-704	207	3	sectional	sectional	ADJ
hjic-704	207	4	view	view	NOUN
hjic-704	207	5	of	of	ADP
hjic-704	207	6	the	the	DET
hjic-704	207	7	doa	doa	PROPN
hjic-704	207	8	estimate	estimate	NOUN
hjic-704	207	9	of	of	ADP
hjic-704	207	10	the	the	DET
hjic-704	207	11	4d	4d	NUM
hjic-704	207	12	lv	lv	PROPN
hjic-704	207	13	system	system	NOUN
hjic-704	207	14	.	.	PUNCT
hjic-704	208	1	computational	computational	ADJ
hjic-704	208	2	stability	stability	NOUN
hjic-704	208	3	analysis	analysis	NOUN
hjic-704	208	4	of	of	ADP
hjic-704	208	5	lotka	lotka	PROPN
hjic-704	208	6	-	-	PUNCT
hjic-704	208	7	volterra	volterra	PROPN
hjic-704	208	8	systems	system	NOUN
hjic-704	208	9	44(2	44(2	PROPN
hjic-704	208	10	)	)	PUNCT
hjic-704	209	1	pp	pp	ADV
hjic-704	209	2	.	.	PUNCT
hjic-704	210	1	113–120	113–120	NUM
hjic-704	210	2	(	(	PUNCT
hjic-704	210	3	2016	2016	NUM
hjic-704	210	4	)	)	PUNCT
hjic-704	210	5	doi	doi	NOUN
hjic-704	210	6	:	:	PUNCT
hjic-704	210	7	10.1515	10.1515	NUM
hjic-704	210	8	/	/	SYM
hjic-704	210	9	hjic-2016	hjic-2016	NOUN
hjic-704	210	10	-	-	PUNCT
hjic-704	210	11	0014	0014	NUM
hjic-704	210	12	119	119	NUM
hjic-704	210	13	the	the	DET
hjic-704	210	14	equilibrium	equilibrium	NOUN
hjic-704	210	15	point	point	NOUN
hjic-704	210	16	of	of	ADP
hjic-704	210	17	the	the	DET
hjic-704	210	18	uncertain	uncertain	ADJ
hjic-704	210	19	system	system	NOUN
hjic-704	210	20	is	be	AUX
hjic-704	210	21	an	an	DET
hjic-704	210	22	affine	affine	ADJ
hjic-704	210	23	function	function	NOUN
hjic-704	210	24	of	of	ADP
hjic-704	210	25	the	the	DET
hjic-704	210	26	uncertain	uncertain	ADJ
hjic-704	210	27	parameter	parameter	PROPN
hjic-704	210	28	δ	δ	PROPN
hjic-704	210	29	:	:	PUNCT
hjic-704	210	30	𝑥∗	𝑥∗	PROPN
hjic-704	210	31	δ	δ	PROPN
hjic-704	210	32	=	=	PROPN
hjic-704	210	33	𝐴	𝐴	PROPN
hjic-704	210	34	!	!	PUNCT
hjic-704	210	35	!	!	PUNCT
hjic-704	211	1	−𝐾δ	−𝐾δ	X
hjic-704	212	1	−	−	NOUN
hjic-704	212	2	b	b	NOUN
hjic-704	212	3	=	=	PUNCT
hjic-704	212	4	−𝐴!!𝐾δ	−𝐴!!𝐾δ	X
hjic-704	212	5	+	+	CCONJ
hjic-704	212	6	𝑥!∗	𝑥!∗	NOUN
hjic-704	212	7	,	,	PUNCT
hjic-704	212	8	(	(	PUNCT
hjic-704	212	9	16	16	NUM
hjic-704	212	10	)	)	PUNCT
hjic-704	212	11	where	where	SCONJ
hjic-704	212	12	𝑥!∗	𝑥!∗	NOUN
hjic-704	212	13	is	be	AUX
hjic-704	212	14	the	the	DET
hjic-704	212	15	equilibrium	equilibrium	NOUN
hjic-704	212	16	point	point	NOUN
hjic-704	212	17	of	of	ADP
hjic-704	212	18	the	the	DET
hjic-704	212	19	system	system	NOUN
hjic-704	212	20	presented	present	VERB
hjic-704	212	21	in	in	ADP
hjic-704	212	22	section	section	NOUN
hjic-704	212	23	5.1	5.1	NUM
hjic-704	212	24	,	,	PUNCT
hjic-704	212	25	i.e.	i.e.	X
hjic-704	212	26	when	when	SCONJ
hjic-704	212	27	δ	δ	PROPN
hjic-704	212	28	=	=	SYM
hjic-704	212	29	0	0	PROPN
hjic-704	212	30	.	.	PUNCT
hjic-704	212	31	eq.(15	eq.(15	NOUN
hjic-704	212	32	)	)	PUNCT
hjic-704	212	33	is	be	AUX
hjic-704	212	34	translated	translate	VERB
hjic-704	212	35	into	into	ADP
hjic-704	212	36	the	the	DET
hjic-704	212	37	following	follow	VERB
hjic-704	212	38	form	form	NOUN
hjic-704	212	39	:	:	PUNCT
hjic-704	212	40	𝑥	𝑥	NOUN
hjic-704	212	41	=	=	PUNCT
hjic-704	212	42	𝑑𝑖𝑎𝑔(𝑥)𝐴	𝑑𝑖𝑎𝑔(𝑥)𝐴	VERB
hjic-704	212	43	𝑥	𝑥	PRON
hjic-704	212	44	−	−	PUNCT
hjic-704	212	45	𝑥∗(δ	𝑥∗(δ	PROPN
hjic-704	212	46	)	)	PUNCT
hjic-704	212	47	.	.	PUNCT
hjic-704	213	1	(	(	PUNCT
hjic-704	213	2	17	17	NUM
hjic-704	213	3	)	)	PUNCT
hjic-704	213	4	the	the	DET
hjic-704	213	5	centred	centred	ADJ
hjic-704	213	6	model	model	NOUN
hjic-704	213	7	of	of	ADP
hjic-704	213	8	the	the	DET
hjic-704	213	9	system	system	NOUN
hjic-704	213	10	around	around	ADP
hjic-704	213	11	the	the	DET
hjic-704	213	12	uncertain	uncertain	ADJ
hjic-704	213	13	equilibrium	equilibrium	NOUN
hjic-704	213	14	point	point	NOUN
hjic-704	213	15	x*(δ	x*(δ	NOUN
hjic-704	213	16	)	)	PUNCT
hjic-704	213	17	can	can	AUX
hjic-704	213	18	be	be	AUX
hjic-704	213	19	calculated	calculate	VERB
hjic-704	213	20	if	if	SCONJ
hjic-704	213	21	the	the	DET
hjic-704	213	22	new	new	ADJ
hjic-704	213	23	state	state	NOUN
hjic-704	213	24	vector	vector	NOUN
hjic-704	213	25	x	x	PUNCT
hjic-704	213	26	=	=	SYM
hjic-704	213	27	𝑥	𝑥	PROPN
hjic-704	213	28	–	–	PUNCT
hjic-704	213	29	x*(δ	x*(δ	NOUN
hjic-704	213	30	)	)	PUNCT
hjic-704	213	31	is	be	AUX
hjic-704	213	32	introduced	introduce	VERB
hjic-704	213	33	.	.	PUNCT
hjic-704	214	1	the	the	DET
hjic-704	214	2	equation	equation	NOUN
hjic-704	214	3	of	of	ADP
hjic-704	214	4	the	the	DET
hjic-704	214	5	centred	centre	VERB
hjic-704	214	6	system	system	NOUN
hjic-704	214	7	is	be	AUX
hjic-704	214	8	the	the	DET
hjic-704	214	9	following	following	NOUN
hjic-704	214	10	:	:	PUNCT
hjic-704	214	11	𝑥	𝑥	X
hjic-704	214	12	=	=	PUNCT
hjic-704	214	13	𝑑𝑖𝑎𝑔	𝑑𝑖𝑎𝑔	VERB
hjic-704	214	14	𝑥	𝑥	X
hjic-704	214	15	+	+	CCONJ
hjic-704	214	16	𝑥∗	𝑥∗	ADJ
hjic-704	214	17	δ	δ	NOUN
hjic-704	215	1	𝐴𝑥	𝐴𝑥	NOUN
hjic-704	215	2	.	.	PUNCT
hjic-704	216	1	(	(	PUNCT
hjic-704	216	2	18	18	NUM
hjic-704	216	3	)	)	PUNCT
hjic-704	216	4	if	if	SCONJ
hjic-704	216	5	the	the	DET
hjic-704	216	6	lyapunov	lyapunov	NOUN
hjic-704	216	7	function	function	NOUN
hjic-704	216	8	depends	depend	VERB
hjic-704	216	9	on	on	ADP
hjic-704	216	10	δ	δ	PROPN
hjic-704	216	11	,	,	PUNCT
hjic-704	216	12	especially	especially	ADV
hjic-704	216	13	when	when	SCONJ
hjic-704	216	14	possessing	possess	VERB
hjic-704	216	15	an	an	DET
hjic-704	216	16	uncertain	uncertain	ADJ
hjic-704	216	17	equilibrium	equilibrium	NOUN
hjic-704	216	18	point	point	NOUN
hjic-704	216	19	,	,	PUNCT
hjic-704	216	20	it	it	PRON
hjic-704	216	21	is	be	AUX
hjic-704	216	22	not	not	PART
hjic-704	216	23	straightforward	straightforward	ADJ
hjic-704	216	24	to	to	PART
hjic-704	216	25	determine	determine	VERB
hjic-704	216	26	an	an	DET
hjic-704	216	27	invariant	invariant	ADJ
hjic-704	216	28	region	region	NOUN
hjic-704	216	29	by	by	ADP
hjic-704	216	30	considering	consider	VERB
hjic-704	216	31	the	the	DET
hjic-704	216	32	α	α	NUM
hjic-704	216	33	-	-	PUNCT
hjic-704	216	34	level	level	NOUN
hjic-704	216	35	set	set	NOUN
hjic-704	216	36	of	of	ADP
hjic-704	216	37	the	the	DET
hjic-704	216	38	lyapunov	lyapunov	ADJ
hjic-704	216	39	function	function	NOUN
hjic-704	216	40	.	.	PUNCT
hjic-704	217	1	however	however	ADV
hjic-704	217	2	,	,	PUNCT
hjic-704	217	3	it	it	PRON
hjic-704	217	4	is	be	AUX
hjic-704	217	5	possible	possible	ADJ
hjic-704	217	6	to	to	PART
hjic-704	217	7	compute	compute	VERB
hjic-704	217	8	a	a	DET
hjic-704	217	9	region	region	NOUN
hjic-704	217	10	ℑ	ℑ	PROPN
hjic-704	217	11	,	,	PUNCT
hjic-704	217	12	which	which	PRON
hjic-704	217	13	is	be	AUX
hjic-704	217	14	“	"	PUNCT
hjic-704	217	15	invariant	invariant	ADJ
hjic-704	217	16	with	with	ADP
hjic-704	217	17	respect	respect	NOUN
hjic-704	217	18	to	to	ADP
hjic-704	217	19	”	"	PUNCT
hjic-704	217	20	a	a	DET
hjic-704	217	21	larger	large	ADJ
hjic-704	217	22	region	region	NOUN
hjic-704	217	23	𝔘	𝔘	NOUN
hjic-704	217	24	(	(	PUNCT
hjic-704	217	25	ℑ	ℑ	PROPN
hjic-704	217	26	⊂	⊂	PROPN
hjic-704	217	27	𝔘	𝔘	PROPN
hjic-704	217	28	)	)	PUNCT
hjic-704	217	29	,	,	PUNCT
hjic-704	217	30	in	in	ADP
hjic-704	217	31	the	the	DET
hjic-704	217	32	sense	sense	NOUN
hjic-704	217	33	that	that	SCONJ
hjic-704	217	34	every	every	DET
hjic-704	217	35	trajectory	trajectory	NOUN
hjic-704	217	36	with	with	ADP
hjic-704	217	37	an	an	DET
hjic-704	217	38	initial	initial	ADJ
hjic-704	217	39	condition	condition	NOUN
hjic-704	217	40	from	from	ADP
hjic-704	217	41	ℑ	ℑ	PROPN
hjic-704	217	42	will	will	AUX
hjic-704	217	43	not	not	PART
hjic-704	217	44	leave	leave	VERB
hjic-704	217	45	𝔘.	𝔘.	PROPN
hjic-704	217	46	in	in	ADP
hjic-704	217	47	order	order	NOUN
hjic-704	217	48	to	to	PART
hjic-704	217	49	compute	compute	VERB
hjic-704	217	50	ℑ	ℑ	PROPN
hjic-704	217	51	and	and	CCONJ
hjic-704	217	52	𝔘	𝔘	PROPN
hjic-704	217	53	,	,	PUNCT
hjic-704	217	54	the	the	DET
hjic-704	217	55	α	α	NOUN
hjic-704	217	56	-	-	PUNCT
hjic-704	217	57	level	level	NOUN
hjic-704	217	58	set	set	NOUN
hjic-704	217	59	ε!(δ	ε!(δ	NUM
hjic-704	217	60	)	)	PUNCT
hjic-704	217	61	of	of	ADP
hjic-704	217	62	the	the	DET
hjic-704	217	63	obtained	obtain	VERB
hjic-704	217	64	lyapunov	lyapunov	NOUN
hjic-704	217	65	function	function	NOUN
hjic-704	217	66	v(x	v(x	PROPN
hjic-704	217	67	,	,	PUNCT
hjic-704	217	68	δ	δ	PROPN
hjic-704	217	69	)	)	PUNCT
hjic-704	217	70	is	be	AUX
hjic-704	217	71	determined	determine	VERB
hjic-704	217	72	in	in	ADP
hjic-704	217	73	the	the	DET
hjic-704	217	74	coordinates	coordinate	NOUN
hjic-704	217	75	system	system	NOUN
hjic-704	217	76	of	of	ADP
hjic-704	217	77	the	the	DET
hjic-704	217	78	original	original	ADJ
hjic-704	217	79	system	system	NOUN
hjic-704	217	80	and	and	CCONJ
hjic-704	217	81	at	at	ADP
hjic-704	217	82	the	the	DET
hjic-704	217	83	corresponding	corresponding	ADJ
hjic-704	217	84	equilibrium	equilibrium	NOUN
hjic-704	217	85	point	point	NOUN
hjic-704	217	86	for	for	ADP
hjic-704	217	87	every	every	DET
hjic-704	217	88	δ	δ	PROPN
hjic-704	217	89	∈	∈	PROPN
hjic-704	217	90	𝒟.	𝒟.	PROPN
hjic-704	217	91	the	the	DET
hjic-704	217	92	overlining	overlining	NOUN
hjic-704	217	93	in	in	ADP
hjic-704	217	94	the	the	DET
hjic-704	217	95	notation	notation	NOUN
hjic-704	217	96	ε!(δ	ε!(δ	NUM
hjic-704	217	97	)	)	PUNCT
hjic-704	217	98	means	mean	VERB
hjic-704	217	99	that	that	SCONJ
hjic-704	217	100	this	this	DET
hjic-704	217	101	level	level	NOUN
hjic-704	217	102	set	set	NOUN
hjic-704	217	103	is	be	AUX
hjic-704	217	104	translated	translate	VERB
hjic-704	217	105	into	into	ADP
hjic-704	217	106	the	the	DET
hjic-704	217	107	original	original	ADJ
hjic-704	217	108	coordinates	coordinate	NOUN
hjic-704	217	109	system	system	NOUN
hjic-704	217	110	.	.	PUNCT
hjic-704	218	1	as	as	ADP
hjic-704	218	2	fig.9	fig.9	PROPN
hjic-704	218	3	illustrates	illustrate	NOUN
hjic-704	218	4	,	,	PUNCT
hjic-704	218	5	the	the	DET
hjic-704	218	6	intersection	intersection	NOUN
hjic-704	218	7	ℑ	ℑ	PROPN
hjic-704	218	8	and	and	CCONJ
hjic-704	218	9	the	the	DET
hjic-704	218	10	union	union	NOUN
hjic-704	218	11	𝔘	𝔘	PROPN
hjic-704	218	12	of	of	ADP
hjic-704	218	13	the	the	DET
hjic-704	218	14	α	α	NOUN
hjic-704	218	15	-	-	PUNCT
hjic-704	218	16	level	level	NOUN
hjic-704	218	17	sets	set	NOUN
hjic-704	218	18	obtained	obtain	VERB
hjic-704	218	19	for	for	ADP
hjic-704	218	20	different	different	ADJ
hjic-704	218	21	values	value	NOUN
hjic-704	218	22	of	of	ADP
hjic-704	218	23	δ	δ	PROPN
hjic-704	218	24	have	have	AUX
hjic-704	218	25	been	be	AUX
hjic-704	218	26	computed	compute	VERB
hjic-704	218	27	.	.	PUNCT
hjic-704	219	1	it	it	PRON
hjic-704	219	2	can	can	AUX
hjic-704	219	3	be	be	AUX
hjic-704	219	4	stated	state	VERB
hjic-704	219	5	that	that	SCONJ
hjic-704	219	6	every	every	DET
hjic-704	219	7	trajectory	trajectory	NOUN
hjic-704	219	8	starting	start	VERB
hjic-704	219	9	from	from	ADP
hjic-704	219	10	region	region	NOUN
hjic-704	219	11	ℑ	ℑ	PROPN
hjic-704	219	12	will	will	AUX
hjic-704	219	13	not	not	PART
hjic-704	219	14	leave	leave	VERB
hjic-704	219	15	region	region	NOUN
hjic-704	219	16	𝔘.	𝔘.	PROPN
hjic-704	219	17	6	6	NUM
hjic-704	219	18	.	.	PUNCT
hjic-704	220	1	conclusion	conclusion	NOUN
hjic-704	220	2	in	in	ADP
hjic-704	220	3	this	this	DET
hjic-704	220	4	work	work	NOUN
hjic-704	220	5	,	,	PUNCT
hjic-704	220	6	the	the	DET
hjic-704	220	7	lyapunov	lyapunov	ADJ
hjic-704	220	8	function	function	NOUN
hjic-704	220	9	of	of	ADP
hjic-704	220	10	n	n	CCONJ
hjic-704	220	11	-	-	PUNCT
hjic-704	220	12	dimensional	dimensional	ADJ
hjic-704	220	13	lv	lv	PROPN
hjic-704	220	14	systems	system	NOUN
hjic-704	220	15	(	(	PUNCT
hjic-704	220	16	n	n	NOUN
hjic-704	220	17	=	=	SYM
hjic-704	220	18	2	2	NUM
hjic-704	220	19	,	,	PUNCT
hjic-704	220	20	3	3	NUM
hjic-704	220	21	,	,	PUNCT
hjic-704	220	22	4	4	NUM
hjic-704	220	23	)	)	PUNCT
hjic-704	220	24	was	be	AUX
hjic-704	220	25	successfully	successfully	ADV
hjic-704	220	26	computed	compute	VERB
hjic-704	220	27	by	by	ADP
hjic-704	220	28	using	use	VERB
hjic-704	220	29	the	the	DET
hjic-704	220	30	improved	improved	ADJ
hjic-704	220	31	optimization	optimization	NOUN
hjic-704	220	32	-	-	PUNCT
hjic-704	220	33	based	base	VERB
hjic-704	220	34	method	method	NOUN
hjic-704	220	35	[	[	X
hjic-704	220	36	6	6	NUM
hjic-704	220	37	,	,	PUNCT
hjic-704	220	38	15	15	NUM
hjic-704	220	39	]	]	PUNCT
hjic-704	220	40	.	.	PUNCT
hjic-704	221	1	in	in	ADP
hjic-704	221	2	the	the	DET
hjic-704	221	3	case	case	NOUN
hjic-704	221	4	of	of	ADP
hjic-704	221	5	each	each	DET
hjic-704	221	6	deterministic	deterministic	ADJ
hjic-704	221	7	system	system	NOUN
hjic-704	221	8	,	,	PUNCT
hjic-704	221	9	an	an	DET
hjic-704	221	10	invariant	invariant	ADJ
hjic-704	221	11	region	region	NOUN
hjic-704	221	12	was	be	AUX
hjic-704	221	13	given	give	VERB
hjic-704	221	14	,	,	PUNCT
hjic-704	221	15	as	as	ADP
hjic-704	221	16	the	the	DET
hjic-704	221	17	estimated	estimate	VERB
hjic-704	221	18	doa	doa	NOUN
hjic-704	221	19	.	.	PUNCT
hjic-704	222	1	in	in	ADP
hjic-704	222	2	the	the	DET
hjic-704	222	3	case	case	NOUN
hjic-704	222	4	of	of	ADP
hjic-704	222	5	an	an	DET
hjic-704	222	6	uncertain	uncertain	ADJ
hjic-704	222	7	lv	lv	PROPN
hjic-704	222	8	system	system	NOUN
hjic-704	222	9	with	with	ADP
hjic-704	222	10	an	an	DET
hjic-704	222	11	uncertain	uncertain	ADJ
hjic-704	222	12	interior	interior	ADJ
hjic-704	222	13	equilibrium	equilibrium	NOUN
hjic-704	222	14	point	point	NOUN
hjic-704	222	15	,	,	PUNCT
hjic-704	222	16	two	two	NUM
hjic-704	222	17	regions	region	NOUN
hjic-704	222	18	(	(	PUNCT
hjic-704	222	19	ℑ	ℑ	PROPN
hjic-704	222	20	⊂	⊂	PROPN
hjic-704	222	21	𝔘	𝔘	PROPN
hjic-704	222	22	)	)	PUNCT
hjic-704	222	23	were	be	AUX
hjic-704	222	24	given	give	VERB
hjic-704	222	25	,	,	PUNCT
hjic-704	222	26	which	which	PRON
hjic-704	222	27	describe	describe	VERB
hjic-704	222	28	the	the	DET
hjic-704	222	29	stable	stable	ADJ
hjic-704	222	30	regions	region	NOUN
hjic-704	222	31	of	of	ADP
hjic-704	222	32	the	the	DET
hjic-704	222	33	system	system	NOUN
hjic-704	222	34	.	.	PUNCT
hjic-704	223	1	symbols	symbol	NOUN
hjic-704	223	2	𝑥	𝑥	PROPN
hjic-704	223	3	denotes	denote	VERB
hjic-704	223	4	the	the	DET
hjic-704	223	5	time	time	NOUN
hjic-704	223	6	-	-	PUNCT
hjic-704	223	7	derivative	derivative	NOUN
hjic-704	223	8	of	of	ADP
hjic-704	223	9	function	function	NOUN
hjic-704	223	10	x(t	x(t	PROPN
hjic-704	223	11	)	)	PUNCT
hjic-704	223	12	lt	lt	PRON
hjic-704	223	13	denotes	denote	VERB
hjic-704	223	14	the	the	DET
hjic-704	223	15	transpose	transpose	NOUN
hjic-704	223	16	of	of	ADP
hjic-704	223	17	a	a	DET
hjic-704	223	18	matrix	matrix	NOUN
hjic-704	223	19	l	l	NOUN
hjic-704	223	20	𝜗(∙	𝜗(∙	NOUN
hjic-704	223	21	)	)	PUNCT
hjic-704	223	22	denotes	denote	VERB
hjic-704	223	23	the	the	DET
hjic-704	223	24	corner	corner	NOUN
hjic-704	223	25	points	point	NOUN
hjic-704	223	26	of	of	ADP
hjic-704	223	27	a	a	DET
hjic-704	223	28	polytope	polytope	NOUN
hjic-704	223	29	diag(x	diag(x	NOUN
hjic-704	223	30	)	)	PUNCT
hjic-704	223	31	denotes	denote	VERB
hjic-704	223	32	the	the	DET
hjic-704	223	33	diagonal	diagonal	ADJ
hjic-704	223	34	matrix	matrix	NOUN
hjic-704	223	35	x	x	PUNCT
hjic-704	223	36	=	=	SYM
hjic-704	223	37	x(t	x(t	PROPN
hjic-704	223	38	)	)	PUNCT
hjic-704	223	39	∈	∈	PROPN
hjic-704	223	40	ℝ	ℝ	PROPN
hjic-704	223	41	!	!	PROPN
hjic-704	223	42	represents	represent	VERB
hjic-704	223	43	the	the	DET
hjic-704	223	44	state	state	NOUN
hjic-704	223	45	variables	variable	NOUN
hjic-704	223	46	of	of	ADP
hjic-704	223	47	a	a	DET
hjic-704	223	48	dynamical	dynamical	ADJ
hjic-704	223	49	system	system	NOUN
hjic-704	223	50	δ	δ	PROPN
hjic-704	223	51	∈	∈	PROPN
hjic-704	223	52	ℝ	ℝ	PROPN
hjic-704	223	53	!	!	PUNCT
hjic-704	223	54	vector	vector	NOUN
hjic-704	223	55	of	of	ADP
hjic-704	223	56	uncertain	uncertain	ADJ
hjic-704	223	57	parameters	parameter	NOUN
hjic-704	223	58	π	π	X
hjic-704	223	59	∈	∈	PROPN
hjic-704	223	60	ℝ	ℝ	PROPN
hjic-704	223	61	!	!	PROPN
hjic-704	223	62	vector	vector	NOUN
hjic-704	223	63	valued	value	VERB
hjic-704	223	64	function	function	NOUN
hjic-704	223	65	,	,	PUNCT
hjic-704	223	66	which	which	PRON
hjic-704	223	67	represents	represent	VERB
hjic-704	223	68	the	the	DET
hjic-704	223	69	set	set	NOUN
hjic-704	223	70	of	of	ADP
hjic-704	223	71	monomial	monomial	ADJ
hjic-704	223	72	and	and	CCONJ
hjic-704	223	73	rational	rational	ADJ
hjic-704	223	74	nonlinear	nonlinear	ADJ
hjic-704	223	75	terms	term	NOUN
hjic-704	223	76	to	to	PART
hjic-704	223	77	be	be	AUX
hjic-704	223	78	considered	consider	VERB
hjic-704	223	79	in	in	ADP
hjic-704	223	80	the	the	DET
hjic-704	223	81	lyapunov	lyapunov	NOUN
hjic-704	223	82	function	function	NOUN
hjic-704	223	83	π	π	PROPN
hjic-704	223	84	∈	∈	PROPN
hjic-704	223	85	ℝ	ℝ	PROPN
hjic-704	223	86	!	!	PUNCT
hjic-704	223	87	!	!	PUNCT
hjic-704	223	88	!	!	PUNCT
hjic-704	223	89	!	!	PUNCT
hjic-704	223	90	!	!	PUNCT
hjic-704	224	1	auxiliary	auxiliary	ADJ
hjic-704	224	2	variable	variable	NOUN
hjic-704	224	3	denoting	denote	VERB
hjic-704	224	4	𝑥𝜋	𝑥𝜋	ADP
hjic-704	224	5	v(x	v(x	PROPN
hjic-704	224	6	)	)	PUNCT
hjic-704	224	7	denotes	denote	VERB
hjic-704	224	8	the	the	DET
hjic-704	224	9	lyapunov	lyapunov	NOUN
hjic-704	224	10	function	function	VERB
hjic-704	224	11	𝒳	𝒳	PROPN
hjic-704	224	12	⊂	⊂	PROPN
hjic-704	224	13	ℝ	ℝ	PROPN
hjic-704	224	14	!	!	PUNCT
hjic-704	224	15	,	,	PUNCT
hjic-704	224	16	𝒟,𝒟	𝒟,𝒟	VERB
hjic-704	224	17	⊂	⊂	PROPN
hjic-704	224	18	ℝ	ℝ	PROPN
hjic-704	224	19	!	!	PROPN
hjic-704	224	20	bounded	bound	VERB
hjic-704	224	21	polytopes	polytopes	PROPN
hjic-704	224	22	acknowledgement	acknowledgement	NOUN
hjic-704	224	23	this	this	DET
hjic-704	224	24	research	research	NOUN
hjic-704	224	25	was	be	AUX
hjic-704	224	26	supported	support	VERB
hjic-704	224	27	by	by	ADP
hjic-704	224	28	otka	otka	PROPN
hjic-704	224	29	nf	nf	NUM
hjic-704	224	30	104706	104706	NUM
hjic-704	224	31	references	reference	NOUN
hjic-704	224	32	[	[	X
hjic-704	224	33	1	1	NUM
hjic-704	224	34	]	]	PUNCT
hjic-704	224	35	chesi	chesi	NOUN
hjic-704	224	36	,	,	PUNCT
hjic-704	224	37	g.	g.	NOUN
hjic-704	224	38	:	:	PUNCT
hjic-704	224	39	domain	domain	NOUN
hjic-704	224	40	of	of	ADP
hjic-704	224	41	attraction	attraction	NOUN
hjic-704	224	42	:	:	PUNCT
hjic-704	224	43	analysis	analysis	NOUN
hjic-704	224	44	and	and	CCONJ
hjic-704	224	45	control	control	NOUN
hjic-704	224	46	via	via	ADP
hjic-704	224	47	sos	sos	PROPN
hjic-704	224	48	programming	programming	PROPN
hjic-704	224	49	(	(	PUNCT
hjic-704	224	50	springer	springer	NOUN
hjic-704	224	51	-	-	PUNCT
hjic-704	224	52	verlag	verlag	PROPN
hjic-704	224	53	,	,	PUNCT
hjic-704	224	54	london	london	PROPN
hjic-704	224	55	,	,	PUNCT
hjic-704	224	56	uk	uk	PROPN
hjic-704	224	57	)	)	PUNCT
hjic-704	224	58	vol	vol	NOUN
hjic-704	224	59	.	.	PUNCT
hjic-704	225	1	415	415	NUM
hjic-704	225	2	,	,	PUNCT
hjic-704	225	3	2011	2011	NUM
hjic-704	225	4	doi	doi	NOUN
hjic-704	225	5	:	:	PUNCT
hjic-704	225	6	10.1007/978	10.1007/978	NUM
hjic-704	225	7	-	-	SYM
hjic-704	225	8	085729	085729	NUM
hjic-704	225	9	-	-	PUNCT
hjic-704	225	10	959	959	NUM
hjic-704	225	11	-	-	SYM
hjic-704	225	12	8	8	NUM
hjic-704	225	13	[	[	SYM
hjic-704	225	14	2	2	NUM
hjic-704	225	15	]	]	PUNCT
hjic-704	225	16	boyd	boyd	PROPN
hjic-704	225	17	,	,	PUNCT
hjic-704	225	18	s.	s.	PROPN
hjic-704	225	19	;	;	PUNCT
hjic-704	225	20	el	el	PROPN
hjic-704	225	21	ghaoui	ghaoui	PROPN
hjic-704	225	22	,	,	PUNCT
hjic-704	225	23	l.	l.	PROPN
hjic-704	225	24	;	;	PUNCT
hjic-704	225	25	feron	feron	PROPN
hjic-704	225	26	,	,	PUNCT
hjic-704	225	27	e.	e.	PROPN
hjic-704	225	28	,	,	PUNCT
hjic-704	225	29	balakrishnan	balakrishnan	PROPN
hjic-704	225	30	,	,	PUNCT
hjic-704	225	31	v.	v.	ADJ
hjic-704	225	32	:	:	PUNCT
hjic-704	225	33	linear	linear	ADJ
hjic-704	225	34	matrix	matrix	NOUN
hjic-704	225	35	inequalities	inequality	NOUN
hjic-704	225	36	in	in	ADP
hjic-704	225	37	system	system	NOUN
hjic-704	225	38	and	and	CCONJ
hjic-704	225	39	control	control	NOUN
hjic-704	225	40	theory	theory	NOUN
hjic-704	225	41	,	,	PUNCT
hjic-704	225	42	in	in	ADP
hjic-704	225	43	studies	study	NOUN
hjic-704	225	44	in	in	ADP
hjic-704	225	45	applied	applied	ADJ
hjic-704	225	46	mathematics	mathematic	NOUN
hjic-704	225	47	(	(	PUNCT
hjic-704	225	48	siam	siam	PROPN
hjic-704	225	49	,	,	PUNCT
hjic-704	225	50	philadelphia	philadelphia	PROPN
hjic-704	225	51	,	,	PUNCT
hjic-704	225	52	pa	pa	PROPN
hjic-704	225	53	,	,	PUNCT
hjic-704	225	54	usa	usa	PROPN
hjic-704	225	55	)	)	PUNCT
hjic-704	225	56	vol	vol	NOUN
hjic-704	225	57	.	.	PROPN
hjic-704	225	58	15	15	NUM
hjic-704	225	59	,	,	PUNCT
hjic-704	225	60	1994	1994	NUM
hjic-704	225	61	doi	doi	NOUN
hjic-704	225	62	:	:	PUNCT
hjic-704	225	63	10.1137/1.9781611970777	10.1137/1.9781611970777	NUM
hjic-704	226	1	[	[	X
hjic-704	226	2	3	3	NUM
hjic-704	226	3	]	]	X
hjic-704	226	4	scherer	scherer	PROPN
hjic-704	226	5	,	,	PUNCT
hjic-704	226	6	c.	c.	PROPN
hjic-704	226	7	;	;	PUNCT
hjic-704	226	8	weiland	weiland	PROPN
hjic-704	226	9	,	,	PUNCT
hjic-704	226	10	s.	s.	PROPN
hjic-704	226	11	:	:	PUNCT
hjic-704	226	12	linear	linear	ADJ
hjic-704	226	13	matrix	matrix	NOUN
hjic-704	226	14	inequalities	inequality	NOUN
hjic-704	226	15	in	in	ADP
hjic-704	226	16	control	control	NOUN
hjic-704	226	17	,	,	PUNCT
hjic-704	226	18	lecture	lecture	NOUN
hjic-704	226	19	notes	note	NOUN
hjic-704	226	20	(	(	PUNCT
hjic-704	226	21	dutch	dutch	PROPN
hjic-704	226	22	institute	institute	PROPN
hjic-704	226	23	for	for	ADP
hjic-704	226	24	systems	system	NOUN
hjic-704	226	25	and	and	CCONJ
hjic-704	226	26	control	control	NOUN
hjic-704	226	27	,	,	PUNCT
hjic-704	226	28	delft	delft	NOUN
hjic-704	226	29	,	,	PUNCT
hjic-704	226	30	the	the	DET
hjic-704	226	31	netherlands	netherlands	PROPN
hjic-704	226	32	)	)	PUNCT
hjic-704	226	33	2000	2000	NUM
hjic-704	226	34	doi	doi	NOUN
hjic-704	226	35	:	:	PUNCT
hjic-704	226	36	10.1201	10.1201	NUM
hjic-704	226	37	/	/	SYM
hjic-704	226	38	b10384	b10384	PROPN
hjic-704	226	39	-	-	NOUN
hjic-704	226	40	28	28	NUM
hjic-704	227	1	[	[	X
hjic-704	227	2	4	4	NUM
hjic-704	227	3	]	]	X
hjic-704	227	4	trofino	trofino	NOUN
hjic-704	227	5	,	,	PUNCT
hjic-704	227	6	a.	a.	NOUN
hjic-704	227	7	;	;	PUNCT
hjic-704	227	8	dezuo	dezuo	NOUN
hjic-704	227	9	,	,	PUNCT
hjic-704	227	10	t.j.m	t.j.m	ADP
hjic-704	227	11	.	.	PUNCT
hjic-704	227	12	:	:	PUNCT
hjic-704	228	1	lmi	lmi	PROPN
hjic-704	228	2	stability	stability	NOUN
hjic-704	228	3	conditions	condition	NOUN
hjic-704	228	4	for	for	ADP
hjic-704	228	5	uncertain	uncertain	ADJ
hjic-704	228	6	rational	rational	ADJ
hjic-704	228	7	nonlinear	nonlinear	ADJ
hjic-704	228	8	systems	system	NOUN
hjic-704	228	9	,	,	PUNCT
hjic-704	228	10	int	int	NOUN
hjic-704	228	11	.	.	PUNCT
hjic-704	229	1	j.	j.	PROPN
hjic-704	229	2	robust	robust	ADJ
hjic-704	229	3	nonlinear	nonlinear	PROPN
hjic-704	229	4	control	control	NOUN
hjic-704	229	5	2013	2013	NUM
hjic-704	229	6	24(18	24(18	NUM
hjic-704	229	7	)	)	PUNCT
hjic-704	229	8	,	,	PUNCT
hjic-704	229	9	3124–3169	3124–3169	NUM
hjic-704	229	10	doi	doi	NOUN
hjic-704	229	11	:	:	PUNCT
hjic-704	229	12	10.1002	10.1002	NUM
hjic-704	229	13	/	/	SYM
hjic-704	229	14	rnc.3047	rnc.3047	NOUN
hjic-704	229	15	figure	figure	NOUN
hjic-704	229	16	9	9	NUM
hjic-704	229	17	.	.	PUNCT
hjic-704	230	1	α	α	X
hjic-704	230	2	-	-	PUNCT
hjic-704	230	3	level	level	NOUN
hjic-704	230	4	set	set	NOUN
hjic-704	230	5	ε!(δ	ε!(δ	NUM
hjic-704	230	6	!	!	PUNCT
hjic-704	230	7	)	)	PUNCT
hjic-704	230	8	of	of	ADP
hjic-704	230	9	the	the	DET
hjic-704	230	10	lyapunov	lyapunov	ADJ
hjic-704	230	11	function	function	NOUN
hjic-704	230	12	in	in	ADP
hjic-704	230	13	the	the	DET
hjic-704	230	14	original	original	ADJ
hjic-704	230	15	coordinates	coordinate	NOUN
hjic-704	230	16	system	system	NOUN
hjic-704	230	17	for	for	ADP
hjic-704	230	18	some	some	DET
hjic-704	230	19	values	value	NOUN
hjic-704	230	20	δi	δi	VERB
hjic-704	230	21	of	of	ADP
hjic-704	230	22	the	the	DET
hjic-704	230	23	uncertain	uncertain	ADJ
hjic-704	230	24	parameter	parameter	NOUN
hjic-704	230	25	and	and	CCONJ
hjic-704	230	26	the	the	DET
hjic-704	230	27	corresponding	corresponding	ADJ
hjic-704	230	28	equilibrium	equilibrium	NOUN
hjic-704	230	29	point	point	NOUN
hjic-704	230	30	x∗(δi	x∗(δi	NUM
hjic-704	230	31	)	)	PUNCT
hjic-704	230	32	of	of	ADP
hjic-704	230	33	the	the	DET
hjic-704	230	34	same	same	ADJ
hjic-704	230	35	color	color	NOUN
hjic-704	230	36	.	.	PUNCT
hjic-704	231	1	the	the	DET
hjic-704	231	2	redfilled	redfilled	ADJ
hjic-704	231	3	region	region	NOUN
hjic-704	231	4	is	be	AUX
hjic-704	231	5	the	the	DET
hjic-704	231	6	intersection	intersection	NOUN
hjic-704	231	7	of	of	ADP
hjic-704	231	8	the	the	DET
hjic-704	231	9	level	level	NOUN
hjic-704	231	10	sets	set	NOUN
hjic-704	231	11	for	for	ADP
hjic-704	231	12	every	every	DET
hjic-704	231	13	possible	possible	ADJ
hjic-704	231	14	value	value	NOUN
hjic-704	231	15	of	of	ADP
hjic-704	231	16	δ	δ	PROPN
hjic-704	231	17	.	.	PUNCT
hjic-704	232	1	the	the	DET
hjic-704	232	2	black	black	ADJ
hjic-704	232	3	line	line	NOUN
hjic-704	232	4	shows	show	VERB
hjic-704	232	5	the	the	DET
hjic-704	232	6	contour	contour	NOUN
hjic-704	232	7	of	of	ADP
hjic-704	232	8	the	the	DET
hjic-704	232	9	union	union	NOUN
hjic-704	232	10	of	of	ADP
hjic-704	232	11	the	the	DET
hjic-704	232	12	level	level	NOUN
hjic-704	232	13	sets	set	NOUN
hjic-704	232	14	.	.	PUNCT
hjic-704	233	1	polcz	polcz	PROPN
hjic-704	233	2	and	and	CCONJ
hjic-704	233	3	szederkényi	szederkényi	PROPN
hjic-704	233	4	hungarian	hungarian	ADJ
hjic-704	233	5	journal	journal	PROPN
hjic-704	233	6	of	of	ADP
hjic-704	233	7	industry	industry	NOUN
hjic-704	233	8	and	and	CCONJ
hjic-704	233	9	chemistry	chemistry	NOUN
hjic-704	233	10	120	120	NUM
hjic-704	233	11	[	[	X
hjic-704	233	12	5	5	NUM
hjic-704	233	13	]	]	X
hjic-704	233	14	polcz	polcz	NOUN
hjic-704	233	15	,	,	PUNCT
hjic-704	233	16	p.	p.	NOUN
hjic-704	233	17	;	;	PUNCT
hjic-704	233	18	szederkényi	szederkényi	PROPN
hjic-704	233	19	,	,	PUNCT
hjic-704	233	20	g.	g.	PROPN
hjic-704	233	21	;	;	PUNCT
hjic-704	233	22	péni	péni	NOUN
hjic-704	233	23	,	,	PUNCT
hjic-704	233	24	t.	t.	PROPN
hjic-704	233	25	:	:	PUNCT
hjic-704	233	26	an	an	DET
hjic-704	233	27	improved	improved	ADJ
hjic-704	233	28	method	method	NOUN
hjic-704	233	29	for	for	ADP
hjic-704	233	30	estimating	estimate	VERB
hjic-704	233	31	the	the	DET
hjic-704	233	32	domain	domain	NOUN
hjic-704	233	33	of	of	ADP
hjic-704	233	34	attraction	attraction	NOUN
hjic-704	233	35	of	of	ADP
hjic-704	233	36	nonlinear	nonlinear	ADJ
hjic-704	233	37	systems	system	NOUN
hjic-704	233	38	containing	contain	VERB
hjic-704	233	39	rational	rational	ADJ
hjic-704	233	40	functions	function	NOUN
hjic-704	233	41	,	,	PUNCT
hjic-704	233	42	j.	j.	PROPN
hjic-704	233	43	physics	physics	PROPN
hjic-704	233	44	:	:	PUNCT
hjic-704	233	45	conf	conf	PROPN
hjic-704	233	46	.	.	PUNCT
hjic-704	233	47	ser	ser	PROPN
hjic-704	233	48	.	.	PROPN
hjic-704	233	49	2015	2015	NUM
hjic-704	233	50	659(1	659(1	NUM
hjic-704	233	51	)	)	PUNCT
hjic-704	233	52	,	,	PUNCT
hjic-704	233	53	012038	012038	NUM
hjic-704	233	54	doi	doi	NOUN
hjic-704	233	55	:	:	PUNCT
hjic-704	233	56	10.1088/1742	10.1088/1742	NUM
hjic-704	233	57	-	-	SYM
hjic-704	233	58	6596/659/1/012038	6596/659/1/012038	NUM
hjic-704	234	1	[	[	X
hjic-704	234	2	6	6	NUM
hjic-704	234	3	]	]	X
hjic-704	234	4	polcz	polcz	NOUN
hjic-704	234	5	,	,	PUNCT
hjic-704	234	6	p.	p.	NOUN
hjic-704	234	7	;	;	PUNCT
hjic-704	234	8	szederkényi	szederkényi	PROPN
hjic-704	234	9	,	,	PUNCT
hjic-704	234	10	g.	g.	PROPN
hjic-704	234	11	;	;	PUNCT
hjic-704	234	12	hangos	hangos	PROPN
hjic-704	234	13	,	,	PUNCT
hjic-704	234	14	k.m	k.m	PROPN
hjic-704	234	15	.	.	PROPN
hjic-704	234	16	:	:	PUNCT
hjic-704	235	1	computational	computational	ADJ
hjic-704	235	2	stability	stability	NOUN
hjic-704	235	3	analysis	analysis	NOUN
hjic-704	235	4	of	of	ADP
hjic-704	235	5	an	an	DET
hjic-704	235	6	uncertain	uncertain	ADJ
hjic-704	235	7	bioreactor	bioreactor	NOUN
hjic-704	235	8	model	model	NOUN
hjic-704	235	9	,	,	PUNCT
hjic-704	235	10	proc	proc	NOUN
hjic-704	235	11	.	.	PUNCT
hjic-704	236	1	int	int	NOUN
hjic-704	236	2	.	.	PUNCT
hjic-704	237	1	symp	symp	PROPN
hjic-704	237	2	.	.	PUNCT
hjic-704	238	1	stability	stability	NOUN
hjic-704	238	2	,	,	PUNCT
hjic-704	238	3	vibration	vibration	NOUN
hjic-704	238	4	,	,	PUNCT
hjic-704	238	5	and	and	CCONJ
hjic-704	238	6	control	control	NOUN
hjic-704	238	7	of	of	ADP
hjic-704	238	8	machines	machine	NOUN
hjic-704	238	9	and	and	CCONJ
hjic-704	238	10	structures	structure	NOUN
hjic-704	238	11	(	(	PUNCT
hjic-704	238	12	svcs	svcs	PROPN
hjic-704	238	13	2016	2016	NUM
hjic-704	238	14	,	,	PUNCT
hjic-704	238	15	budapest	budapest	PROPN
hjic-704	238	16	,	,	PUNCT
hjic-704	238	17	hungary	hungary	PROPN
hjic-704	238	18	)	)	PUNCT
hjic-704	238	19	pp	pp	ADP
hjic-704	238	20	.	.	PUNCT
hjic-704	239	1	1	1	NUM
hjic-704	239	2	-	-	SYM
hjic-704	239	3	12	12	NUM
hjic-704	239	4	,	,	PUNCT
hjic-704	239	5	2016	2016	NUM
hjic-704	239	6	[	[	X
hjic-704	239	7	7	7	NUM
hjic-704	239	8	]	]	PUNCT
hjic-704	239	9	rocha	rocha	PROPN
hjic-704	239	10	filho	filho	PROPN
hjic-704	239	11	,	,	PUNCT
hjic-704	239	12	t.m	t.m	PROPN
hjic-704	239	13	.	.	PROPN
hjic-704	239	14	;	;	PUNCT
hjic-704	239	15	gléria	gléria	PROPN
hjic-704	239	16	,	,	PUNCT
hjic-704	239	17	i.m	i.m	PROPN
hjic-704	239	18	.	.	PROPN
hjic-704	239	19	;	;	PUNCT
hjic-704	239	20	figueiredo	figueiredo	PROPN
hjic-704	239	21	,	,	PUNCT
hjic-704	239	22	a.	a.	NOUN
hjic-704	239	23	;	;	PUNCT
hjic-704	239	24	brenig	brenig	NOUN
hjic-704	239	25	,	,	PUNCT
hjic-704	239	26	l.	l.	PROPN
hjic-704	239	27	:	:	PUNCT
hjic-704	239	28	the	the	DET
hjic-704	239	29	lotka	lotka	PROPN
hjic-704	239	30	–	–	PUNCT
hjic-704	239	31	volterra	volterra	NOUN
hjic-704	239	32	canonical	canonical	ADJ
hjic-704	239	33	format	format	NOUN
hjic-704	239	34	,	,	PUNCT
hjic-704	239	35	ecol	ecol	NOUN
hjic-704	239	36	.	.	PUNCT
hjic-704	240	1	mod	mod	PROPN
hjic-704	240	2	.	.	PROPN
hjic-704	240	3	2005	2005	NUM
hjic-704	240	4	183(1	183(1	NUM
hjic-704	240	5	)	)	PUNCT
hjic-704	240	6	,	,	PUNCT
hjic-704	240	7	95–106	95–106	PROPN
hjic-704	240	8	doi	doi	NOUN
hjic-704	240	9	:	:	PUNCT
hjic-704	240	10	10.1016	10.1016	NUM
hjic-704	240	11	/	/	SYM
hjic-704	240	12	j.ecolmodel.2004.07.023	j.ecolmodel.2004.07.023	X
hjic-704	241	1	[	[	X
hjic-704	241	2	8	8	NUM
hjic-704	241	3	]	]	X
hjic-704	241	4	noonburg	noonburg	NOUN
hjic-704	241	5	,	,	PUNCT
hjic-704	241	6	v.w	v.w	PROPN
hjic-704	241	7	.	.	PROPN
hjic-704	241	8	:	:	PUNCT
hjic-704	242	1	a	a	DET
hjic-704	242	2	neural	neural	ADJ
hjic-704	242	3	network	network	NOUN
hjic-704	242	4	modeled	model	VERB
hjic-704	242	5	by	by	ADP
hjic-704	242	6	an	an	DET
hjic-704	242	7	adaptive	adaptive	ADJ
hjic-704	242	8	lotka	lotka	PROPN
hjic-704	242	9	-	-	PUNCT
hjic-704	242	10	volterra	volterra	NOUN
hjic-704	242	11	system	system	NOUN
hjic-704	242	12	,	,	PUNCT
hjic-704	242	13	siam	siam	PROPN
hjic-704	242	14	j.	j.	PROPN
hjic-704	242	15	appl	appl	PROPN
hjic-704	242	16	.	.	PROPN
hjic-704	242	17	math	math	PROPN
hjic-704	242	18	.	.	PUNCT
hjic-704	243	1	1989	1989	NUM
hjic-704	243	2	49(6	49(6	NOUN
hjic-704	243	3	)	)	PUNCT
hjic-704	243	4	,	,	PUNCT
hjic-704	243	5	1779–1792	1779–1792	NUM
hjic-704	243	6	doi	doi	NOUN
hjic-704	243	7	:	:	PUNCT
hjic-704	243	8	10.1137/0149109	10.1137/0149109	NUM
hjic-704	243	9	[	[	X
hjic-704	243	10	9	9	NUM
hjic-704	243	11	]	]	X
hjic-704	243	12	bhargava	bhargava	NOUN
hjic-704	243	13	,	,	PUNCT
hjic-704	243	14	s.	s.	PROPN
hjic-704	243	15	:	:	PUNCT
hjic-704	243	16	generalized	generalized	ADJ
hjic-704	243	17	lotka	lotka	PROPN
hjic-704	243	18	-	-	PUNCT
hjic-704	243	19	volterra	volterra	NOUN
hjic-704	243	20	equations	equation	NOUN
hjic-704	243	21	and	and	CCONJ
hjic-704	243	22	the	the	DET
hjic-704	243	23	mechanism	mechanism	NOUN
hjic-704	243	24	of	of	ADP
hjic-704	243	25	technological	technological	ADJ
hjic-704	243	26	substitution	substitution	NOUN
hjic-704	243	27	,	,	PUNCT
hjic-704	243	28	technol	technol	NOUN
hjic-704	243	29	.	.	PUNCT
hjic-704	243	30	forecast	forecast	PROPN
hjic-704	243	31	.	.	PUNCT
hjic-704	244	1	soc	soc	PROPN
hjic-704	244	2	.	.	PUNCT
hjic-704	245	1	change	change	VERB
hjic-704	245	2	1989	1989	NUM
hjic-704	245	3	35(4	35(4	NOUN
hjic-704	245	4	)	)	PUNCT
hjic-704	245	5	,	,	PUNCT
hjic-704	245	6	319–326	319–326	NUM
hjic-704	245	7	doi	doi	NOUN
hjic-704	245	8	:	:	PUNCT
hjic-704	245	9	10.1016/0040	10.1016/0040	NUM
hjic-704	245	10	-	-	SYM
hjic-704	245	11	1625(89)90068	1625(89)90068	NUM
hjic-704	245	12	-	-	SYM
hjic-704	245	13	1	1	NUM
hjic-704	246	1	[	[	X
hjic-704	246	2	10	10	NUM
hjic-704	246	3	]	]	X
hjic-704	246	4	goodwin	goodwin	PROPN
hjic-704	246	5	,	,	PUNCT
hjic-704	246	6	r.m	r.m	PROPN
hjic-704	246	7	.	.	PROPN
hjic-704	246	8	:	:	PUNCT
hjic-704	246	9	a	a	DET
hjic-704	246	10	growth	growth	NOUN
hjic-704	246	11	cycle	cycle	NOUN
hjic-704	246	12	,	,	PUNCT
hjic-704	246	13	in	in	ADP
hjic-704	246	14	essays	essay	NOUN
hjic-704	246	15	in	in	ADP
hjic-704	246	16	economic	economic	ADJ
hjic-704	246	17	dynamics	dynamic	NOUN
hjic-704	246	18	(	(	PUNCT
hjic-704	246	19	palgrave	palgrave	PROPN
hjic-704	246	20	,	,	PUNCT
hjic-704	246	21	macmillan	macmillan	PROPN
hjic-704	246	22	,	,	PUNCT
hjic-704	246	23	uk	uk	PROPN
hjic-704	246	24	)	)	PUNCT
hjic-704	246	25	pp	pp	ADP
hjic-704	246	26	.	.	PUNCT
hjic-704	247	1	165–170	165–170	NUM
hjic-704	247	2	,	,	PUNCT
hjic-704	247	3	1982	1982	NUM
hjic-704	247	4	doi	doi	NOUN
hjic-704	247	5	:	:	PUNCT
hjic-704	247	6	10.1007/978	10.1007/978	NUM
hjic-704	247	7	-	-	SYM
hjic-704	247	8	1	1	NUM
hjic-704	247	9	-	-	PUNCT
hjic-704	247	10	349	349	NUM
hjic-704	247	11	-	-	PUNCT
hjic-704	247	12	05504	05504	NUM
hjic-704	247	13	-	-	SYM
hjic-704	247	14	3	3	NUM
hjic-704	247	15	[	[	X
hjic-704	247	16	11	11	NUM
hjic-704	247	17	]	]	X
hjic-704	247	18	huu	huu	PROPN
hjic-704	247	19	,	,	PUNCT
hjic-704	247	20	a.n	a.n	PROPN
hjic-704	247	21	.	.	PROPN
hjic-704	247	22	;	;	PUNCT
hjic-704	247	23	costa	costa	PROPN
hjic-704	247	24	-	-	PUNCT
hjic-704	247	25	lima	lima	PROPN
hjic-704	247	26	,	,	PUNCT
hjic-704	247	27	b.	b.	PROPN
hjic-704	247	28	:	:	PUNCT
hjic-704	247	29	orbits	orbit	NOUN
hjic-704	247	30	in	in	ADP
hjic-704	247	31	a	a	DET
hjic-704	247	32	stochastic	stochastic	ADJ
hjic-704	247	33	goodwin	goodwin	NOUN
hjic-704	247	34	–	–	PUNCT
hjic-704	247	35	lotka	lotka	PROPN
hjic-704	247	36	–	–	PUNCT
hjic-704	247	37	volterra	volterra	NOUN
hjic-704	247	38	model	model	NOUN
hjic-704	247	39	,	,	PUNCT
hjic-704	247	40	j.	j.	PROPN
hjic-704	247	41	math	math	PROPN
hjic-704	247	42	.	.	PUNCT
hjic-704	248	1	anal	anal	PROPN
hjic-704	248	2	.	.	PUNCT
hjic-704	249	1	appl	appl	PROPN
hjic-704	249	2	.	.	PUNCT
hjic-704	250	1	2014	2014	NUM
hjic-704	250	2	419(1	419(1	NUM
hjic-704	250	3	)	)	PUNCT
hjic-704	250	4	,	,	PUNCT
hjic-704	250	5	48–67	48–67	NUM
hjic-704	250	6	doi	doi	NOUN
hjic-704	250	7	:	:	PUNCT
hjic-704	250	8	10.1016	10.1016	NUM
hjic-704	250	9	/	/	SYM
hjic-704	250	10	j.jmaa.2014.04.035	j.jmaa.2014.04.035	X
hjic-704	251	1	[	[	X
hjic-704	251	2	12	12	NUM
hjic-704	251	3	]	]	X
hjic-704	251	4	hernández	hernández	PROPN
hjic-704	251	5	-	-	PUNCT
hjic-704	251	6	bermejo	bermejo	PROPN
hjic-704	251	7	,	,	PUNCT
hjic-704	251	8	b.	b.	PROPN
hjic-704	251	9	;	;	PUNCT
hjic-704	251	10	fairén	fairén	PROPN
hjic-704	251	11	,	,	PUNCT
hjic-704	251	12	v.	v.	PROPN
hjic-704	251	13	:	:	PUNCT
hjic-704	251	14	lotka	lotka	PROPN
hjic-704	251	15	volterra	volterra	PROPN
hjic-704	251	16	representation	representation	NOUN
hjic-704	251	17	of	of	ADP
hjic-704	251	18	general	general	ADJ
hjic-704	251	19	nonlinear	nonlinear	PROPN
hjic-704	251	20	systems	systems	PROPN
hjic-704	251	21	,	,	PUNCT
hjic-704	251	22	math	math	NOUN
hjic-704	251	23	.	.	PUNCT
hjic-704	252	1	biosci	biosci	PROPN
hjic-704	252	2	.	.	PUNCT
hjic-704	253	1	1997	1997	NUM
hjic-704	253	2	140(1	140(1	NUM
hjic-704	253	3	)	)	PUNCT
hjic-704	253	4	,	,	PUNCT
hjic-704	253	5	1–32	1–32	PROPN
hjic-704	253	6	doi	doi	NOUN
hjic-704	253	7	:	:	PUNCT
hjic-704	253	8	10.1016	10.1016	NUM
hjic-704	253	9	/	/	SYM
hjic-704	253	10	s0025	s0025	PROPN
hjic-704	253	11	-	-	PUNCT
hjic-704	253	12	5564(96)00131	5564(96)00131	NUM
hjic-704	253	13	-	-	SYM
hjic-704	253	14	9	9	NUM
hjic-704	253	15	[	[	SYM
hjic-704	253	16	13	13	NUM
hjic-704	253	17	]	]	SYM
hjic-704	253	18	takeuchi	takeuchi	PROPN
hjic-704	253	19	,	,	PUNCT
hjic-704	253	20	y.	y.	NOUN
hjic-704	253	21	:	:	PUNCT
hjic-704	253	22	global	global	ADJ
hjic-704	253	23	dynamical	dynamical	ADJ
hjic-704	253	24	properties	property	NOUN
hjic-704	253	25	of	of	ADP
hjic-704	253	26	lotka	lotka	PROPN
hjic-704	253	27	-	-	PUNCT
hjic-704	253	28	volterra	volterra	PROPN
hjic-704	253	29	systems	system	NOUN
hjic-704	253	30	(	(	PUNCT
hjic-704	253	31	world	world	NOUN
hjic-704	253	32	scientific	scientific	ADJ
hjic-704	253	33	,	,	PUNCT
hjic-704	253	34	singapore	singapore	PROPN
hjic-704	253	35	)	)	PUNCT
hjic-704	253	36	1996	1996	NUM
hjic-704	253	37	�	�	PROPN
hjic-704	253	38	doi	doi	PROPN
hjic-704	253	39	:	:	PUNCT
hjic-704	253	40	10.1142/9789812830548	10.1142/9789812830548	NUM
hjic-704	254	1	[	[	X
hjic-704	254	2	14	14	NUM
hjic-704	254	3	]	]	X
hjic-704	254	4	plank	plank	NOUN
hjic-704	254	5	,	,	PUNCT
hjic-704	254	6	m.	m.	NOUN
hjic-704	254	7	:	:	PUNCT
hjic-704	254	8	hamiltonian	hamiltonian	ADJ
hjic-704	254	9	structures	structure	NOUN
hjic-704	254	10	for	for	ADP
hjic-704	254	11	the	the	DET
hjic-704	254	12	n	n	DET
hjic-704	254	13	dimensional	dimensional	ADJ
hjic-704	254	14	lotka	lotka	PROPN
hjic-704	254	15	–	–	PUNCT
hjic-704	254	16	volterra	volterra	NOUN
hjic-704	254	17	equations	equation	NOUN
hjic-704	254	18	,	,	PUNCT
hjic-704	254	19	j.	j.	PROPN
hjic-704	254	20	math	math	PROPN
hjic-704	254	21	.	.	PUNCT
hjic-704	255	1	phys	phy	NOUN
hjic-704	255	2	.	.	PUNCT
hjic-704	256	1	1995	1995	NUM
hjic-704	256	2	36(7	36(7	NOUN
hjic-704	256	3	)	)	PUNCT
hjic-704	256	4	,	,	PUNCT
hjic-704	256	5	3520–3534	3520–3534	NUM
hjic-704	256	6	�	�	PROPN
hjic-704	256	7	doi	doi	PROPN
hjic-704	256	8	:	:	PUNCT
hjic-704	256	9	10.1063/1.530978	10.1063/1.530978	NUM
hjic-704	256	10	[	[	SYM
hjic-704	256	11	15	15	NUM
hjic-704	256	12	]	]	X
hjic-704	256	13	polcz	polcz	NOUN
hjic-704	256	14	,	,	PUNCT
hjic-704	256	15	p.	p.	NOUN
hjic-704	256	16	;	;	PUNCT
hjic-704	256	17	szederkényi	szederkényi	PROPN
hjic-704	256	18	,	,	PUNCT
hjic-704	256	19	g.	g.	PROPN
hjic-704	256	20	:	:	PUNCT
hjic-704	256	21	an	an	DET
hjic-704	256	22	improved	improved	ADJ
hjic-704	256	23	method	method	NOUN
hjic-704	256	24	for	for	ADP
hjic-704	256	25	estimating	estimate	VERB
hjic-704	256	26	the	the	DET
hjic-704	256	27	domain	domain	NOUN
hjic-704	256	28	of	of	ADP
hjic-704	256	29	attraction	attraction	NOUN
hjic-704	256	30	of	of	ADP
hjic-704	256	31	uncertain	uncertain	ADJ
hjic-704	256	32	rational	rational	ADJ
hjic-704	256	33	systems	system	NOUN
hjic-704	256	34	using	use	VERB
hjic-704	256	35	linear	linear	ADJ
hjic-704	256	36	matrix	matrix	NOUN
hjic-704	256	37	inequality	inequality	NOUN
hjic-704	256	38	conditions	condition	NOUN
hjic-704	256	39	and	and	CCONJ
hjic-704	256	40	sdp	sdp	NOUN
hjic-704	256	41	optimization	optimization	NOUN
hjic-704	256	42	,	,	PUNCT
hjic-704	256	43	technical	technical	ADJ
hjic-704	256	44	report	report	NOUN
hjic-704	256	45	(	(	PUNCT
hjic-704	256	46	faculty	faculty	NOUN
hjic-704	256	47	of	of	ADP
hjic-704	256	48	inform	inform	NOUN
hjic-704	256	49	.	.	PUNCT
hjic-704	257	1	techn	techn	VERB
hjic-704	257	2	.	.	PROPN
hjic-704	258	1	and	and	CCONJ
hjic-704	258	2	bionics	bionic	NOUN
hjic-704	258	3	,	,	PUNCT
hjic-704	258	4	pázmány	pázmány	PROPN
hjic-704	258	5	péter	péter	PROPN
hjic-704	258	6	catholic	catholic	PROPN
hjic-704	258	7	univ	univ	PROPN
hjic-704	258	8	.	.	PROPN
hjic-704	258	9	,	,	PUNCT
hjic-704	258	10	budapest	budapest	PROPN
hjic-704	258	11	,	,	PUNCT
hjic-704	258	12	hungary	hungary	PROPN
hjic-704	258	13	)	)	PUNCT
hjic-704	258	14	,	,	PUNCT
hjic-704	258	15	2016	2016	NUM
hjic-704	258	16	users.itk.ppke.hu/~polpe/techreport2016apr.pdf	users.itk.ppke.hu/~polpe/techreport2016apr.pdf	NOUN
hjic-704	258	17	[	[	X
hjic-704	258	18	16	16	NUM
hjic-704	258	19	]	]	PUNCT
hjic-704	258	20	�	�	PROPN
hjic-704	258	21	hecker	hecker	PROPN
hjic-704	258	22	,	,	PUNCT
hjic-704	258	23	s.	s.	PROPN
hjic-704	258	24	;	;	PUNCT
hjic-704	258	25	varga	varga	PROPN
hjic-704	258	26	,	,	PUNCT
hjic-704	258	27	a.	a.	PROPN
hjic-704	258	28	;	;	PUNCT
hjic-704	258	29	magni	magni	PROPN
hjic-704	258	30	,	,	PUNCT
hjic-704	258	31	j.f	j.f	PROPN
hjic-704	258	32	.	.	PROPN
hjic-704	258	33	:	:	PUNCT
hjic-704	258	34	enhanced	enhance	VERB
hjic-704	258	35	lfrtoolbox	lfrtoolbox	NOUN
hjic-704	258	36	for	for	ADP
hjic-704	258	37	matlab	matlab	PROPN
hjic-704	258	38	,	,	PUNCT
hjic-704	258	39	proc	proc	NOUN
hjic-704	258	40	.	.	PUNCT
hjic-704	259	1	ieee	ieee	PROPN
hjic-704	259	2	int	int	PROPN
hjic-704	259	3	.	.	PUNCT
hjic-704	260	1	symp	symp	PROPN
hjic-704	260	2	.	.	PUNCT
hjic-704	261	1	computer	computer	NOUN
hjic-704	261	2	aided	aid	VERB
hjic-704	261	3	control	control	NOUN
hjic-704	261	4	systems	system	NOUN
hjic-704	261	5	design	design	NOUN
hjic-704	261	6	pp	pp	X
hjic-704	261	7	.	.	PUNCT
hjic-704	262	1	25	25	NUM
hjic-704	262	2	–	–	PUNCT
hjic-704	262	3	29	29	NUM
hjic-704	262	4	,	,	PUNCT
hjic-704	262	5	2004	2004	NUM
hjic-704	262	6	doi	doi	NOUN
hjic-704	262	7	:	:	PUNCT
hjic-704	262	8	10.1109	10.1109	NUM
hjic-704	262	9	/	/	SYM
hjic-704	262	10	cacsd.2004.1393845	cacsd.2004.1393845	NOUN
hjic-704	263	1	[	[	X
hjic-704	263	2	17	17	NUM
hjic-704	263	3	]	]	X
hjic-704	263	4	magni	magni	X
hjic-704	263	5	,	,	PUNCT
hjic-704	263	6	j.f	j.f	PROPN
hjic-704	263	7	.	.	PROPN
hjic-704	263	8	:	:	PUNCT
hjic-704	263	9	linear	linear	ADJ
hjic-704	263	10	fractional	fractional	ADJ
hjic-704	263	11	representation	representation	NOUN
hjic-704	263	12	toolbox	toolbox	NOUN
hjic-704	263	13	(	(	PUNCT
hjic-704	263	14	ver	ver	NOUN
hjic-704	263	15	.	.	PROPN
hjic-704	263	16	2.0	2.0	NUM
hjic-704	263	17	)	)	PUNCT
hjic-704	263	18	for	for	ADP
hjic-704	263	19	use	use	NOUN
hjic-704	263	20	with	with	ADP
hjic-704	263	21	matlab	matlab	PROPN
hjic-704	263	22	,	,	PUNCT
hjic-704	263	23	2006	2006	NUM
hjic-704	263	24	www.cert	www.cert	NOUN
hjic-704	263	25	.	.	PUNCT
hjic-704	264	1	fr	fr	PROPN
hjic-704	264	2	/	/	SYM
hjic-704	264	3	dcsd	dcsd	PROPN
hjic-704	264	4	/	/	SYM
hjic-704	264	5	idco	idco	NOUN
hjic-704	264	6	/	/	SYM
hjic-704	264	7	perso/~magni	perso/~magni	NOUN
hjic-704	265	1	[	[	X
hjic-704	265	2	18	18	NUM
hjic-704	265	3	]	]	PUNCT
hjic-704	265	4	loefberg	loefberg	NOUN
hjic-704	265	5	,	,	PUNCT
hjic-704	265	6	j.	j.	PROPN
hjic-704	265	7	:	:	PUNCT
hjic-704	265	8	yalmip	yalmip	ADV
hjic-704	265	9	:	:	PUNCT
hjic-704	265	10	a	a	DET
hjic-704	265	11	toolbox	toolbox	NOUN
hjic-704	265	12	for	for	ADP
hjic-704	265	13	modeling	modeling	NOUN
hjic-704	265	14	and	and	CCONJ
hjic-704	265	15	optimization	optimization	NOUN
hjic-704	265	16	in	in	ADP
hjic-704	265	17	matlab	matlab	PROPN
hjic-704	265	18	,	,	PUNCT
hjic-704	265	19	proc	proc	NOUN
hjic-704	265	20	.	.	PUNCT
hjic-704	266	1	cacsd	cacsd	PROPN
hjic-704	266	2	conference	conference	PROPN
hjic-704	266	3	(	(	PUNCT
hjic-704	266	4	taipei	taipei	PROPN
hjic-704	266	5	,	,	PUNCT
hjic-704	266	6	taiwan	taiwan	PROPN
hjic-704	266	7	)	)	PUNCT
hjic-704	266	8	,	,	PUNCT
hjic-704	266	9	2012	2012	NUM
hjic-704	266	10	users.isy.liu.se/	users.isy.liu.se/	NUM
hjic-704	266	11	johanl	johanl	NOUN
hjic-704	266	12	/	/	SYM
hjic-704	266	13	yalmip	yalmip	NOUN