id	sid	tid	token	lemma	pos
ejpam-6072	1	1	european	european	PROPN
ejpam-6072	1	2	journal	journal	PROPN
ejpam-6072	1	3	of	of	ADP
ejpam-6072	1	4	pure	pure	ADJ
ejpam-6072	1	5	and	and	CCONJ
ejpam-6072	1	6	applied	applied	ADJ
ejpam-6072	1	7	mathematics	mathematic	NOUN
ejpam-6072	1	8	2025	2025	NUM
ejpam-6072	1	9	,	,	PUNCT
ejpam-6072	1	10	vol	vol	NOUN
ejpam-6072	1	11	.	.	PROPN
ejpam-6072	1	12	18	18	NUM
ejpam-6072	1	13	,	,	PUNCT
ejpam-6072	1	14	issue	issue	NOUN
ejpam-6072	1	15	2	2	NUM
ejpam-6072	1	16	,	,	PUNCT
ejpam-6072	1	17	article	article	NOUN
ejpam-6072	1	18	number	number	NOUN
ejpam-6072	1	19	6072	6072	NUM
ejpam-6072	1	20	issn	issn	VERB
ejpam-6072	1	21	1307	1307	NUM
ejpam-6072	1	22	-	-	SYM
ejpam-6072	1	23	5543	5543	NUM
ejpam-6072	1	24	–	–	PUNCT
ejpam-6072	1	25	ejpam.com	ejpam.com	X
ejpam-6072	1	26	published	publish	VERB
ejpam-6072	1	27	by	by	ADP
ejpam-6072	1	28	new	new	PROPN
ejpam-6072	1	29	york	york	PROPN
ejpam-6072	1	30	business	business	PROPN
ejpam-6072	1	31	global	global	PROPN
ejpam-6072	1	32	common	common	ADJ
ejpam-6072	1	33	riccati	riccati	PROPN
ejpam-6072	1	34	stability	stability	NOUN
ejpam-6072	1	35	and	and	CCONJ
ejpam-6072	1	36	time	time	NOUN
ejpam-6072	1	37	-	-	PUNCT
ejpam-6072	1	38	delay	delay	NOUN
ejpam-6072	1	39	systems	systems	PROPN
ejpam-6072	1	40	ali	ali	PROPN
ejpam-6072	1	41	algefary1,∗	algefary1,∗	PROPN
ejpam-6072	1	42	,	,	PUNCT
ejpam-6072	1	43	khulud	khulud	PROPN
ejpam-6072	1	44	abdullah	abdullah	PROPN
ejpam-6072	1	45	alqufari2	alqufari2	PROPN
ejpam-6072	1	46	1	1	NUM
ejpam-6072	1	47	department	department	NOUN
ejpam-6072	1	48	of	of	ADP
ejpam-6072	1	49	mathematics	mathematic	NOUN
ejpam-6072	1	50	,	,	PUNCT
ejpam-6072	1	51	college	college	NOUN
ejpam-6072	1	52	of	of	ADP
ejpam-6072	1	53	science	science	NOUN
ejpam-6072	1	54	,	,	PUNCT
ejpam-6072	1	55	qassim	qassim	PROPN
ejpam-6072	1	56	university	university	PROPN
ejpam-6072	1	57	,	,	PUNCT
ejpam-6072	1	58	p.o	p.o	PROPN
ejpam-6072	1	59	.	.	PROPN
ejpam-6072	1	60	box	box	PROPN
ejpam-6072	1	61	6644	6644	NUM
ejpam-6072	1	62	,	,	PUNCT
ejpam-6072	1	63	buraydah	buraydah	NOUN
ejpam-6072	1	64	51452	51452	NUM
ejpam-6072	1	65	,	,	PUNCT
ejpam-6072	1	66	saudi	saudi	PROPN
ejpam-6072	1	67	arabia	arabia	PROPN
ejpam-6072	1	68	.	.	PUNCT
ejpam-6072	2	1	2	2	NUM
ejpam-6072	2	2	department	department	NOUN
ejpam-6072	2	3	of	of	ADP
ejpam-6072	2	4	statistics	statistic	NOUN
ejpam-6072	2	5	and	and	CCONJ
ejpam-6072	2	6	operation	operation	NOUN
ejpam-6072	2	7	research	research	NOUN
ejpam-6072	2	8	,	,	PUNCT
ejpam-6072	2	9	college	college	NOUN
ejpam-6072	2	10	of	of	ADP
ejpam-6072	2	11	science	science	NOUN
ejpam-6072	2	12	,	,	PUNCT
ejpam-6072	2	13	qassim	qassim	PROPN
ejpam-6072	2	14	university	university	PROPN
ejpam-6072	2	15	,	,	PUNCT
ejpam-6072	2	16	p.o	p.o	PROPN
ejpam-6072	2	17	.	.	PROPN
ejpam-6072	2	18	box	box	PROPN
ejpam-6072	2	19	6644	6644	NUM
ejpam-6072	2	20	,	,	PUNCT
ejpam-6072	2	21	buraydah	buraydah	NOUN
ejpam-6072	2	22	51452	51452	NUM
ejpam-6072	2	23	,	,	PUNCT
ejpam-6072	2	24	saudi	saudi	PROPN
ejpam-6072	2	25	arabia	arabia	PROPN
ejpam-6072	2	26	abstract	abstract	NOUN
ejpam-6072	2	27	.	.	PUNCT
ejpam-6072	3	1	this	this	DET
ejpam-6072	3	2	paper	paper	NOUN
ejpam-6072	3	3	investigates	investigate	VERB
ejpam-6072	3	4	the	the	DET
ejpam-6072	3	5	stability	stability	NOUN
ejpam-6072	3	6	properties	property	NOUN
ejpam-6072	3	7	of	of	ADP
ejpam-6072	3	8	matrix	matrix	NOUN
ejpam-6072	3	9	families	family	NOUN
ejpam-6072	3	10	through	through	ADP
ejpam-6072	3	11	the	the	DET
ejpam-6072	3	12	lens	lens	NOUN
ejpam-6072	3	13	of	of	ADP
ejpam-6072	3	14	riccati	riccati	PROPN
ejpam-6072	3	15	,	,	PUNCT
ejpam-6072	3	16	lyapunov	lyapunov	NOUN
ejpam-6072	3	17	,	,	PUNCT
ejpam-6072	3	18	and	and	CCONJ
ejpam-6072	3	19	schur	schur	ADJ
ejpam-6072	3	20	stability	stability	NOUN
ejpam-6072	3	21	.	.	PUNCT
ejpam-6072	4	1	we	we	PRON
ejpam-6072	4	2	focus	focus	VERB
ejpam-6072	4	3	on	on	ADP
ejpam-6072	4	4	establishing	establish	VERB
ejpam-6072	4	5	connections	connection	NOUN
ejpam-6072	4	6	between	between	ADP
ejpam-6072	4	7	these	these	DET
ejpam-6072	4	8	stability	stability	NOUN
ejpam-6072	4	9	concepts	concept	NOUN
ejpam-6072	4	10	,	,	PUNCT
ejpam-6072	4	11	particularly	particularly	ADV
ejpam-6072	4	12	in	in	ADP
ejpam-6072	4	13	the	the	DET
ejpam-6072	4	14	context	context	NOUN
ejpam-6072	4	15	of	of	ADP
ejpam-6072	4	16	continuous	continuous	ADJ
ejpam-6072	4	17	and	and	CCONJ
ejpam-6072	4	18	discrete	discrete	ADJ
ejpam-6072	4	19	-	-	PUNCT
ejpam-6072	4	20	time	time	NOUN
ejpam-6072	4	21	systems	system	NOUN
ejpam-6072	4	22	,	,	PUNCT
ejpam-6072	4	23	as	as	ADV
ejpam-6072	4	24	well	well	ADV
ejpam-6072	4	25	as	as	ADP
ejpam-6072	4	26	time	time	NOUN
ejpam-6072	4	27	-	-	PUNCT
ejpam-6072	4	28	delay	delay	NOUN
ejpam-6072	4	29	systems	system	NOUN
ejpam-6072	4	30	.	.	PUNCT
ejpam-6072	5	1	the	the	DET
ejpam-6072	5	2	results	result	NOUN
ejpam-6072	5	3	provide	provide	VERB
ejpam-6072	5	4	criteria	criterion	NOUN
ejpam-6072	5	5	for	for	ADP
ejpam-6072	5	6	common	common	ADJ
ejpam-6072	5	7	riccati	riccati	NOUN
ejpam-6072	5	8	stability	stability	NOUN
ejpam-6072	5	9	,	,	PUNCT
ejpam-6072	5	10	exploring	explore	VERB
ejpam-6072	5	11	its	its	PRON
ejpam-6072	5	12	implications	implication	NOUN
ejpam-6072	5	13	on	on	ADP
ejpam-6072	5	14	lyapunov	lyapunov	PROPN
ejpam-6072	5	15	and	and	CCONJ
ejpam-6072	5	16	schur	schur	VERB
ejpam-6072	5	17	stability	stability	NOUN
ejpam-6072	5	18	across	across	ADP
ejpam-6072	5	19	matrix	matrix	NOUN
ejpam-6072	5	20	families	family	NOUN
ejpam-6072	5	21	.	.	PUNCT
ejpam-6072	6	1	furthermore	furthermore	ADV
ejpam-6072	6	2	,	,	PUNCT
ejpam-6072	6	3	we	we	PRON
ejpam-6072	6	4	examine	examine	VERB
ejpam-6072	6	5	the	the	DET
ejpam-6072	6	6	effects	effect	NOUN
ejpam-6072	6	7	of	of	ADP
ejpam-6072	6	8	scaling	scale	VERB
ejpam-6072	6	9	transformations	transformation	NOUN
ejpam-6072	6	10	and	and	CCONJ
ejpam-6072	6	11	similarity	similarity	NOUN
ejpam-6072	6	12	transformations	transformation	NOUN
ejpam-6072	6	13	on	on	ADP
ejpam-6072	6	14	common	common	ADJ
ejpam-6072	6	15	riccati	riccati	NOUN
ejpam-6072	6	16	stability	stability	NOUN
ejpam-6072	6	17	,	,	PUNCT
ejpam-6072	6	18	demonstrating	demonstrate	VERB
ejpam-6072	6	19	its	its	PRON
ejpam-6072	6	20	robustness	robustness	NOUN
ejpam-6072	6	21	under	under	ADP
ejpam-6072	6	22	scalar	scalar	ADJ
ejpam-6072	6	23	multiplication	multiplication	NOUN
ejpam-6072	6	24	and	and	CCONJ
ejpam-6072	6	25	similarity	similarity	NOUN
ejpam-6072	6	26	changes	change	NOUN
ejpam-6072	6	27	.	.	PUNCT
ejpam-6072	7	1	the	the	DET
ejpam-6072	7	2	findings	finding	NOUN
ejpam-6072	7	3	contribute	contribute	VERB
ejpam-6072	7	4	to	to	ADP
ejpam-6072	7	5	a	a	DET
ejpam-6072	7	6	deeper	deep	ADJ
ejpam-6072	7	7	understanding	understanding	NOUN
ejpam-6072	7	8	of	of	ADP
ejpam-6072	7	9	matrix	matrix	NOUN
ejpam-6072	7	10	stability	stability	NOUN
ejpam-6072	7	11	in	in	ADP
ejpam-6072	7	12	control	control	NOUN
ejpam-6072	7	13	systems	system	NOUN
ejpam-6072	7	14	,	,	PUNCT
ejpam-6072	7	15	offering	offer	VERB
ejpam-6072	7	16	insights	insight	NOUN
ejpam-6072	7	17	into	into	ADP
ejpam-6072	7	18	the	the	DET
ejpam-6072	7	19	structural	structural	ADJ
ejpam-6072	7	20	preservation	preservation	NOUN
ejpam-6072	7	21	of	of	ADP
ejpam-6072	7	22	stability	stability	NOUN
ejpam-6072	7	23	properties	property	NOUN
ejpam-6072	7	24	under	under	ADP
ejpam-6072	7	25	various	various	ADJ
ejpam-6072	7	26	transformations	transformation	NOUN
ejpam-6072	7	27	.	.	PUNCT
ejpam-6072	8	1	this	this	DET
ejpam-6072	8	2	work	work	NOUN
ejpam-6072	8	3	has	have	VERB
ejpam-6072	8	4	potential	potential	ADJ
ejpam-6072	8	5	applications	application	NOUN
ejpam-6072	8	6	in	in	ADP
ejpam-6072	8	7	robust	robust	ADJ
ejpam-6072	8	8	control	control	NOUN
ejpam-6072	8	9	and	and	CCONJ
ejpam-6072	8	10	the	the	DET
ejpam-6072	8	11	stability	stability	NOUN
ejpam-6072	8	12	analysis	analysis	NOUN
ejpam-6072	8	13	of	of	ADP
ejpam-6072	8	14	complex	complex	ADJ
ejpam-6072	8	15	systems	system	NOUN
ejpam-6072	8	16	subject	subject	ADJ
ejpam-6072	8	17	to	to	ADP
ejpam-6072	8	18	time	time	NOUN
ejpam-6072	8	19	delays	delay	NOUN
ejpam-6072	8	20	and	and	CCONJ
ejpam-6072	8	21	structural	structural	ADJ
ejpam-6072	8	22	modifications	modification	NOUN
ejpam-6072	8	23	.	.	PUNCT
ejpam-6072	9	1	2020	2020	NUM
ejpam-6072	9	2	mathematics	mathematic	NOUN
ejpam-6072	9	3	subject	subject	NOUN
ejpam-6072	9	4	classifications	classification	NOUN
ejpam-6072	9	5	:	:	PUNCT
ejpam-6072	9	6	15a45	15a45	NUM
ejpam-6072	9	7	,	,	PUNCT
ejpam-6072	9	8	15b48	15b48	NUM
ejpam-6072	9	9	,	,	PUNCT
ejpam-6072	9	10	93d05	93d05	NUM
ejpam-6072	9	11	,	,	PUNCT
ejpam-6072	9	12	34k25	34k25	NUM
ejpam-6072	9	13	,	,	PUNCT
ejpam-6072	9	14	34k05	34k05	PRON
ejpam-6072	9	15	key	key	ADJ
ejpam-6072	9	16	words	word	NOUN
ejpam-6072	9	17	and	and	CCONJ
ejpam-6072	9	18	phrases	phrase	NOUN
ejpam-6072	9	19	:	:	PUNCT
ejpam-6072	9	20	common	common	ADJ
ejpam-6072	9	21	riccati	riccati	NOUN
ejpam-6072	9	22	stability	stability	NOUN
ejpam-6072	9	23	,	,	PUNCT
ejpam-6072	9	24	differential	differential	ADJ
ejpam-6072	9	25	equations	equation	NOUN
ejpam-6072	9	26	,	,	PUNCT
ejpam-6072	9	27	lyapunov	lyapunov	NOUN
ejpam-6072	9	28	functions	function	NOUN
ejpam-6072	9	29	,	,	PUNCT
ejpam-6072	9	30	positive	positive	ADJ
ejpam-6072	9	31	definite	definite	ADJ
ejpam-6072	9	32	matrices	matrix	NOUN
ejpam-6072	9	33	,	,	PUNCT
ejpam-6072	9	34	common	common	ADJ
ejpam-6072	9	35	lyapunov	lyapunov	ADJ
ejpam-6072	9	36	stability	stability	NOUN
ejpam-6072	9	37	1	1	NUM
ejpam-6072	9	38	.	.	PUNCT
ejpam-6072	10	1	introduction	introduction	NOUN
ejpam-6072	10	2	the	the	DET
ejpam-6072	10	3	work	work	NOUN
ejpam-6072	10	4	in	in	ADP
ejpam-6072	10	5	this	this	DET
ejpam-6072	10	6	paper	paper	NOUN
ejpam-6072	10	7	considers	consider	VERB
ejpam-6072	10	8	only	only	ADJ
ejpam-6072	10	9	matrices	matrix	NOUN
ejpam-6072	10	10	in	in	ADP
ejpam-6072	10	11	the	the	DET
ejpam-6072	10	12	real	real	ADJ
ejpam-6072	10	13	space	space	NOUN
ejpam-6072	10	14	rn×n	rn×n	NOUN
ejpam-6072	10	15	.	.	PUNCT
ejpam-6072	11	1	we	we	PRON
ejpam-6072	11	2	use	use	VERB
ejpam-6072	11	3	the	the	DET
ejpam-6072	11	4	notation	notation	NOUN
ejpam-6072	11	5	x	x	PUNCT
ejpam-6072	11	6	≻	≻	PROPN
ejpam-6072	11	7	0	0	NUM
ejpam-6072	11	8	(	(	PUNCT
ejpam-6072	11	9	x	x	NOUN
ejpam-6072	11	10	≺	≺	NOUN
ejpam-6072	11	11	0	0	NUM
ejpam-6072	11	12	,	,	PUNCT
ejpam-6072	11	13	respectively	respectively	ADV
ejpam-6072	11	14	)	)	PUNCT
ejpam-6072	11	15	to	to	PART
ejpam-6072	11	16	indicate	indicate	VERB
ejpam-6072	11	17	that	that	SCONJ
ejpam-6072	11	18	a	a	DET
ejpam-6072	11	19	matrix	matrix	NOUN
ejpam-6072	11	20	x	x	SYM
ejpam-6072	11	21	∈	∈	NOUN
ejpam-6072	11	22	rn×n	rn×n	NOUN
ejpam-6072	11	23	is	be	AUX
ejpam-6072	11	24	positive	positive	ADJ
ejpam-6072	11	25	definite	definite	ADJ
ejpam-6072	11	26	(	(	PUNCT
ejpam-6072	11	27	negative	negative	ADJ
ejpam-6072	11	28	definite	definite	ADJ
ejpam-6072	11	29	,	,	PUNCT
ejpam-6072	11	30	respectively	respectively	ADV
ejpam-6072	11	31	)	)	PUNCT
ejpam-6072	11	32	.	.	PUNCT
ejpam-6072	12	1	similarly	similarly	ADV
ejpam-6072	12	2	,	,	PUNCT
ejpam-6072	12	3	we	we	PRON
ejpam-6072	12	4	denote	denote	VERB
ejpam-6072	12	5	a	a	DET
ejpam-6072	12	6	positive	positive	ADJ
ejpam-6072	12	7	semidefinite	semidefinite	NOUN
ejpam-6072	12	8	(	(	PUNCT
ejpam-6072	12	9	negative	negative	ADJ
ejpam-6072	12	10	semidefinite	semidefinite	NOUN
ejpam-6072	12	11	,	,	PUNCT
ejpam-6072	12	12	respectively	respectively	ADV
ejpam-6072	12	13	)	)	PUNCT
ejpam-6072	12	14	matrix	matrix	NOUN
ejpam-6072	12	15	by	by	ADP
ejpam-6072	12	16	x	x	PUNCT
ejpam-6072	12	17	⪰	⪰	NOUN
ejpam-6072	12	18	0	0	PUNCT
ejpam-6072	12	19	(	(	PUNCT
ejpam-6072	12	20	x	x	X
ejpam-6072	12	21	⪯	⪯	NOUN
ejpam-6072	12	22	0	0	NUM
ejpam-6072	12	23	,	,	PUNCT
ejpam-6072	12	24	respectively	respectively	ADV
ejpam-6072	12	25	)	)	PUNCT
ejpam-6072	12	26	.	.	PUNCT
ejpam-6072	13	1	unless	unless	SCONJ
ejpam-6072	13	2	stated	state	VERB
ejpam-6072	13	3	otherwise	otherwise	ADV
ejpam-6072	13	4	,	,	PUNCT
ejpam-6072	13	5	a	a	DET
ejpam-6072	13	6	positive	positive	ADJ
ejpam-6072	13	7	or	or	CCONJ
ejpam-6072	13	8	negative	negative	ADJ
ejpam-6072	13	9	definite	definite	ADJ
ejpam-6072	13	10	or	or	CCONJ
ejpam-6072	13	11	semidefinite	semidefinite	NOUN
ejpam-6072	13	12	matrix	matrix	NOUN
ejpam-6072	13	13	is	be	AUX
ejpam-6072	13	14	assumed	assume	VERB
ejpam-6072	13	15	to	to	PART
ejpam-6072	13	16	be	be	AUX
ejpam-6072	13	17	symmetric	symmetric	ADJ
ejpam-6072	13	18	.	.	PUNCT
ejpam-6072	14	1	for	for	ADP
ejpam-6072	14	2	a	a	DET
ejpam-6072	14	3	matrix	matrix	NOUN
ejpam-6072	14	4	x	x	SYM
ejpam-6072	14	5	∈	∈	NOUN
ejpam-6072	14	6	rn×n	rn×n	NOUN
ejpam-6072	14	7	,	,	PUNCT
ejpam-6072	14	8	we	we	PRON
ejpam-6072	14	9	write	write	VERB
ejpam-6072	14	10	xt	xt	PROPN
ejpam-6072	14	11	to	to	PART
ejpam-6072	14	12	denote	denote	VERB
ejpam-6072	14	13	the	the	DET
ejpam-6072	14	14	transpose	transpose	NOUN
ejpam-6072	14	15	of	of	ADP
ejpam-6072	14	16	x	x	PRON
ejpam-6072	14	17	,	,	PUNCT
ejpam-6072	14	18	we	we	PRON
ejpam-6072	14	19	also	also	ADV
ejpam-6072	14	20	write	write	VERB
ejpam-6072	14	21	x−1	x−1	PROPN
ejpam-6072	14	22	to	to	PART
ejpam-6072	14	23	refer	refer	VERB
ejpam-6072	14	24	to	to	ADP
ejpam-6072	14	25	the	the	DET
ejpam-6072	14	26	inverse	inverse	NOUN
ejpam-6072	14	27	of	of	ADP
ejpam-6072	14	28	x	x	X
ejpam-6072	14	29	,	,	PUNCT
ejpam-6072	14	30	and	and	CCONJ
ejpam-6072	14	31	x−t	x−t	PROPN
ejpam-6072	14	32	for	for	ADP
ejpam-6072	14	33	its	its	PRON
ejpam-6072	14	34	inverse	inverse	NOUN
ejpam-6072	14	35	transpose	transpose	NOUN
ejpam-6072	14	36	,	,	PUNCT
ejpam-6072	14	37	defined	define	VERB
ejpam-6072	14	38	as	as	ADP
ejpam-6072	14	39	x−t	x−t	PROPN
ejpam-6072	14	40	=	=	SYM
ejpam-6072	14	41	(	(	PUNCT
ejpam-6072	14	42	xt	xt	PROPN
ejpam-6072	14	43	)	)	PUNCT
ejpam-6072	14	44	−1	−1	NOUN
ejpam-6072	15	1	=	=	SYM
ejpam-6072	15	2	(	(	PUNCT
ejpam-6072	15	3	x−1)t	x−1)t	PROPN
ejpam-6072	15	4	.	.	PUNCT
ejpam-6072	16	1	additionally	additionally	ADV
ejpam-6072	16	2	,	,	PUNCT
ejpam-6072	16	3	we	we	PRON
ejpam-6072	16	4	use	use	VERB
ejpam-6072	16	5	i	i	PRON
ejpam-6072	16	6	to	to	PART
ejpam-6072	16	7	denote	denote	VERB
ejpam-6072	16	8	the	the	DET
ejpam-6072	16	9	identity	identity	NOUN
ejpam-6072	16	10	matrix	matrix	NOUN
ejpam-6072	16	11	with	with	ADP
ejpam-6072	16	12	its	its	PRON
ejpam-6072	16	13	size	size	NOUN
ejpam-6072	16	14	implied	imply	VERB
ejpam-6072	16	15	by	by	ADP
ejpam-6072	16	16	the	the	DET
ejpam-6072	16	17	context	context	NOUN
ejpam-6072	16	18	.	.	PUNCT
ejpam-6072	17	1	∗corresponding	∗corresponde	VERB
ejpam-6072	17	2	author	author	NOUN
ejpam-6072	17	3	.	.	PUNCT
ejpam-6072	18	1	doi	doi	NOUN
ejpam-6072	18	2	:	:	PUNCT
ejpam-6072	18	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6072	https://doi.org/10.29020/nybg.ejpam.v18i2.6072	DET
ejpam-6072	18	4	email	email	NOUN
ejpam-6072	18	5	addresses	address	VERB
ejpam-6072	18	6	:	:	PUNCT
ejpam-6072	18	7	a.algefary@qu.edu.sa	a.algefary@qu.edu.sa	PROPN
ejpam-6072	18	8	(	(	PUNCT
ejpam-6072	18	9	a.	a.	NOUN
ejpam-6072	18	10	algefary	algefary	ADJ
ejpam-6072	18	11	)	)	PUNCT
ejpam-6072	18	12	,	,	PUNCT
ejpam-6072	18	13	432206823@qu.edu.sa	432206823@qu.edu.sa	NUM
ejpam-6072	18	14	(	(	PUNCT
ejpam-6072	18	15	k.	k.	PROPN
ejpam-6072	18	16	a.	a.	PROPN
ejpam-6072	18	17	alqufari	alqufari	PROPN
ejpam-6072	18	18	)	)	PUNCT
ejpam-6072	18	19	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6072	18	20	1	1	NUM
ejpam-6072	18	21	copyright	copyright	NOUN
ejpam-6072	18	22	:	:	PUNCT
ejpam-6072	19	1	©	©	PROPN
ejpam-6072	19	2	2025	2025	NUM
ejpam-6072	19	3	the	the	DET
ejpam-6072	19	4	author(s	author(s	NOUN
ejpam-6072	19	5	)	)	PUNCT
ejpam-6072	19	6	.	.	PUNCT
ejpam-6072	20	1	(	(	PUNCT
ejpam-6072	20	2	cc	cc	NOUN
ejpam-6072	20	3	by	by	ADP
ejpam-6072	20	4	-	-	PUNCT
ejpam-6072	20	5	nc	nc	PROPN
ejpam-6072	20	6	4.0	4.0	NUM
ejpam-6072	20	7	)	)	PUNCT
ejpam-6072	20	8	a.	a.	NOUN
ejpam-6072	20	9	algefary	algefary	PROPN
ejpam-6072	20	10	,	,	PUNCT
ejpam-6072	20	11	k.	k.	PROPN
ejpam-6072	20	12	a.	a.	PROPN
ejpam-6072	20	13	alqufari	alqufari	PROPN
ejpam-6072	20	14	/	/	SYM
ejpam-6072	20	15	eur	eur	PROPN
ejpam-6072	20	16	.	.	PUNCT
ejpam-6072	21	1	j.	j.	PROPN
ejpam-6072	21	2	pure	pure	PROPN
ejpam-6072	21	3	appl	appl	PROPN
ejpam-6072	21	4	.	.	PROPN
ejpam-6072	21	5	math	math	PROPN
ejpam-6072	21	6	,	,	PUNCT
ejpam-6072	21	7	18	18	NUM
ejpam-6072	21	8	(	(	PUNCT
ejpam-6072	21	9	2	2	NUM
ejpam-6072	21	10	)	)	PUNCT
ejpam-6072	21	11	(	(	PUNCT
ejpam-6072	21	12	2025	2025	NUM
ejpam-6072	21	13	)	)	PUNCT
ejpam-6072	21	14	,	,	PUNCT
ejpam-6072	21	15	6072	6072	NUM
ejpam-6072	21	16	2	2	NUM
ejpam-6072	21	17	of	of	ADP
ejpam-6072	21	18	14	14	NUM
ejpam-6072	21	19	consider	consider	VERB
ejpam-6072	21	20	a	a	DET
ejpam-6072	21	21	matrix	matrix	NOUN
ejpam-6072	21	22	x	x	SYM
ejpam-6072	21	23	∈	∈	NOUN
ejpam-6072	21	24	rn×n	rn×n	NOUN
ejpam-6072	21	25	.	.	PUNCT
ejpam-6072	22	1	in	in	ADP
ejpam-6072	22	2	this	this	DET
ejpam-6072	22	3	paper	paper	NOUN
ejpam-6072	22	4	,	,	PUNCT
ejpam-6072	22	5	we	we	PRON
ejpam-6072	22	6	use	use	VERB
ejpam-6072	22	7	σ(x	σ(x	NOUN
ejpam-6072	22	8	)	)	PUNCT
ejpam-6072	22	9	to	to	PART
ejpam-6072	22	10	represent	represent	VERB
ejpam-6072	22	11	the	the	DET
ejpam-6072	22	12	spectrum	spectrum	NOUN
ejpam-6072	22	13	of	of	ADP
ejpam-6072	22	14	x	x	X
ejpam-6072	22	15	and	and	CCONJ
ejpam-6072	22	16	ρ(x	ρ(x	NOUN
ejpam-6072	22	17	)	)	PUNCT
ejpam-6072	22	18	to	to	PART
ejpam-6072	22	19	indicate	indicate	VERB
ejpam-6072	22	20	its	its	PRON
ejpam-6072	22	21	spectral	spectral	ADJ
ejpam-6072	22	22	radius	radius	NOUN
ejpam-6072	22	23	.	.	PUNCT
ejpam-6072	23	1	the	the	DET
ejpam-6072	23	2	spectral	spectral	ADJ
ejpam-6072	23	3	abscissa	abscissa	NOUN
ejpam-6072	23	4	of	of	ADP
ejpam-6072	23	5	x	x	PRON
ejpam-6072	23	6	,	,	PUNCT
ejpam-6072	23	7	represented	represent	VERB
ejpam-6072	23	8	by	by	ADP
ejpam-6072	23	9	α(x	α(x	PROPN
ejpam-6072	23	10	)	)	PUNCT
ejpam-6072	23	11	,	,	PUNCT
ejpam-6072	23	12	is	be	AUX
ejpam-6072	23	13	defined	define	VERB
ejpam-6072	23	14	as	as	ADP
ejpam-6072	23	15	the	the	DET
ejpam-6072	23	16	largest	large	ADJ
ejpam-6072	23	17	real	real	ADJ
ejpam-6072	23	18	part	part	NOUN
ejpam-6072	23	19	among	among	ADP
ejpam-6072	23	20	the	the	DET
ejpam-6072	23	21	eigenvalues	eigenvalue	NOUN
ejpam-6072	23	22	of	of	ADP
ejpam-6072	23	23	x.	x.	NOUN
ejpam-6072	23	24	formally	formally	ADV
ejpam-6072	23	25	,	,	PUNCT
ejpam-6072	23	26	we	we	PRON
ejpam-6072	23	27	write	write	VERB
ejpam-6072	23	28	:	:	PUNCT
ejpam-6072	23	29	α(x	α(x	NOUN
ejpam-6072	23	30	)	)	PUNCT
ejpam-6072	23	31	=	=	SYM
ejpam-6072	23	32	max{re(λ	max{re(λ	X
ejpam-6072	23	33	)	)	PUNCT
ejpam-6072	24	1	|	|	ADV
ejpam-6072	24	2	λ	λ	X
ejpam-6072	24	3	∈	∈	PROPN
ejpam-6072	24	4	σ(x	σ(x	PROPN
ejpam-6072	24	5	)	)	PUNCT
ejpam-6072	24	6	}	}	PUNCT
ejpam-6072	24	7	.	.	PUNCT
ejpam-6072	25	1	for	for	ADP
ejpam-6072	25	2	further	further	ADJ
ejpam-6072	25	3	details	detail	NOUN
ejpam-6072	25	4	,	,	PUNCT
ejpam-6072	25	5	refer	refer	VERB
ejpam-6072	25	6	to	to	ADP
ejpam-6072	25	7	[	[	X
ejpam-6072	25	8	1	1	NUM
ejpam-6072	25	9	,	,	PUNCT
ejpam-6072	25	10	2	2	NUM
ejpam-6072	25	11	]	]	PUNCT
ejpam-6072	25	12	.	.	PUNCT
ejpam-6072	26	1	let	let	VERB
ejpam-6072	26	2	us	we	PRON
ejpam-6072	26	3	start	start	VERB
ejpam-6072	26	4	by	by	ADP
ejpam-6072	26	5	reviewing	review	VERB
ejpam-6072	26	6	some	some	DET
ejpam-6072	26	7	key	key	ADJ
ejpam-6072	26	8	definitions	definition	NOUN
ejpam-6072	26	9	related	relate	VERB
ejpam-6072	26	10	to	to	ADP
ejpam-6072	26	11	types	type	NOUN
ejpam-6072	26	12	of	of	ADP
ejpam-6072	26	13	matrix	matrix	NOUN
ejpam-6072	26	14	stability	stability	NOUN
ejpam-6072	26	15	relevant	relevant	ADJ
ejpam-6072	26	16	to	to	ADP
ejpam-6072	26	17	this	this	DET
ejpam-6072	26	18	study	study	NOUN
ejpam-6072	26	19	.	.	PUNCT
ejpam-6072	27	1	definition	definition	NOUN
ejpam-6072	27	2	1	1	NUM
ejpam-6072	27	3	.	.	PUNCT
ejpam-6072	28	1	[	[	X
ejpam-6072	28	2	3	3	X
ejpam-6072	28	3	]	]	PUNCT
ejpam-6072	28	4	let	let	VERB
ejpam-6072	28	5	a	a	PRON
ejpam-6072	28	6	be	be	AUX
ejpam-6072	28	7	a	a	DET
ejpam-6072	28	8	matrix	matrix	NOUN
ejpam-6072	28	9	in	in	ADP
ejpam-6072	28	10	rn×n	rn×n	PROPN
ejpam-6072	28	11	.	.	PUNCT
ejpam-6072	29	1	the	the	DET
ejpam-6072	29	2	matrix	matrix	NOUN
ejpam-6072	29	3	a	a	PRON
ejpam-6072	29	4	is	be	AUX
ejpam-6072	29	5	called	call	VERB
ejpam-6072	29	6	hurwitz	hurwitz	PROPN
ejpam-6072	29	7	(	(	PUNCT
ejpam-6072	29	8	or	or	CCONJ
ejpam-6072	29	9	hurwitz	hurwitz	PROPN
ejpam-6072	29	10	stable	stable	ADJ
ejpam-6072	29	11	)	)	PUNCT
ejpam-6072	29	12	if	if	SCONJ
ejpam-6072	29	13	all	all	DET
ejpam-6072	29	14	its	its	PRON
ejpam-6072	29	15	eigenvalues	eigenvalue	NOUN
ejpam-6072	29	16	are	be	AUX
ejpam-6072	29	17	located	locate	VERB
ejpam-6072	29	18	in	in	ADP
ejpam-6072	29	19	the	the	DET
ejpam-6072	29	20	open	open	ADJ
ejpam-6072	29	21	left	leave	VERB
ejpam-6072	29	22	half	half	NOUN
ejpam-6072	29	23	of	of	ADP
ejpam-6072	29	24	the	the	DET
ejpam-6072	29	25	complex	complex	ADJ
ejpam-6072	29	26	plane	plane	NOUN
ejpam-6072	29	27	,	,	PUNCT
ejpam-6072	29	28	meaning	mean	VERB
ejpam-6072	29	29	α(a	α(a	NOUN
ejpam-6072	29	30	)	)	PUNCT
ejpam-6072	29	31	<	<	X
ejpam-6072	30	1	0	0	X
ejpam-6072	30	2	.	.	PUNCT
ejpam-6072	31	1	a	a	DET
ejpam-6072	31	2	well	well	ADV
ejpam-6072	31	3	-	-	PUNCT
ejpam-6072	31	4	known	know	VERB
ejpam-6072	31	5	characterization	characterization	NOUN
ejpam-6072	31	6	of	of	ADP
ejpam-6072	31	7	hurwitz	hurwitz	PROPN
ejpam-6072	31	8	stability	stability	NOUN
ejpam-6072	31	9	for	for	ADP
ejpam-6072	31	10	a	a	DET
ejpam-6072	31	11	matrix	matrix	NOUN
ejpam-6072	31	12	a	a	DET
ejpam-6072	31	13	∈	∈	ADJ
ejpam-6072	31	14	rn×n	rn×n	NOUN
ejpam-6072	31	15	involves	involve	VERB
ejpam-6072	31	16	the	the	DET
ejpam-6072	31	17	lyapunov	lyapunov	ADJ
ejpam-6072	31	18	equation	equation	NOUN
ejpam-6072	31	19	atp	atp	PROPN
ejpam-6072	31	20	+	+	CCONJ
ejpam-6072	31	21	pa+q	pa+q	PROPN
ejpam-6072	31	22	=	=	SYM
ejpam-6072	31	23	0	0	PROPN
ejpam-6072	31	24	,	,	PUNCT
ejpam-6072	31	25	where	where	SCONJ
ejpam-6072	31	26	p	p	X
ejpam-6072	31	27	,	,	PUNCT
ejpam-6072	31	28	q	q	NOUN
ejpam-6072	31	29	∈	∈	NOUN
ejpam-6072	31	30	rn×n	rn×n	NOUN
ejpam-6072	31	31	with	with	ADP
ejpam-6072	31	32	p	p	PROPN
ejpam-6072	31	33	≻	≻	PROPN
ejpam-6072	31	34	0	0	NUM
ejpam-6072	31	35	and	and	CCONJ
ejpam-6072	31	36	q	q	ADJ
ejpam-6072	31	37	≻	≻	PROPN
ejpam-6072	31	38	0	0	NUM
ejpam-6072	31	39	;	;	PUNCT
ejpam-6072	31	40	see	see	VERB
ejpam-6072	31	41	[	[	X
ejpam-6072	31	42	3	3	NUM
ejpam-6072	31	43	]	]	PUNCT
ejpam-6072	31	44	.	.	PUNCT
ejpam-6072	32	1	this	this	DET
ejpam-6072	32	2	result	result	NOUN
ejpam-6072	32	3	is	be	AUX
ejpam-6072	32	4	fundamental	fundamental	ADJ
ejpam-6072	32	5	in	in	ADP
ejpam-6072	32	6	assessing	assess	VERB
ejpam-6072	32	7	the	the	DET
ejpam-6072	32	8	stability	stability	NOUN
ejpam-6072	32	9	of	of	ADP
ejpam-6072	32	10	continuous	continuous	ADJ
ejpam-6072	32	11	linear	linear	PROPN
ejpam-6072	32	12	systems	system	NOUN
ejpam-6072	32	13	described	describe	VERB
ejpam-6072	32	14	by	by	ADP
ejpam-6072	32	15	ẋ(t	ẋ(t	NOUN
ejpam-6072	32	16	)	)	PUNCT
ejpam-6072	32	17	=	=	SYM
ejpam-6072	32	18	ax(t	ax(t	NUM
ejpam-6072	32	19	)	)	PUNCT
ejpam-6072	32	20	,	,	PUNCT
ejpam-6072	32	21	(	(	PUNCT
ejpam-6072	32	22	1	1	X
ejpam-6072	32	23	)	)	PUNCT
ejpam-6072	32	24	where	where	SCONJ
ejpam-6072	32	25	a	a	DET
ejpam-6072	32	26	∈	∈	ADJ
ejpam-6072	32	27	rn×n	rn×n	NOUN
ejpam-6072	32	28	and	and	CCONJ
ejpam-6072	32	29	x(t	x(t	PROPN
ejpam-6072	32	30	)	)	PUNCT
ejpam-6072	32	31	∈	∈	PROPN
ejpam-6072	32	32	rn	rn	PROPN
ejpam-6072	32	33	.	.	PROPN
ejpam-6072	33	1	specifically	specifically	ADV
ejpam-6072	33	2	,	,	PUNCT
ejpam-6072	33	3	if	if	SCONJ
ejpam-6072	33	4	there	there	PRON
ejpam-6072	33	5	exists	exist	VERB
ejpam-6072	33	6	a	a	DET
ejpam-6072	33	7	p	p	X
ejpam-6072	33	8	≻	≻	X
ejpam-6072	33	9	0	0	PUNCT
ejpam-6072	33	10	satisfying	satisfy	VERB
ejpam-6072	33	11	the	the	DET
ejpam-6072	33	12	lyapunov	lyapunov	ADJ
ejpam-6072	33	13	equation	equation	NOUN
ejpam-6072	33	14	,	,	PUNCT
ejpam-6072	33	15	then	then	ADV
ejpam-6072	33	16	the	the	DET
ejpam-6072	33	17	linear	linear	ADJ
ejpam-6072	33	18	system	system	NOUN
ejpam-6072	33	19	in	in	ADP
ejpam-6072	33	20	(	(	PUNCT
ejpam-6072	33	21	1	1	X
ejpam-6072	33	22	)	)	PUNCT
ejpam-6072	33	23	is	be	AUX
ejpam-6072	33	24	associated	associate	VERB
ejpam-6072	33	25	with	with	ADP
ejpam-6072	33	26	a	a	DET
ejpam-6072	33	27	lyapunov	lyapunov	NOUN
ejpam-6072	33	28	function	function	NOUN
ejpam-6072	33	29	v	v	ADP
ejpam-6072	33	30	(	(	PUNCT
ejpam-6072	33	31	x	x	NOUN
ejpam-6072	33	32	)	)	PUNCT
ejpam-6072	33	33	=	=	SYM
ejpam-6072	33	34	xtpx	xtpx	ADJ
ejpam-6072	33	35	,	,	PUNCT
ejpam-6072	33	36	confirming	confirm	VERB
ejpam-6072	33	37	the	the	DET
ejpam-6072	33	38	system	system	NOUN
ejpam-6072	33	39	equilibrium	equilibrium	NOUN
ejpam-6072	33	40	is	be	AUX
ejpam-6072	33	41	asymptotic	asymptotic	ADJ
ejpam-6072	33	42	stability	stability	NOUN
ejpam-6072	33	43	.	.	PUNCT
ejpam-6072	34	1	this	this	DET
ejpam-6072	34	2	criterion	criterion	NOUN
ejpam-6072	34	3	for	for	ADP
ejpam-6072	34	4	hurwitz	hurwitz	PROPN
ejpam-6072	34	5	stability	stability	NOUN
ejpam-6072	34	6	is	be	AUX
ejpam-6072	34	7	presented	present	VERB
ejpam-6072	34	8	in	in	ADP
ejpam-6072	34	9	the	the	DET
ejpam-6072	34	10	following	follow	VERB
ejpam-6072	34	11	lemma	lemma	PROPN
ejpam-6072	34	12	,	,	PUNCT
ejpam-6072	34	13	known	know	VERB
ejpam-6072	34	14	as	as	ADP
ejpam-6072	34	15	lyapunov	lyapunov	PROPN
ejpam-6072	34	16	’s	’s	PART
ejpam-6072	34	17	theorem	theorem	PROPN
ejpam-6072	34	18	.	.	PUNCT
ejpam-6072	35	1	lemma	lemma	PROPN
ejpam-6072	35	2	1	1	NUM
ejpam-6072	35	3	.	.	PUNCT
ejpam-6072	36	1	[	[	X
ejpam-6072	36	2	3	3	NUM
ejpam-6072	36	3	,	,	PUNCT
ejpam-6072	36	4	4	4	NUM
ejpam-6072	36	5	]	]	PUNCT
ejpam-6072	36	6	a	a	DET
ejpam-6072	36	7	matrix	matrix	NOUN
ejpam-6072	36	8	a	a	DET
ejpam-6072	36	9	∈	∈	PROPN
ejpam-6072	36	10	rn×n	rn×n	NOUN
ejpam-6072	36	11	is	be	AUX
ejpam-6072	36	12	hurwitz	hurwitz	PROPN
ejpam-6072	36	13	stable	stable	ADJ
ejpam-6072	36	14	if	if	SCONJ
ejpam-6072	36	15	there	there	PRON
ejpam-6072	36	16	exist	exist	VERB
ejpam-6072	36	17	positive	positive	ADJ
ejpam-6072	36	18	definite	definite	ADJ
ejpam-6072	36	19	matrices	matrix	NOUN
ejpam-6072	36	20	p	p	NOUN
ejpam-6072	36	21	,	,	PUNCT
ejpam-6072	36	22	q	q	NOUN
ejpam-6072	36	23	∈	∈	NOUN
ejpam-6072	36	24	rn×n	rn×n	NOUN
ejpam-6072	36	25	such	such	ADJ
ejpam-6072	36	26	that	that	DET
ejpam-6072	36	27	atp	atp	PROPN
ejpam-6072	36	28	+	+	CCONJ
ejpam-6072	36	29	pa	pa	PROPN
ejpam-6072	36	30	=	=	PUNCT
ejpam-6072	36	31	−q	−q	NOUN
ejpam-6072	36	32	.	.	PUNCT
ejpam-6072	37	1	alternatively	alternatively	ADV
ejpam-6072	37	2	,	,	PUNCT
ejpam-6072	37	3	lemma	lemma	PROPN
ejpam-6072	37	4	1	1	NUM
ejpam-6072	37	5	can	can	AUX
ejpam-6072	37	6	be	be	AUX
ejpam-6072	37	7	restated	restate	VERB
ejpam-6072	37	8	using	use	VERB
ejpam-6072	37	9	the	the	DET
ejpam-6072	37	10	lyapunov	lyapunov	ADJ
ejpam-6072	37	11	inequality	inequality	NOUN
ejpam-6072	37	12	:	:	PUNCT
ejpam-6072	37	13	a	a	PRON
ejpam-6072	37	14	is	be	AUX
ejpam-6072	37	15	hurwitz	hurwitz	NOUN
ejpam-6072	37	16	stable	stable	ADJ
ejpam-6072	37	17	if	if	SCONJ
ejpam-6072	37	18	and	and	CCONJ
ejpam-6072	37	19	only	only	ADV
ejpam-6072	37	20	if	if	SCONJ
ejpam-6072	37	21	there	there	PRON
ejpam-6072	37	22	exists	exist	VERB
ejpam-6072	37	23	a	a	DET
ejpam-6072	37	24	positive	positive	ADJ
ejpam-6072	37	25	definite	definite	ADJ
ejpam-6072	37	26	matrix	matrix	NOUN
ejpam-6072	37	27	p	p	NOUN
ejpam-6072	37	28	∈	∈	ADJ
ejpam-6072	37	29	rn×n	rn×n	NOUN
ejpam-6072	37	30	such	such	ADJ
ejpam-6072	37	31	that	that	DET
ejpam-6072	37	32	atp	atp	PROPN
ejpam-6072	37	33	+	+	CCONJ
ejpam-6072	37	34	pa	pa	PROPN
ejpam-6072	37	35	≺	≺	NOUN
ejpam-6072	37	36	0	0	NUM
ejpam-6072	37	37	.	.	PUNCT
ejpam-6072	38	1	(	(	PUNCT
ejpam-6072	38	2	2	2	NUM
ejpam-6072	38	3	)	)	PUNCT
ejpam-6072	38	4	within	within	ADP
ejpam-6072	38	5	this	this	DET
ejpam-6072	38	6	context	context	NOUN
ejpam-6072	38	7	,	,	PUNCT
ejpam-6072	38	8	p	p	NOUN
ejpam-6072	38	9	is	be	AUX
ejpam-6072	38	10	referred	refer	VERB
ejpam-6072	38	11	to	to	ADP
ejpam-6072	38	12	as	as	ADP
ejpam-6072	38	13	a	a	DET
ejpam-6072	38	14	lyapunov	lyapunov	ADJ
ejpam-6072	38	15	solution	solution	NOUN
ejpam-6072	38	16	for	for	ADP
ejpam-6072	38	17	matrix	matrix	NOUN
ejpam-6072	38	18	a	a	PRON
ejpam-6072	38	19	or	or	CCONJ
ejpam-6072	38	20	the	the	DET
ejpam-6072	38	21	lyapunov	lyapunov	ADJ
ejpam-6072	38	22	inequality	inequality	NOUN
ejpam-6072	38	23	.	.	PUNCT
ejpam-6072	39	1	the	the	DET
ejpam-6072	39	2	concept	concept	NOUN
ejpam-6072	39	3	of	of	ADP
ejpam-6072	39	4	hurwitz	hurwitz	PROPN
ejpam-6072	39	5	stability	stability	NOUN
ejpam-6072	39	6	for	for	ADP
ejpam-6072	39	7	a	a	DET
ejpam-6072	39	8	single	single	ADJ
ejpam-6072	39	9	matrix	matrix	NOUN
ejpam-6072	39	10	a	a	DET
ejpam-6072	39	11	∈	∈	PROPN
ejpam-6072	39	12	rn×n	rn×n	NOUN
ejpam-6072	39	13	has	have	AUX
ejpam-6072	39	14	been	be	AUX
ejpam-6072	39	15	extended	extend	VERB
ejpam-6072	39	16	in	in	ADP
ejpam-6072	39	17	the	the	DET
ejpam-6072	39	18	literature	literature	NOUN
ejpam-6072	39	19	(	(	PUNCT
ejpam-6072	39	20	see	see	VERB
ejpam-6072	39	21	[	[	X
ejpam-6072	39	22	5–8	5–8	NOUN
ejpam-6072	39	23	]	]	PUNCT
ejpam-6072	39	24	)	)	PUNCT
ejpam-6072	39	25	to	to	PART
ejpam-6072	39	26	consider	consider	VERB
ejpam-6072	39	27	families	family	NOUN
ejpam-6072	39	28	of	of	ADP
ejpam-6072	39	29	real	real	ADJ
ejpam-6072	39	30	matrices	matrix	NOUN
ejpam-6072	39	31	through	through	ADP
ejpam-6072	39	32	the	the	DET
ejpam-6072	39	33	notion	notion	NOUN
ejpam-6072	39	34	of	of	ADP
ejpam-6072	39	35	common	common	ADJ
ejpam-6072	39	36	lyapunov	lyapunov	ADJ
ejpam-6072	39	37	stability	stability	NOUN
ejpam-6072	39	38	.	.	PUNCT
ejpam-6072	40	1	this	this	DET
ejpam-6072	40	2	extension	extension	NOUN
ejpam-6072	40	3	is	be	AUX
ejpam-6072	40	4	particularly	particularly	ADV
ejpam-6072	40	5	significant	significant	ADJ
ejpam-6072	40	6	in	in	ADP
ejpam-6072	40	7	control	control	NOUN
ejpam-6072	40	8	theory	theory	NOUN
ejpam-6072	40	9	,	,	PUNCT
ejpam-6072	40	10	especially	especially	ADV
ejpam-6072	40	11	in	in	ADP
ejpam-6072	40	12	the	the	DET
ejpam-6072	40	13	analysis	analysis	NOUN
ejpam-6072	40	14	of	of	ADP
ejpam-6072	40	15	switched	switch	VERB
ejpam-6072	40	16	systems	system	NOUN
ejpam-6072	40	17	and	and	CCONJ
ejpam-6072	40	18	robustness	robustness	NOUN
ejpam-6072	40	19	,	,	PUNCT
ejpam-6072	40	20	where	where	SCONJ
ejpam-6072	40	21	ensuring	ensure	VERB
ejpam-6072	40	22	stability	stability	NOUN
ejpam-6072	40	23	across	across	ADP
ejpam-6072	40	24	multiple	multiple	ADJ
ejpam-6072	40	25	system	system	NOUN
ejpam-6072	40	26	configurations	configuration	NOUN
ejpam-6072	40	27	is	be	AUX
ejpam-6072	40	28	crucial	crucial	ADJ
ejpam-6072	40	29	[	[	X
ejpam-6072	40	30	9	9	NUM
ejpam-6072	40	31	,	,	PUNCT
ejpam-6072	40	32	10	10	NUM
ejpam-6072	40	33	]	]	PUNCT
ejpam-6072	40	34	.	.	PUNCT
ejpam-6072	41	1	a.	a.	PROPN
ejpam-6072	41	2	algefary	algefary	PROPN
ejpam-6072	41	3	,	,	PUNCT
ejpam-6072	41	4	k.	k.	PROPN
ejpam-6072	41	5	a.	a.	PROPN
ejpam-6072	41	6	alqufari	alqufari	PROPN
ejpam-6072	41	7	/	/	SYM
ejpam-6072	41	8	eur	eur	PROPN
ejpam-6072	41	9	.	.	PUNCT
ejpam-6072	42	1	j.	j.	PROPN
ejpam-6072	42	2	pure	pure	PROPN
ejpam-6072	42	3	appl	appl	PROPN
ejpam-6072	42	4	.	.	PROPN
ejpam-6072	42	5	math	math	PROPN
ejpam-6072	42	6	,	,	PUNCT
ejpam-6072	42	7	18	18	NUM
ejpam-6072	42	8	(	(	PUNCT
ejpam-6072	42	9	2	2	NUM
ejpam-6072	42	10	)	)	PUNCT
ejpam-6072	42	11	(	(	PUNCT
ejpam-6072	42	12	2025	2025	NUM
ejpam-6072	42	13	)	)	PUNCT
ejpam-6072	42	14	,	,	PUNCT
ejpam-6072	42	15	6072	6072	NUM
ejpam-6072	42	16	3	3	NUM
ejpam-6072	42	17	of	of	ADP
ejpam-6072	42	18	14	14	NUM
ejpam-6072	42	19	specifically	specifically	ADV
ejpam-6072	42	20	,	,	PUNCT
ejpam-6072	42	21	a	a	DET
ejpam-6072	42	22	family	family	NOUN
ejpam-6072	42	23	of	of	ADP
ejpam-6072	42	24	real	real	ADJ
ejpam-6072	42	25	matrices	matrix	NOUN
ejpam-6072	42	26	a	a	DET
ejpam-6072	42	27	=	=	NOUN
ejpam-6072	42	28	{	{	PUNCT
ejpam-6072	42	29	a1	a1	NOUN
ejpam-6072	42	30	,	,	PUNCT
ejpam-6072	42	31	.	.	PUNCT
ejpam-6072	42	32	.	.	PUNCT
ejpam-6072	43	1	.	.	PUNCT
ejpam-6072	44	1	,	,	PUNCT
ejpam-6072	44	2	am	be	AUX
ejpam-6072	44	3	}	}	PUNCT
ejpam-6072	44	4	is	be	AUX
ejpam-6072	44	5	said	say	VERB
ejpam-6072	44	6	to	to	PART
ejpam-6072	44	7	have	have	VERB
ejpam-6072	44	8	common	common	ADJ
ejpam-6072	44	9	lyapunov	lyapunov	ADJ
ejpam-6072	44	10	stability	stability	NOUN
ejpam-6072	44	11	if	if	SCONJ
ejpam-6072	44	12	there	there	PRON
ejpam-6072	44	13	exists	exist	VERB
ejpam-6072	44	14	a	a	DET
ejpam-6072	44	15	positive	positive	ADJ
ejpam-6072	44	16	definite	definite	ADJ
ejpam-6072	44	17	matrix	matrix	NOUN
ejpam-6072	44	18	p	p	NOUN
ejpam-6072	44	19	such	such	ADJ
ejpam-6072	44	20	that	that	PRON
ejpam-6072	44	21	for	for	ADP
ejpam-6072	44	22	each	each	DET
ejpam-6072	44	23	i	i	NOUN
ejpam-6072	44	24	=	=	NOUN
ejpam-6072	44	25	1	1	NUM
ejpam-6072	44	26	,	,	PUNCT
ejpam-6072	44	27	.	.	PUNCT
ejpam-6072	44	28	.	.	PUNCT
ejpam-6072	44	29	.	.	PUNCT
ejpam-6072	45	1	,	,	PUNCT
ejpam-6072	45	2	m	m	PROPN
ejpam-6072	45	3	,	,	PUNCT
ejpam-6072	45	4	at	at	ADP
ejpam-6072	45	5	i	i	PRON
ejpam-6072	45	6	p	p	PROPN
ejpam-6072	46	1	+	+	CCONJ
ejpam-6072	46	2	pai	pai	NOUN
ejpam-6072	46	3	≺	≺	NOUN
ejpam-6072	46	4	0	0	NUM
ejpam-6072	46	5	.	.	PUNCT
ejpam-6072	47	1	(	(	PUNCT
ejpam-6072	47	2	3	3	X
ejpam-6072	47	3	)	)	PUNCT
ejpam-6072	47	4	the	the	DET
ejpam-6072	47	5	existence	existence	NOUN
ejpam-6072	47	6	of	of	ADP
ejpam-6072	47	7	such	such	DET
ejpam-6072	47	8	a	a	DET
ejpam-6072	47	9	matrix	matrix	NOUN
ejpam-6072	47	10	p	p	NOUN
ejpam-6072	47	11	implies	imply	VERB
ejpam-6072	47	12	simultaneous	simultaneous	ADJ
ejpam-6072	47	13	hurwitz	hurwitz	PROPN
ejpam-6072	47	14	stability	stability	NOUN
ejpam-6072	47	15	for	for	ADP
ejpam-6072	47	16	the	the	DET
ejpam-6072	47	17	matrices	matrix	NOUN
ejpam-6072	47	18	in	in	ADP
ejpam-6072	47	19	a.	a.	NOUN
ejpam-6072	47	20	in	in	ADP
ejpam-6072	47	21	other	other	ADJ
ejpam-6072	47	22	words	word	NOUN
ejpam-6072	47	23	,	,	PUNCT
ejpam-6072	47	24	the	the	DET
ejpam-6072	47	25	linear	linear	PROPN
ejpam-6072	47	26	systems	system	NOUN
ejpam-6072	47	27	associated	associate	VERB
ejpam-6072	47	28	with	with	ADP
ejpam-6072	47	29	the	the	DET
ejpam-6072	47	30	matrices	matrix	NOUN
ejpam-6072	47	31	in	in	ADP
ejpam-6072	47	32	the	the	DET
ejpam-6072	47	33	family	family	NOUN
ejpam-6072	47	34	a	a	DET
ejpam-6072	47	35	share	share	NOUN
ejpam-6072	47	36	a	a	DET
ejpam-6072	47	37	common	common	ADJ
ejpam-6072	47	38	lyapunov	lyapunov	ADJ
ejpam-6072	47	39	function	function	NOUN
ejpam-6072	47	40	given	give	VERB
ejpam-6072	47	41	by	by	ADP
ejpam-6072	47	42	v	v	PROPN
ejpam-6072	47	43	(	(	PUNCT
ejpam-6072	47	44	x	x	NOUN
ejpam-6072	47	45	)	)	PUNCT
ejpam-6072	47	46	=	=	SYM
ejpam-6072	47	47	xtpx	xtpx	PROPN
ejpam-6072	47	48	,	,	PUNCT
ejpam-6072	47	49	(	(	PUNCT
ejpam-6072	47	50	4	4	X
ejpam-6072	47	51	)	)	PUNCT
ejpam-6072	47	52	which	which	PRON
ejpam-6072	47	53	serves	serve	VERB
ejpam-6072	47	54	as	as	ADP
ejpam-6072	47	55	a	a	DET
ejpam-6072	47	56	unified	unified	ADJ
ejpam-6072	47	57	measure	measure	NOUN
ejpam-6072	47	58	to	to	PART
ejpam-6072	47	59	demonstrate	demonstrate	VERB
ejpam-6072	47	60	the	the	DET
ejpam-6072	47	61	stability	stability	NOUN
ejpam-6072	47	62	of	of	ADP
ejpam-6072	47	63	each	each	DET
ejpam-6072	47	64	system	system	NOUN
ejpam-6072	47	65	in	in	ADP
ejpam-6072	47	66	the	the	DET
ejpam-6072	47	67	family	family	NOUN
ejpam-6072	47	68	.	.	PUNCT
ejpam-6072	48	1	the	the	DET
ejpam-6072	48	2	concepts	concept	NOUN
ejpam-6072	48	3	of	of	ADP
ejpam-6072	48	4	hurwitz	hurwitz	PROPN
ejpam-6072	48	5	stability	stability	NOUN
ejpam-6072	48	6	and	and	CCONJ
ejpam-6072	48	7	common	common	ADJ
ejpam-6072	48	8	lyapunov	lyapunov	ADJ
ejpam-6072	48	9	stability	stability	NOUN
ejpam-6072	48	10	have	have	AUX
ejpam-6072	48	11	been	be	AUX
ejpam-6072	48	12	further	far	ADV
ejpam-6072	48	13	extended	extend	VERB
ejpam-6072	48	14	to	to	ADP
ejpam-6072	48	15	diagonal	diagonal	ADJ
ejpam-6072	48	16	lyapunov	lyapunov	ADJ
ejpam-6072	48	17	stability	stability	NOUN
ejpam-6072	48	18	[	[	X
ejpam-6072	48	19	4	4	NUM
ejpam-6072	48	20	,	,	PUNCT
ejpam-6072	48	21	11	11	NUM
ejpam-6072	48	22	,	,	PUNCT
ejpam-6072	48	23	12	12	NUM
ejpam-6072	48	24	]	]	PUNCT
ejpam-6072	48	25	and	and	CCONJ
ejpam-6072	48	26	common	common	ADJ
ejpam-6072	48	27	diagonal	diagonal	ADJ
ejpam-6072	48	28	lyapunov	lyapunov	ADJ
ejpam-6072	48	29	stability	stability	NOUN
ejpam-6072	49	1	[	[	X
ejpam-6072	49	2	4	4	NUM
ejpam-6072	49	3	,	,	PUNCT
ejpam-6072	49	4	13	13	NUM
ejpam-6072	49	5	,	,	PUNCT
ejpam-6072	49	6	14	14	NUM
ejpam-6072	49	7	]	]	PUNCT
ejpam-6072	49	8	,	,	PUNCT
ejpam-6072	49	9	respectively	respectively	ADV
ejpam-6072	49	10	.	.	PUNCT
ejpam-6072	50	1	this	this	DET
ejpam-6072	50	2	extension	extension	NOUN
ejpam-6072	50	3	focuses	focus	VERB
ejpam-6072	50	4	on	on	ADP
ejpam-6072	50	5	identifying	identify	VERB
ejpam-6072	50	6	a	a	DET
ejpam-6072	50	7	diagonal	diagonal	ADJ
ejpam-6072	50	8	positive	positive	ADJ
ejpam-6072	50	9	definite	definite	ADJ
ejpam-6072	50	10	matrix	matrix	NOUN
ejpam-6072	50	11	p	p	X
ejpam-6072	50	12	=	=	NOUN
ejpam-6072	50	13	diag(p1	diag(p1	NOUN
ejpam-6072	50	14	,	,	PUNCT
ejpam-6072	50	15	p2	p2	NOUN
ejpam-6072	50	16	,	,	PUNCT
ejpam-6072	50	17	.	.	PUNCT
ejpam-6072	50	18	.	.	PUNCT
ejpam-6072	51	1	.	.	PUNCT
ejpam-6072	52	1	,	,	PUNCT
ejpam-6072	52	2	pn	pn	PROPN
ejpam-6072	52	3	)	)	PUNCT
ejpam-6072	52	4	such	such	ADJ
ejpam-6072	52	5	that	that	SCONJ
ejpam-6072	52	6	,	,	PUNCT
ejpam-6072	52	7	for	for	ADP
ejpam-6072	52	8	a	a	DET
ejpam-6072	52	9	single	single	ADJ
ejpam-6072	52	10	matrix	matrix	NOUN
ejpam-6072	52	11	a	a	PRON
ejpam-6072	52	12	,	,	PUNCT
ejpam-6072	52	13	the	the	DET
ejpam-6072	52	14	lyapunov	lyapunov	ADJ
ejpam-6072	52	15	inequality	inequality	NOUN
ejpam-6072	52	16	(	(	PUNCT
ejpam-6072	52	17	2	2	NUM
ejpam-6072	52	18	)	)	PUNCT
ejpam-6072	52	19	is	be	AUX
ejpam-6072	52	20	satisfied	satisfied	ADJ
ejpam-6072	52	21	.	.	PUNCT
ejpam-6072	53	1	this	this	DET
ejpam-6072	53	2	formulation	formulation	NOUN
ejpam-6072	53	3	simplifies	simplify	VERB
ejpam-6072	53	4	the	the	DET
ejpam-6072	53	5	task	task	NOUN
ejpam-6072	53	6	by	by	ADP
ejpam-6072	53	7	narrowing	narrow	VERB
ejpam-6072	53	8	it	it	PRON
ejpam-6072	53	9	down	down	ADP
ejpam-6072	53	10	to	to	ADP
ejpam-6072	53	11	finding	find	VERB
ejpam-6072	53	12	the	the	DET
ejpam-6072	53	13	positive	positive	ADJ
ejpam-6072	53	14	diagonal	diagonal	ADJ
ejpam-6072	53	15	elements	element	NOUN
ejpam-6072	53	16	pi	pi	ADV
ejpam-6072	53	17	,	,	PUNCT
ejpam-6072	53	18	taking	take	VERB
ejpam-6072	53	19	advantage	advantage	NOUN
ejpam-6072	53	20	of	of	ADP
ejpam-6072	53	21	the	the	DET
ejpam-6072	53	22	diagonal	diagonal	ADJ
ejpam-6072	53	23	structure	structure	NOUN
ejpam-6072	53	24	for	for	ADP
ejpam-6072	53	25	easier	easy	ADJ
ejpam-6072	53	26	computations	computation	NOUN
ejpam-6072	53	27	.	.	PUNCT
ejpam-6072	54	1	in	in	ADP
ejpam-6072	54	2	a	a	DET
ejpam-6072	54	3	similar	similar	ADJ
ejpam-6072	54	4	way	way	NOUN
ejpam-6072	54	5	,	,	PUNCT
ejpam-6072	54	6	for	for	ADP
ejpam-6072	54	7	a	a	DET
ejpam-6072	54	8	family	family	NOUN
ejpam-6072	54	9	of	of	ADP
ejpam-6072	54	10	matrices	matrix	NOUN
ejpam-6072	54	11	a	a	DET
ejpam-6072	54	12	=	=	NOUN
ejpam-6072	54	13	{	{	PUNCT
ejpam-6072	54	14	a1	a1	NOUN
ejpam-6072	54	15	,	,	PUNCT
ejpam-6072	54	16	.	.	PUNCT
ejpam-6072	54	17	.	.	PUNCT
ejpam-6072	54	18	.	.	PUNCT
ejpam-6072	55	1	,	,	PUNCT
ejpam-6072	55	2	am	be	AUX
ejpam-6072	55	3	}	}	PUNCT
ejpam-6072	55	4	,	,	PUNCT
ejpam-6072	55	5	common	common	ADJ
ejpam-6072	55	6	diagonal	diagonal	ADJ
ejpam-6072	55	7	lyapunov	lyapunov	ADJ
ejpam-6072	55	8	stability	stability	NOUN
ejpam-6072	55	9	entails	entail	VERB
ejpam-6072	55	10	finding	find	VERB
ejpam-6072	55	11	a	a	DET
ejpam-6072	55	12	single	single	ADJ
ejpam-6072	55	13	diagonal	diagonal	ADJ
ejpam-6072	55	14	positive	positive	ADJ
ejpam-6072	55	15	definite	definite	ADJ
ejpam-6072	55	16	matrix	matrix	NOUN
ejpam-6072	55	17	p	p	NOUN
ejpam-6072	55	18	that	that	PRON
ejpam-6072	55	19	meets	meet	VERB
ejpam-6072	55	20	the	the	DET
ejpam-6072	55	21	inequalities	inequality	NOUN
ejpam-6072	55	22	(	(	PUNCT
ejpam-6072	55	23	3	3	NUM
ejpam-6072	55	24	)	)	PUNCT
ejpam-6072	55	25	.	.	PUNCT
ejpam-6072	56	1	in	in	ADP
ejpam-6072	56	2	this	this	DET
ejpam-6072	56	3	case	case	NOUN
ejpam-6072	56	4	,	,	PUNCT
ejpam-6072	56	5	p	p	NOUN
ejpam-6072	56	6	is	be	AUX
ejpam-6072	56	7	referred	refer	VERB
ejpam-6072	56	8	to	to	ADP
ejpam-6072	56	9	as	as	ADP
ejpam-6072	56	10	a	a	DET
ejpam-6072	56	11	common	common	ADJ
ejpam-6072	56	12	lyapunov	lyapunov	ADJ
ejpam-6072	56	13	solution	solution	NOUN
ejpam-6072	56	14	for	for	ADP
ejpam-6072	56	15	the	the	DET
ejpam-6072	56	16	family	family	NOUN
ejpam-6072	56	17	a.	a.	NOUN
ejpam-6072	56	18	equivalently	equivalently	ADV
ejpam-6072	56	19	,	,	PUNCT
ejpam-6072	56	20	the	the	DET
ejpam-6072	56	21	family	family	NOUN
ejpam-6072	56	22	a	a	PRON
ejpam-6072	56	23	has	have	VERB
ejpam-6072	56	24	common	common	ADJ
ejpam-6072	56	25	lyapunov	lyapunov	ADJ
ejpam-6072	56	26	stability	stability	NOUN
ejpam-6072	56	27	if	if	SCONJ
ejpam-6072	56	28	there	there	PRON
ejpam-6072	56	29	exist	exist	VERB
ejpam-6072	56	30	positive	positive	ADJ
ejpam-6072	56	31	definite	definite	ADJ
ejpam-6072	56	32	matrices	matrix	NOUN
ejpam-6072	56	33	p	p	NOUN
ejpam-6072	56	34	,	,	PUNCT
ejpam-6072	56	35	q1	q1	PROPN
ejpam-6072	56	36	,	,	PUNCT
ejpam-6072	56	37	.	.	PUNCT
ejpam-6072	56	38	.	.	PUNCT
ejpam-6072	57	1	.	.	PUNCT
ejpam-6072	58	1	,	,	PUNCT
ejpam-6072	58	2	qm	qm	PROPN
ejpam-6072	58	3	∈	∈	PROPN
ejpam-6072	58	4	rn×n	rn×n	PROPN
ejpam-6072	58	5	such	such	ADJ
ejpam-6072	58	6	that	that	PRON
ejpam-6072	58	7	at	at	ADP
ejpam-6072	58	8	i	i	PRON
ejpam-6072	58	9	p	p	PROPN
ejpam-6072	59	1	+	+	CCONJ
ejpam-6072	59	2	pai	pai	PROPN
ejpam-6072	59	3	+	+	PROPN
ejpam-6072	59	4	qi	qi	X
ejpam-6072	59	5	=	=	SYM
ejpam-6072	59	6	0	0	NUM
ejpam-6072	59	7	,	,	PUNCT
ejpam-6072	59	8	for	for	ADP
ejpam-6072	59	9	i	i	PROPN
ejpam-6072	59	10	=	=	NOUN
ejpam-6072	59	11	1	1	NUM
ejpam-6072	59	12	,	,	PUNCT
ejpam-6072	59	13	.	.	PUNCT
ejpam-6072	59	14	.	.	PUNCT
ejpam-6072	59	15	.	.	PUNCT
ejpam-6072	60	1	,	,	PUNCT
ejpam-6072	60	2	m.	m.	NOUN
ejpam-6072	60	3	this	this	DET
ejpam-6072	60	4	approach	approach	NOUN
ejpam-6072	60	5	proves	prove	VERB
ejpam-6072	60	6	especially	especially	ADV
ejpam-6072	60	7	valuable	valuable	ADJ
ejpam-6072	60	8	in	in	ADP
ejpam-6072	60	9	large	large	ADJ
ejpam-6072	60	10	-	-	PUNCT
ejpam-6072	60	11	scale	scale	NOUN
ejpam-6072	60	12	systems	system	NOUN
ejpam-6072	60	13	or	or	CCONJ
ejpam-6072	60	14	in	in	ADP
ejpam-6072	60	15	cases	case	NOUN
ejpam-6072	60	16	involving	involve	VERB
ejpam-6072	60	17	decoupled	decouple	VERB
ejpam-6072	60	18	or	or	CCONJ
ejpam-6072	60	19	weakly	weakly	ADV
ejpam-6072	60	20	coupled	couple	VERB
ejpam-6072	60	21	subsystems	subsystem	NOUN
ejpam-6072	60	22	,	,	PUNCT
ejpam-6072	60	23	where	where	SCONJ
ejpam-6072	60	24	computational	computational	ADJ
ejpam-6072	60	25	simplicity	simplicity	NOUN
ejpam-6072	60	26	and	and	CCONJ
ejpam-6072	60	27	efficiency	efficiency	NOUN
ejpam-6072	60	28	are	be	AUX
ejpam-6072	60	29	key	key	ADJ
ejpam-6072	60	30	.	.	PUNCT
ejpam-6072	61	1	by	by	ADP
ejpam-6072	61	2	restricting	restrict	VERB
ejpam-6072	61	3	p	p	NOUN
ejpam-6072	61	4	to	to	PART
ejpam-6072	61	5	be	be	AUX
ejpam-6072	61	6	diagonal	diagonal	ADJ
ejpam-6072	61	7	,	,	PUNCT
ejpam-6072	61	8	we	we	PRON
ejpam-6072	61	9	lower	lower	VERB
ejpam-6072	61	10	the	the	DET
ejpam-6072	61	11	problem	problem	NOUN
ejpam-6072	61	12	’s	’s	PART
ejpam-6072	61	13	complexity	complexity	NOUN
ejpam-6072	61	14	while	while	SCONJ
ejpam-6072	61	15	maintaining	maintain	VERB
ejpam-6072	61	16	a	a	DET
ejpam-6072	61	17	unified	unified	ADJ
ejpam-6072	61	18	framework	framework	NOUN
ejpam-6072	61	19	for	for	ADP
ejpam-6072	61	20	proving	prove	VERB
ejpam-6072	61	21	the	the	DET
ejpam-6072	61	22	stability	stability	NOUN
ejpam-6072	61	23	of	of	ADP
ejpam-6072	61	24	each	each	DET
ejpam-6072	61	25	system	system	NOUN
ejpam-6072	61	26	in	in	ADP
ejpam-6072	61	27	the	the	DET
ejpam-6072	61	28	family	family	NOUN
ejpam-6072	61	29	.	.	PUNCT
ejpam-6072	62	1	building	build	VERB
ejpam-6072	62	2	upon	upon	SCONJ
ejpam-6072	62	3	the	the	DET
ejpam-6072	62	4	continuous	continuous	ADJ
ejpam-6072	62	5	-	-	PUNCT
ejpam-6072	62	6	time	time	NOUN
ejpam-6072	62	7	case	case	NOUN
ejpam-6072	62	8	,	,	PUNCT
ejpam-6072	62	9	we	we	PRON
ejpam-6072	62	10	now	now	ADV
ejpam-6072	62	11	consider	consider	VERB
ejpam-6072	62	12	discrete	discrete	ADJ
ejpam-6072	62	13	-	-	PUNCT
ejpam-6072	62	14	time	time	NOUN
ejpam-6072	62	15	difference	difference	NOUN
ejpam-6072	62	16	systems	system	NOUN
ejpam-6072	62	17	,	,	PUNCT
ejpam-6072	62	18	which	which	PRON
ejpam-6072	62	19	are	be	AUX
ejpam-6072	62	20	fundamental	fundamental	ADJ
ejpam-6072	62	21	in	in	ADP
ejpam-6072	62	22	digital	digital	ADJ
ejpam-6072	62	23	control	control	NOUN
ejpam-6072	62	24	and	and	CCONJ
ejpam-6072	62	25	signal	signal	NOUN
ejpam-6072	62	26	processing	processing	NOUN
ejpam-6072	62	27	[	[	X
ejpam-6072	62	28	15	15	NUM
ejpam-6072	62	29	]	]	PUNCT
ejpam-6072	62	30	.	.	PUNCT
ejpam-6072	63	1	specifically	specifically	ADV
ejpam-6072	63	2	,	,	PUNCT
ejpam-6072	63	3	we	we	PRON
ejpam-6072	63	4	examine	examine	VERB
ejpam-6072	63	5	the	the	DET
ejpam-6072	63	6	system	system	NOUN
ejpam-6072	63	7	:	:	PUNCT
ejpam-6072	63	8	x(k	x(k	PROPN
ejpam-6072	64	1	+	+	PUNCT
ejpam-6072	64	2	1	1	X
ejpam-6072	64	3	)	)	PUNCT
ejpam-6072	64	4	=	=	PUNCT
ejpam-6072	64	5	ax(k	ax(k	NOUN
ejpam-6072	64	6	)	)	PUNCT
ejpam-6072	64	7	.	.	PUNCT
ejpam-6072	65	1	the	the	DET
ejpam-6072	65	2	zero	zero	NUM
ejpam-6072	65	3	equilibrium	equilibrium	NOUN
ejpam-6072	65	4	of	of	ADP
ejpam-6072	65	5	this	this	DET
ejpam-6072	65	6	system	system	NOUN
ejpam-6072	65	7	is	be	AUX
ejpam-6072	65	8	asymptotically	asymptotically	ADV
ejpam-6072	65	9	stable	stable	ADJ
ejpam-6072	65	10	if	if	SCONJ
ejpam-6072	65	11	there	there	PRON
ejpam-6072	65	12	exists	exist	VERB
ejpam-6072	65	13	a	a	DET
ejpam-6072	65	14	positive	positive	ADJ
ejpam-6072	65	15	definite	definite	ADJ
ejpam-6072	65	16	matrix	matrix	NOUN
ejpam-6072	65	17	p	p	NOUN
ejpam-6072	65	18	∈	∈	ADJ
ejpam-6072	65	19	rn×n	rn×n	NOUN
ejpam-6072	65	20	such	such	ADJ
ejpam-6072	65	21	that	that	DET
ejpam-6072	65	22	atpa−	atpa−	NOUN
ejpam-6072	66	1	p	p	X
ejpam-6072	66	2	≺	≺	NOUN
ejpam-6072	66	3	0	0	NUM
ejpam-6072	66	4	.	.	PUNCT
ejpam-6072	66	5	a.	a.	PROPN
ejpam-6072	66	6	algefary	algefary	PROPN
ejpam-6072	66	7	,	,	PUNCT
ejpam-6072	66	8	k.	k.	PROPN
ejpam-6072	66	9	a.	a.	PROPN
ejpam-6072	66	10	alqufari	alqufari	PROPN
ejpam-6072	66	11	/	/	SYM
ejpam-6072	66	12	eur	eur	PROPN
ejpam-6072	66	13	.	.	PUNCT
ejpam-6072	67	1	j.	j.	PROPN
ejpam-6072	67	2	pure	pure	PROPN
ejpam-6072	67	3	appl	appl	PROPN
ejpam-6072	67	4	.	.	PROPN
ejpam-6072	67	5	math	math	PROPN
ejpam-6072	67	6	,	,	PUNCT
ejpam-6072	67	7	18	18	NUM
ejpam-6072	67	8	(	(	PUNCT
ejpam-6072	67	9	2	2	NUM
ejpam-6072	67	10	)	)	PUNCT
ejpam-6072	67	11	(	(	PUNCT
ejpam-6072	67	12	2025	2025	NUM
ejpam-6072	67	13	)	)	PUNCT
ejpam-6072	67	14	,	,	PUNCT
ejpam-6072	67	15	6072	6072	NUM
ejpam-6072	67	16	4	4	NUM
ejpam-6072	67	17	of	of	ADP
ejpam-6072	67	18	14	14	NUM
ejpam-6072	67	19	this	this	DET
ejpam-6072	67	20	condition	condition	NOUN
ejpam-6072	67	21	ensures	ensure	VERB
ejpam-6072	67	22	that	that	SCONJ
ejpam-6072	67	23	the	the	DET
ejpam-6072	67	24	lyapunov	lyapunov	NOUN
ejpam-6072	67	25	function	function	VERB
ejpam-6072	67	26	v	v	ADP
ejpam-6072	67	27	(	(	PUNCT
ejpam-6072	67	28	x	x	NOUN
ejpam-6072	67	29	)	)	PUNCT
ejpam-6072	67	30	=	=	PUNCT
ejpam-6072	67	31	xtpx	xtpx	VERB
ejpam-6072	67	32	decreases	decrease	NOUN
ejpam-6072	67	33	over	over	ADP
ejpam-6072	67	34	time	time	NOUN
ejpam-6072	67	35	,	,	PUNCT
ejpam-6072	67	36	guaranteeing	guarantee	VERB
ejpam-6072	67	37	stability	stability	NOUN
ejpam-6072	67	38	.	.	PUNCT
ejpam-6072	68	1	similar	similar	ADJ
ejpam-6072	68	2	to	to	ADP
ejpam-6072	68	3	the	the	DET
ejpam-6072	68	4	continuous	continuous	ADJ
ejpam-6072	68	5	-	-	PUNCT
ejpam-6072	68	6	time	time	NOUN
ejpam-6072	68	7	scenario	scenario	NOUN
ejpam-6072	68	8	,	,	PUNCT
ejpam-6072	68	9	the	the	DET
ejpam-6072	68	10	stability	stability	NOUN
ejpam-6072	68	11	of	of	ADP
ejpam-6072	68	12	the	the	DET
ejpam-6072	68	13	discretetime	discretetime	NOUN
ejpam-6072	68	14	system	system	NOUN
ejpam-6072	68	15	can	can	AUX
ejpam-6072	68	16	also	also	ADV
ejpam-6072	68	17	be	be	AUX
ejpam-6072	68	18	characterized	characterize	VERB
ejpam-6072	68	19	by	by	ADP
ejpam-6072	68	20	the	the	DET
ejpam-6072	68	21	eigenvalues	eigenvalue	NOUN
ejpam-6072	68	22	of	of	ADP
ejpam-6072	68	23	a.	a.	NOUN
ejpam-6072	68	24	specifically	specifically	ADV
ejpam-6072	68	25	,	,	PUNCT
ejpam-6072	68	26	the	the	DET
ejpam-6072	68	27	system	system	NOUN
ejpam-6072	68	28	is	be	AUX
ejpam-6072	68	29	asymptotically	asymptotically	ADV
ejpam-6072	68	30	stable	stable	ADJ
ejpam-6072	68	31	if	if	SCONJ
ejpam-6072	68	32	all	all	PRON
ejpam-6072	68	33	eigenvalues	eigenvalue	VERB
ejpam-6072	68	34	of	of	ADP
ejpam-6072	68	35	a	a	DET
ejpam-6072	68	36	lie	lie	NOUN
ejpam-6072	68	37	strictly	strictly	ADV
ejpam-6072	68	38	inside	inside	ADP
ejpam-6072	68	39	the	the	DET
ejpam-6072	68	40	open	open	ADJ
ejpam-6072	68	41	unit	unit	NOUN
ejpam-6072	68	42	disk	disk	NOUN
ejpam-6072	68	43	of	of	ADP
ejpam-6072	68	44	the	the	DET
ejpam-6072	68	45	complex	complex	ADJ
ejpam-6072	68	46	plane	plane	NOUN
ejpam-6072	68	47	.	.	PUNCT
ejpam-6072	69	1	when	when	SCONJ
ejpam-6072	69	2	this	this	DET
ejpam-6072	69	3	condition	condition	NOUN
ejpam-6072	69	4	is	be	AUX
ejpam-6072	69	5	met	meet	VERB
ejpam-6072	69	6	,	,	PUNCT
ejpam-6072	69	7	a	a	PRON
ejpam-6072	69	8	is	be	AUX
ejpam-6072	69	9	referred	refer	VERB
ejpam-6072	69	10	to	to	ADP
ejpam-6072	69	11	as	as	ADP
ejpam-6072	69	12	schur	schur	PROPN
ejpam-6072	69	13	stable	stable	ADJ
ejpam-6072	69	14	matrix	matrix	NOUN
ejpam-6072	69	15	.	.	PUNCT
ejpam-6072	70	1	definition	definition	NOUN
ejpam-6072	70	2	2	2	NUM
ejpam-6072	70	3	.	.	PUNCT
ejpam-6072	71	1	[	[	X
ejpam-6072	71	2	4	4	X
ejpam-6072	71	3	]	]	X
ejpam-6072	71	4	a	a	DET
ejpam-6072	71	5	matrix	matrix	NOUN
ejpam-6072	71	6	b	b	NOUN
ejpam-6072	71	7	∈	∈	NOUN
ejpam-6072	71	8	rn×n	rn×n	NOUN
ejpam-6072	71	9	is	be	AUX
ejpam-6072	71	10	called	call	VERB
ejpam-6072	71	11	schur	schur	ADJ
ejpam-6072	71	12	stable	stable	ADJ
ejpam-6072	71	13	if	if	SCONJ
ejpam-6072	71	14	its	its	PRON
ejpam-6072	71	15	spectral	spectral	ADJ
ejpam-6072	71	16	radius	radius	NOUN
ejpam-6072	71	17	satisfies	satisfie	NOUN
ejpam-6072	71	18	ρ(b	ρ(b	PROPN
ejpam-6072	71	19	)	)	PUNCT
ejpam-6072	71	20	<	<	X
ejpam-6072	72	1	1	1	X
ejpam-6072	72	2	.	.	PUNCT
ejpam-6072	72	3	lemma	lemma	PROPN
ejpam-6072	72	4	2	2	NUM
ejpam-6072	72	5	.	.	PUNCT
ejpam-6072	73	1	[	[	X
ejpam-6072	73	2	4	4	X
ejpam-6072	73	3	]	]	X
ejpam-6072	73	4	a	a	DET
ejpam-6072	73	5	matrix	matrix	NOUN
ejpam-6072	73	6	a	a	DET
ejpam-6072	73	7	∈	∈	ADJ
ejpam-6072	73	8	rn×n	rn×n	NOUN
ejpam-6072	73	9	is	be	AUX
ejpam-6072	73	10	schur	schur	NOUN
ejpam-6072	73	11	stable	stable	ADJ
ejpam-6072	73	12	if	if	SCONJ
ejpam-6072	73	13	and	and	CCONJ
ejpam-6072	73	14	only	only	ADV
ejpam-6072	73	15	if	if	SCONJ
ejpam-6072	73	16	there	there	PRON
ejpam-6072	73	17	exist	exist	VERB
ejpam-6072	73	18	positive	positive	ADJ
ejpam-6072	73	19	definite	definite	ADJ
ejpam-6072	73	20	matrices	matrix	NOUN
ejpam-6072	73	21	p	p	NOUN
ejpam-6072	73	22	,	,	PUNCT
ejpam-6072	73	23	q	q	NOUN
ejpam-6072	73	24	∈	∈	NOUN
ejpam-6072	73	25	rn×n	rn×n	NOUN
ejpam-6072	73	26	such	such	ADJ
ejpam-6072	73	27	that	that	PRON
ejpam-6072	73	28	:	:	PUNCT
ejpam-6072	73	29	atpa−	atpa−	NOUN
ejpam-6072	73	30	p	p	NOUN
ejpam-6072	73	31	=	=	NOUN
ejpam-6072	73	32	−q	−q	NOUN
ejpam-6072	73	33	.	.	PUNCT
ejpam-6072	74	1	this	this	DET
ejpam-6072	74	2	equation	equation	NOUN
ejpam-6072	74	3	is	be	AUX
ejpam-6072	74	4	known	know	VERB
ejpam-6072	74	5	as	as	ADP
ejpam-6072	74	6	the	the	DET
ejpam-6072	74	7	stein	stein	PROPN
ejpam-6072	74	8	equation	equation	NOUN
ejpam-6072	74	9	and	and	CCONJ
ejpam-6072	74	10	plays	play	VERB
ejpam-6072	74	11	a	a	DET
ejpam-6072	74	12	significant	significant	ADJ
ejpam-6072	74	13	role	role	NOUN
ejpam-6072	74	14	in	in	ADP
ejpam-6072	74	15	discretetime	discretetime	ADJ
ejpam-6072	74	16	stability	stability	NOUN
ejpam-6072	74	17	analysis	analysis	NOUN
ejpam-6072	74	18	,	,	PUNCT
ejpam-6072	74	19	analogous	analogous	ADJ
ejpam-6072	74	20	to	to	ADP
ejpam-6072	74	21	the	the	DET
ejpam-6072	74	22	lyapunov	lyapunov	ADJ
ejpam-6072	74	23	equation	equation	NOUN
ejpam-6072	74	24	in	in	ADP
ejpam-6072	74	25	continuous	continuous	ADJ
ejpam-6072	74	26	-	-	PUNCT
ejpam-6072	74	27	time	time	NOUN
ejpam-6072	74	28	systems	system	NOUN
ejpam-6072	74	29	.	.	PUNCT
ejpam-6072	75	1	extending	extend	VERB
ejpam-6072	75	2	this	this	DET
ejpam-6072	75	3	notion	notion	NOUN
ejpam-6072	75	4	to	to	ADP
ejpam-6072	75	5	the	the	DET
ejpam-6072	75	6	common	common	ADJ
ejpam-6072	75	7	case	case	NOUN
ejpam-6072	75	8	,	,	PUNCT
ejpam-6072	75	9	consider	consider	VERB
ejpam-6072	75	10	a	a	DET
ejpam-6072	75	11	family	family	NOUN
ejpam-6072	75	12	of	of	ADP
ejpam-6072	75	13	matricesa	matricesa	NOUN
ejpam-6072	75	14	=	=	PUNCT
ejpam-6072	75	15	{	{	PUNCT
ejpam-6072	75	16	a1	a1	PROPN
ejpam-6072	75	17	,	,	PUNCT
ejpam-6072	75	18	a2	a2	PROPN
ejpam-6072	75	19	,	,	PUNCT
ejpam-6072	75	20	.	.	PUNCT
ejpam-6072	75	21	.	.	PUNCT
ejpam-6072	76	1	.	.	PUNCT
ejpam-6072	77	1	,	,	PUNCT
ejpam-6072	77	2	am	be	AUX
ejpam-6072	77	3	}	}	PUNCT
ejpam-6072	77	4	.	.	PUNCT
ejpam-6072	78	1	the	the	DET
ejpam-6072	78	2	family	family	NOUN
ejpam-6072	78	3	a	a	PRON
ejpam-6072	78	4	is	be	AUX
ejpam-6072	78	5	said	say	VERB
ejpam-6072	78	6	to	to	PART
ejpam-6072	78	7	possess	possess	VERB
ejpam-6072	78	8	common	common	ADJ
ejpam-6072	78	9	schur	schur	NOUN
ejpam-6072	78	10	stability	stability	NOUN
ejpam-6072	78	11	if	if	SCONJ
ejpam-6072	78	12	there	there	PRON
ejpam-6072	78	13	exists	exist	VERB
ejpam-6072	78	14	a	a	DET
ejpam-6072	78	15	single	single	ADJ
ejpam-6072	78	16	positive	positive	ADJ
ejpam-6072	78	17	definite	definite	ADJ
ejpam-6072	78	18	matrix	matrix	NOUN
ejpam-6072	78	19	p	p	NOUN
ejpam-6072	78	20	such	such	ADJ
ejpam-6072	78	21	that	that	PRON
ejpam-6072	78	22	for	for	ADP
ejpam-6072	78	23	all	all	DET
ejpam-6072	78	24	i	i	PRON
ejpam-6072	78	25	=	=	NOUN
ejpam-6072	78	26	1	1	NUM
ejpam-6072	78	27	,	,	PUNCT
ejpam-6072	78	28	.	.	PUNCT
ejpam-6072	78	29	.	.	PUNCT
ejpam-6072	78	30	.	.	PUNCT
ejpam-6072	79	1	,	,	PUNCT
ejpam-6072	79	2	m	m	PROPN
ejpam-6072	79	3	,	,	PUNCT
ejpam-6072	79	4	the	the	DET
ejpam-6072	79	5	following	follow	VERB
ejpam-6072	79	6	inequality	inequality	NOUN
ejpam-6072	79	7	holds	hold	VERB
ejpam-6072	79	8	at	at	ADP
ejpam-6072	79	9	i	i	PROPN
ejpam-6072	79	10	pai	pai	NOUN
ejpam-6072	79	11	−	−	PUNCT
ejpam-6072	80	1	p	p	NOUN
ejpam-6072	80	2	≺	≺	NOUN
ejpam-6072	80	3	0	0	NUM
ejpam-6072	80	4	.	.	PUNCT
ejpam-6072	81	1	this	this	DET
ejpam-6072	81	2	p	p	NOUN
ejpam-6072	81	3	is	be	AUX
ejpam-6072	81	4	known	know	VERB
ejpam-6072	81	5	as	as	ADP
ejpam-6072	81	6	the	the	DET
ejpam-6072	81	7	common	common	ADJ
ejpam-6072	81	8	schur	schur	NOUN
ejpam-6072	81	9	solution	solution	NOUN
ejpam-6072	81	10	for	for	ADP
ejpam-6072	81	11	the	the	DET
ejpam-6072	81	12	family	family	NOUN
ejpam-6072	81	13	a.	a.	NOUN
ejpam-6072	81	14	the	the	DET
ejpam-6072	81	15	definition	definition	NOUN
ejpam-6072	81	16	of	of	ADP
ejpam-6072	81	17	common	common	ADJ
ejpam-6072	81	18	schur	schur	PROPN
ejpam-6072	81	19	stability	stability	NOUN
ejpam-6072	81	20	can	can	AUX
ejpam-6072	81	21	stated	state	VERB
ejpam-6072	81	22	using	use	VERB
ejpam-6072	81	23	an	an	DET
ejpam-6072	81	24	equation	equation	NOUN
ejpam-6072	81	25	instead	instead	ADV
ejpam-6072	81	26	of	of	ADP
ejpam-6072	81	27	inequality	inequality	NOUN
ejpam-6072	81	28	.	.	PUNCT
ejpam-6072	82	1	that	that	PRON
ejpam-6072	82	2	is	be	AUX
ejpam-6072	82	3	a	a	DET
ejpam-6072	82	4	has	have	AUX
ejpam-6072	82	5	a	a	DET
ejpam-6072	82	6	common	common	ADJ
ejpam-6072	82	7	schur	schur	NOUN
ejpam-6072	82	8	stability	stability	NOUN
ejpam-6072	82	9	if	if	SCONJ
ejpam-6072	82	10	there	there	PRON
ejpam-6072	82	11	exist	exist	VERB
ejpam-6072	82	12	positive	positive	ADJ
ejpam-6072	82	13	definite	definite	ADJ
ejpam-6072	82	14	matrices	matrix	NOUN
ejpam-6072	82	15	p	p	NOUN
ejpam-6072	82	16	,	,	PUNCT
ejpam-6072	82	17	q1	q1	PROPN
ejpam-6072	82	18	,	,	PUNCT
ejpam-6072	82	19	.	.	PUNCT
ejpam-6072	82	20	.	.	PUNCT
ejpam-6072	83	1	.	.	PUNCT
ejpam-6072	84	1	,	,	PUNCT
ejpam-6072	84	2	qm	qm	PROPN
ejpam-6072	84	3	∈	∈	PROPN
ejpam-6072	84	4	rn×n	rn×n	PROPN
ejpam-6072	84	5	such	such	ADJ
ejpam-6072	84	6	that	that	SCONJ
ejpam-6072	84	7	at	at	ADP
ejpam-6072	84	8	i	i	PRON
ejpam-6072	84	9	pai	pai	NOUN
ejpam-6072	84	10	−	−	PROPN
ejpam-6072	85	1	p	p	X
ejpam-6072	85	2	=	=	NOUN
ejpam-6072	85	3	−qi	−qi	PROPN
ejpam-6072	85	4	,	,	PUNCT
ejpam-6072	85	5	i	i	NOUN
ejpam-6072	85	6	=	=	NOUN
ejpam-6072	85	7	1	1	NUM
ejpam-6072	85	8	,	,	PUNCT
ejpam-6072	85	9	.	.	PUNCT
ejpam-6072	85	10	.	.	PUNCT
ejpam-6072	85	11	.	.	PUNCT
ejpam-6072	86	1	,	,	PUNCT
ejpam-6072	86	2	m.	m.	VERB
ejpam-6072	86	3	the	the	DET
ejpam-6072	86	4	existence	existence	NOUN
ejpam-6072	86	5	of	of	ADP
ejpam-6072	86	6	such	such	DET
ejpam-6072	86	7	a	a	DET
ejpam-6072	86	8	common	common	ADJ
ejpam-6072	86	9	matrix	matrix	NOUN
ejpam-6072	86	10	p	p	NOUN
ejpam-6072	86	11	implies	imply	VERB
ejpam-6072	86	12	that	that	SCONJ
ejpam-6072	86	13	each	each	DET
ejpam-6072	86	14	system	system	NOUN
ejpam-6072	86	15	in	in	ADP
ejpam-6072	86	16	the	the	DET
ejpam-6072	86	17	family	family	NOUN
ejpam-6072	86	18	,	,	PUNCT
ejpam-6072	86	19	described	describe	VERB
ejpam-6072	86	20	by	by	ADP
ejpam-6072	86	21	x(k	x(k	PROPN
ejpam-6072	87	1	+	+	PROPN
ejpam-6072	87	2	1	1	X
ejpam-6072	87	3	)	)	PUNCT
ejpam-6072	87	4	=	=	PUNCT
ejpam-6072	87	5	aix(k	aix(k	PROPN
ejpam-6072	87	6	)	)	PUNCT
ejpam-6072	87	7	,	,	PUNCT
ejpam-6072	87	8	is	be	AUX
ejpam-6072	87	9	asymptotically	asymptotically	ADV
ejpam-6072	87	10	stable	stable	ADJ
ejpam-6072	87	11	.	.	PUNCT
ejpam-6072	88	1	moreover	moreover	ADV
ejpam-6072	88	2	,	,	PUNCT
ejpam-6072	88	3	they	they	PRON
ejpam-6072	88	4	all	all	PRON
ejpam-6072	88	5	share	share	VERB
ejpam-6072	88	6	the	the	DET
ejpam-6072	88	7	common	common	ADJ
ejpam-6072	88	8	lyapunov	lyapunov	ADJ
ejpam-6072	88	9	function	function	NOUN
ejpam-6072	88	10	as	as	ADP
ejpam-6072	88	11	in	in	ADP
ejpam-6072	88	12	(	(	PUNCT
ejpam-6072	88	13	4	4	NUM
ejpam-6072	88	14	)	)	PUNCT
ejpam-6072	88	15	which	which	PRON
ejpam-6072	88	16	serves	serve	VERB
ejpam-6072	88	17	as	as	ADP
ejpam-6072	88	18	a	a	DET
ejpam-6072	88	19	unified	unified	ADJ
ejpam-6072	88	20	tool	tool	NOUN
ejpam-6072	88	21	to	to	PART
ejpam-6072	88	22	demonstrate	demonstrate	VERB
ejpam-6072	88	23	the	the	DET
ejpam-6072	88	24	stability	stability	NOUN
ejpam-6072	88	25	of	of	ADP
ejpam-6072	88	26	all	all	DET
ejpam-6072	88	27	systems	system	NOUN
ejpam-6072	88	28	within	within	ADP
ejpam-6072	88	29	the	the	DET
ejpam-6072	88	30	family	family	NOUN
ejpam-6072	88	31	a.	a.	NOUN
ejpam-6072	88	32	moving	move	VERB
ejpam-6072	88	33	forward	forward	ADV
ejpam-6072	88	34	,	,	PUNCT
ejpam-6072	88	35	consider	consider	VERB
ejpam-6072	88	36	the	the	DET
ejpam-6072	88	37	linear	linear	ADJ
ejpam-6072	88	38	differential	differential	NOUN
ejpam-6072	88	39	systems	system	NOUN
ejpam-6072	88	40	with	with	ADP
ejpam-6072	88	41	time	time	NOUN
ejpam-6072	88	42	delays	delay	NOUN
ejpam-6072	88	43	,	,	PUNCT
ejpam-6072	88	44	which	which	PRON
ejpam-6072	88	45	are	be	AUX
ejpam-6072	88	46	frequent	frequent	ADJ
ejpam-6072	88	47	in	in	ADP
ejpam-6072	88	48	many	many	ADJ
ejpam-6072	88	49	engineering	engineering	NOUN
ejpam-6072	88	50	applications	application	NOUN
ejpam-6072	88	51	where	where	SCONJ
ejpam-6072	88	52	delays	delay	NOUN
ejpam-6072	88	53	are	be	AUX
ejpam-6072	88	54	inevitable	inevitable	ADJ
ejpam-6072	88	55	.	.	PUNCT
ejpam-6072	89	1	specifically	specifically	ADV
ejpam-6072	89	2	,	,	PUNCT
ejpam-6072	89	3	we	we	PRON
ejpam-6072	89	4	examine	examine	VERB
ejpam-6072	89	5	the	the	DET
ejpam-6072	89	6	system	system	NOUN
ejpam-6072	89	7	ẋ(t	ẋ(t	NOUN
ejpam-6072	89	8	)	)	PUNCT
ejpam-6072	89	9	=	=	SYM
ejpam-6072	89	10	ax(t	ax(t	NUM
ejpam-6072	89	11	)	)	PUNCT
ejpam-6072	90	1	+	+	PROPN
ejpam-6072	90	2	bx(t−	bx(t−	PROPN
ejpam-6072	90	3	τ	τ	PROPN
ejpam-6072	90	4	)	)	PUNCT
ejpam-6072	90	5	,	,	PUNCT
ejpam-6072	90	6	(	(	PUNCT
ejpam-6072	90	7	5	5	X
ejpam-6072	90	8	)	)	PUNCT
ejpam-6072	90	9	where	where	SCONJ
ejpam-6072	90	10	a	a	DET
ejpam-6072	90	11	,	,	PUNCT
ejpam-6072	90	12	b	b	PROPN
ejpam-6072	90	13	∈	∈	ADJ
ejpam-6072	90	14	rn×n	rn×n	NOUN
ejpam-6072	90	15	are	be	AUX
ejpam-6072	90	16	constant	constant	ADJ
ejpam-6072	90	17	matrices	matrix	NOUN
ejpam-6072	90	18	,	,	PUNCT
ejpam-6072	90	19	x(t	x(t	PROPN
ejpam-6072	90	20	)	)	PUNCT
ejpam-6072	90	21	∈	∈	PROPN
ejpam-6072	90	22	rn	rn	PROPN
ejpam-6072	90	23	is	be	AUX
ejpam-6072	90	24	the	the	DET
ejpam-6072	90	25	state	state	NOUN
ejpam-6072	90	26	vector	vector	NOUN
ejpam-6072	90	27	,	,	PUNCT
ejpam-6072	90	28	and	and	CCONJ
ejpam-6072	90	29	τ	τ	PROPN
ejpam-6072	90	30	≥	≥	X
ejpam-6072	90	31	0	0	NUM
ejpam-6072	90	32	represents	represent	VERB
ejpam-6072	90	33	an	an	DET
ejpam-6072	90	34	arbitrary	arbitrary	ADJ
ejpam-6072	90	35	time	time	NOUN
ejpam-6072	90	36	delay	delay	NOUN
ejpam-6072	90	37	.	.	PUNCT
ejpam-6072	91	1	understanding	understand	VERB
ejpam-6072	91	2	the	the	DET
ejpam-6072	91	3	stability	stability	NOUN
ejpam-6072	91	4	of	of	ADP
ejpam-6072	91	5	such	such	ADJ
ejpam-6072	91	6	time	time	NOUN
ejpam-6072	91	7	-	-	PUNCT
ejpam-6072	91	8	delay	delay	NOUN
ejpam-6072	91	9	systems	system	NOUN
ejpam-6072	91	10	is	be	AUX
ejpam-6072	91	11	crucial	crucial	ADJ
ejpam-6072	91	12	because	because	SCONJ
ejpam-6072	91	13	delays	delay	NOUN
ejpam-6072	91	14	can	can	AUX
ejpam-6072	91	15	significantly	significantly	ADV
ejpam-6072	91	16	affect	affect	VERB
ejpam-6072	91	17	system	system	NOUN
ejpam-6072	91	18	performance	performance	NOUN
ejpam-6072	91	19	and	and	CCONJ
ejpam-6072	91	20	may	may	AUX
ejpam-6072	91	21	lead	lead	VERB
ejpam-6072	91	22	to	to	ADP
ejpam-6072	91	23	instability	instability	NOUN
ejpam-6072	91	24	if	if	SCONJ
ejpam-6072	91	25	not	not	PART
ejpam-6072	91	26	properly	properly	ADV
ejpam-6072	91	27	accounted	account	VERB
ejpam-6072	91	28	for	for	ADP
ejpam-6072	91	29	[	[	X
ejpam-6072	91	30	16	16	NUM
ejpam-6072	91	31	]	]	PUNCT
ejpam-6072	91	32	.	.	PUNCT
ejpam-6072	92	1	as	as	SCONJ
ejpam-6072	92	2	demonstrated	demonstrate	VERB
ejpam-6072	92	3	in	in	ADP
ejpam-6072	92	4	[	[	X
ejpam-6072	92	5	17	17	NUM
ejpam-6072	92	6	]	]	PUNCT
ejpam-6072	92	7	,	,	PUNCT
ejpam-6072	92	8	the	the	DET
ejpam-6072	92	9	system	system	NOUN
ejpam-6072	92	10	(	(	PUNCT
ejpam-6072	92	11	5	5	X
ejpam-6072	92	12	)	)	PUNCT
ejpam-6072	92	13	admits	admit	VERB
ejpam-6072	92	14	a	a	DET
ejpam-6072	92	15	lyapunov	lyapunov	NOUN
ejpam-6072	92	16	-	-	PUNCT
ejpam-6072	92	17	krasovskii	krasovskii	VERB
ejpam-6072	92	18	functional	functional	ADJ
ejpam-6072	92	19	of	of	ADP
ejpam-6072	92	20	the	the	DET
ejpam-6072	92	21	form	form	NOUN
ejpam-6072	92	22	a.	a.	PROPN
ejpam-6072	92	23	algefary	algefary	PROPN
ejpam-6072	92	24	,	,	PUNCT
ejpam-6072	92	25	k.	k.	PROPN
ejpam-6072	92	26	a.	a.	PROPN
ejpam-6072	92	27	alqufari	alqufari	PROPN
ejpam-6072	92	28	/	/	SYM
ejpam-6072	92	29	eur	eur	PROPN
ejpam-6072	92	30	.	.	PUNCT
ejpam-6072	93	1	j.	j.	PROPN
ejpam-6072	93	2	pure	pure	PROPN
ejpam-6072	93	3	appl	appl	PROPN
ejpam-6072	93	4	.	.	PROPN
ejpam-6072	93	5	math	math	PROPN
ejpam-6072	93	6	,	,	PUNCT
ejpam-6072	93	7	18	18	NUM
ejpam-6072	93	8	(	(	PUNCT
ejpam-6072	93	9	2	2	NUM
ejpam-6072	93	10	)	)	PUNCT
ejpam-6072	93	11	(	(	PUNCT
ejpam-6072	93	12	2025	2025	NUM
ejpam-6072	93	13	)	)	PUNCT
ejpam-6072	93	14	,	,	PUNCT
ejpam-6072	93	15	6072	6072	NUM
ejpam-6072	93	16	5	5	NUM
ejpam-6072	93	17	of	of	ADP
ejpam-6072	93	18	14	14	NUM
ejpam-6072	93	19	v	v	NOUN
ejpam-6072	93	20	(	(	PUNCT
ejpam-6072	93	21	x	x	NOUN
ejpam-6072	93	22	)	)	PUNCT
ejpam-6072	93	23	=	=	SYM
ejpam-6072	94	1	xtpx+	xtpx+	PROPN
ejpam-6072	94	2	∫	∫	PROPN
ejpam-6072	94	3	t	t	PROPN
ejpam-6072	94	4	t−τ	t−τ	PROPN
ejpam-6072	94	5	xt	xt	PROPN
ejpam-6072	94	6	(	(	PUNCT
ejpam-6072	94	7	s)qx(s	s)qx(s	NOUN
ejpam-6072	94	8	)	)	PUNCT
ejpam-6072	94	9	ds	ds	NOUN
ejpam-6072	94	10	,	,	PUNCT
ejpam-6072	94	11	provided	provide	VERB
ejpam-6072	94	12	that	that	SCONJ
ejpam-6072	94	13	there	there	PRON
ejpam-6072	94	14	exist	exist	VERB
ejpam-6072	94	15	positive	positive	ADJ
ejpam-6072	94	16	definite	definite	ADJ
ejpam-6072	94	17	matrices	matrix	NOUN
ejpam-6072	94	18	p	p	NOUN
ejpam-6072	94	19	,	,	PUNCT
ejpam-6072	94	20	q	q	ADJ
ejpam-6072	94	21	,	,	PUNCT
ejpam-6072	94	22	r	r	NOUN
ejpam-6072	94	23	∈	∈	NOUN
ejpam-6072	94	24	rn×n	rn×n	NOUN
ejpam-6072	94	25	satisfying	satisfy	VERB
ejpam-6072	94	26	the	the	DET
ejpam-6072	94	27	riccati	riccati	PROPN
ejpam-6072	94	28	equation	equation	NOUN
ejpam-6072	94	29	atp	atp	NOUN
ejpam-6072	94	30	+	+	CCONJ
ejpam-6072	94	31	pa+q+	pa+q+	PROPN
ejpam-6072	94	32	pbq−1btp	pbq−1btp	PROPN
ejpam-6072	94	33	+	+	NOUN
ejpam-6072	94	34	r	r	NOUN
ejpam-6072	94	35	=	=	SYM
ejpam-6072	94	36	0	0	NUM
ejpam-6072	94	37	.	.	PUNCT
ejpam-6072	95	1	the	the	DET
ejpam-6072	95	2	existence	existence	NOUN
ejpam-6072	95	3	of	of	ADP
ejpam-6072	95	4	this	this	DET
ejpam-6072	95	5	lyapunov	lyapunov	NOUN
ejpam-6072	95	6	-	-	PUNCT
ejpam-6072	95	7	krasovskii	krasovskii	VERB
ejpam-6072	95	8	functional	functional	NOUN
ejpam-6072	95	9	is	be	AUX
ejpam-6072	95	10	significant	significant	ADJ
ejpam-6072	95	11	because	because	SCONJ
ejpam-6072	95	12	it	it	PRON
ejpam-6072	95	13	guarantees	guarantee	VERB
ejpam-6072	95	14	that	that	SCONJ
ejpam-6072	95	15	the	the	DET
ejpam-6072	95	16	equilibrium	equilibrium	NOUN
ejpam-6072	95	17	point	point	NOUN
ejpam-6072	95	18	of	of	ADP
ejpam-6072	95	19	system	system	NOUN
ejpam-6072	95	20	(	(	PUNCT
ejpam-6072	95	21	5	5	NUM
ejpam-6072	95	22	)	)	PUNCT
ejpam-6072	95	23	is	be	AUX
ejpam-6072	95	24	asymptotically	asymptotically	ADV
ejpam-6072	95	25	stable	stable	ADJ
ejpam-6072	95	26	for	for	ADP
ejpam-6072	95	27	all	all	DET
ejpam-6072	95	28	delays	delay	NOUN
ejpam-6072	95	29	τ	τ	PROPN
ejpam-6072	95	30	≥	≥	X
ejpam-6072	95	31	0	0	NUM
ejpam-6072	95	32	see	see	VERB
ejpam-6072	95	33	[	[	X
ejpam-6072	95	34	18	18	NUM
ejpam-6072	95	35	]	]	PUNCT
ejpam-6072	95	36	.	.	PUNCT
ejpam-6072	96	1	the	the	DET
ejpam-6072	96	2	requirement	requirement	NOUN
ejpam-6072	96	3	that	that	SCONJ
ejpam-6072	96	4	positive	positive	ADJ
ejpam-6072	96	5	definite	definite	ADJ
ejpam-6072	96	6	matrices	matrix	NOUN
ejpam-6072	96	7	p	p	NOUN
ejpam-6072	96	8	,	,	PUNCT
ejpam-6072	96	9	q	q	ADJ
ejpam-6072	96	10	,	,	PUNCT
ejpam-6072	96	11	r	r	NOUN
ejpam-6072	96	12	satisfy	satisfy	NOUN
ejpam-6072	96	13	the	the	DET
ejpam-6072	96	14	riccati	riccati	PROPN
ejpam-6072	96	15	equation	equation	NOUN
ejpam-6072	96	16	defines	define	VERB
ejpam-6072	96	17	the	the	DET
ejpam-6072	96	18	concept	concept	NOUN
ejpam-6072	96	19	of	of	ADP
ejpam-6072	96	20	riccati	riccati	PROPN
ejpam-6072	96	21	stability	stability	NOUN
ejpam-6072	96	22	for	for	ADP
ejpam-6072	96	23	a	a	DET
ejpam-6072	96	24	pair	pair	NOUN
ejpam-6072	96	25	of	of	ADP
ejpam-6072	96	26	matrices	matrix	NOUN
ejpam-6072	96	27	(	(	PUNCT
ejpam-6072	96	28	a	a	DET
ejpam-6072	96	29	,	,	PUNCT
ejpam-6072	96	30	b	b	NOUN
ejpam-6072	96	31	)	)	PUNCT
ejpam-6072	96	32	,	,	PUNCT
ejpam-6072	96	33	which	which	PRON
ejpam-6072	96	34	was	be	AUX
ejpam-6072	96	35	introduced	introduce	VERB
ejpam-6072	96	36	in	in	ADP
ejpam-6072	96	37	[	[	X
ejpam-6072	96	38	19	19	NUM
ejpam-6072	96	39	]	]	PUNCT
ejpam-6072	96	40	.	.	PUNCT
ejpam-6072	97	1	the	the	DET
ejpam-6072	97	2	connections	connection	NOUN
ejpam-6072	97	3	between	between	ADP
ejpam-6072	97	4	riccati	riccati	PROPN
ejpam-6072	97	5	stability	stability	NOUN
ejpam-6072	97	6	and	and	CCONJ
ejpam-6072	97	7	classical	classical	ADJ
ejpam-6072	97	8	notions	notion	NOUN
ejpam-6072	97	9	of	of	ADP
ejpam-6072	97	10	stability	stability	NOUN
ejpam-6072	97	11	,	,	PUNCT
ejpam-6072	97	12	such	such	ADJ
ejpam-6072	97	13	as	as	ADP
ejpam-6072	97	14	hurwitz	hurwitz	PROPN
ejpam-6072	97	15	and	and	CCONJ
ejpam-6072	97	16	schur	schur	PROPN
ejpam-6072	97	17	stability	stability	PROPN
ejpam-6072	97	18	,	,	PUNCT
ejpam-6072	97	19	have	have	AUX
ejpam-6072	97	20	been	be	AUX
ejpam-6072	97	21	explored	explore	VERB
ejpam-6072	97	22	in	in	ADP
ejpam-6072	97	23	[	[	X
ejpam-6072	97	24	20	20	NUM
ejpam-6072	97	25	]	]	PUNCT
ejpam-6072	97	26	.	.	PUNCT
ejpam-6072	98	1	moreover	moreover	ADV
ejpam-6072	98	2	,	,	PUNCT
ejpam-6072	98	3	several	several	ADJ
ejpam-6072	98	4	results	result	NOUN
ejpam-6072	98	5	establish	establish	VERB
ejpam-6072	98	6	links	link	NOUN
ejpam-6072	98	7	between	between	ADP
ejpam-6072	98	8	riccati	riccati	PROPN
ejpam-6072	98	9	stability	stability	NOUN
ejpam-6072	98	10	and	and	CCONJ
ejpam-6072	98	11	the	the	DET
ejpam-6072	98	12	stability	stability	NOUN
ejpam-6072	98	13	analysis	analysis	NOUN
ejpam-6072	98	14	of	of	ADP
ejpam-6072	98	15	time	time	NOUN
ejpam-6072	98	16	-	-	PUNCT
ejpam-6072	98	17	delay	delay	NOUN
ejpam-6072	98	18	systems	system	NOUN
ejpam-6072	98	19	,	,	PUNCT
ejpam-6072	98	20	underscoring	underscore	VERB
ejpam-6072	98	21	its	its	PRON
ejpam-6072	98	22	importance	importance	NOUN
ejpam-6072	98	23	in	in	ADP
ejpam-6072	98	24	this	this	DET
ejpam-6072	98	25	area	area	NOUN
ejpam-6072	98	26	of	of	ADP
ejpam-6072	98	27	study	study	NOUN
ejpam-6072	98	28	.	.	PUNCT
ejpam-6072	99	1	similar	similar	ADJ
ejpam-6072	99	2	to	to	ADP
ejpam-6072	99	3	the	the	DET
ejpam-6072	99	4	concept	concept	NOUN
ejpam-6072	99	5	of	of	ADP
ejpam-6072	99	6	common	common	ADJ
ejpam-6072	99	7	lyapunov	lyapunov	ADJ
ejpam-6072	99	8	stability	stability	NOUN
ejpam-6072	99	9	,	,	PUNCT
ejpam-6072	99	10	we	we	PRON
ejpam-6072	99	11	introduce	introduce	VERB
ejpam-6072	99	12	the	the	DET
ejpam-6072	99	13	notion	notion	NOUN
ejpam-6072	99	14	of	of	ADP
ejpam-6072	99	15	common	common	ADJ
ejpam-6072	99	16	riccati	riccati	NOUN
ejpam-6072	99	17	stability	stability	NOUN
ejpam-6072	99	18	.	.	PUNCT
ejpam-6072	100	1	this	this	DET
ejpam-6072	100	2	concept	concept	NOUN
ejpam-6072	100	3	involves	involve	VERB
ejpam-6072	100	4	finding	find	VERB
ejpam-6072	100	5	positive	positive	ADJ
ejpam-6072	100	6	definite	definite	ADJ
ejpam-6072	100	7	matrices	matrix	NOUN
ejpam-6072	100	8	p	p	NOUN
ejpam-6072	100	9	,	,	PUNCT
ejpam-6072	100	10	q	q	ADJ
ejpam-6072	100	11	,	,	PUNCT
ejpam-6072	100	12	ri	ri	PROPN
ejpam-6072	100	13	∈	∈	PROPN
ejpam-6072	100	14	rn×n	rn×n	NOUN
ejpam-6072	100	15	,	,	PUNCT
ejpam-6072	100	16	i	i	PRON
ejpam-6072	100	17	=	=	NOUN
ejpam-6072	100	18	1	1	NUM
ejpam-6072	100	19	,	,	PUNCT
ejpam-6072	100	20	.	.	PUNCT
ejpam-6072	100	21	.	.	PUNCT
ejpam-6072	101	1	.	.	PUNCT
ejpam-6072	102	1	,	,	PUNCT
ejpam-6072	102	2	m	m	PROPN
ejpam-6072	102	3	,	,	PUNCT
ejpam-6072	102	4	that	that	PRON
ejpam-6072	102	5	satisfy	satisfy	VERB
ejpam-6072	102	6	a	a	DET
ejpam-6072	102	7	riccati	riccati	NOUN
ejpam-6072	102	8	equation	equation	NOUN
ejpam-6072	102	9	simultaneously	simultaneously	ADV
ejpam-6072	102	10	for	for	ADP
ejpam-6072	102	11	a	a	DET
ejpam-6072	102	12	family	family	NOUN
ejpam-6072	102	13	of	of	ADP
ejpam-6072	102	14	matrix	matrix	NOUN
ejpam-6072	102	15	pairs	pair	NOUN
ejpam-6072	102	16	u	u	NOUN
ejpam-6072	102	17	=	=	X
ejpam-6072	102	18	{	{	PUNCT
ejpam-6072	102	19	(	(	PUNCT
ejpam-6072	102	20	ai	ai	NOUN
ejpam-6072	102	21	,	,	PUNCT
ejpam-6072	102	22	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	102	23	.	.	PUNCT
ejpam-6072	103	1	definition	definition	NOUN
ejpam-6072	103	2	3	3	X
ejpam-6072	103	3	.	.	PUNCT
ejpam-6072	104	1	let	let	AUX
ejpam-6072	104	2	ai	ai	VERB
ejpam-6072	104	3	,	,	PUNCT
ejpam-6072	104	4	bi	bi	NOUN
ejpam-6072	104	5	∈	∈	PROPN
ejpam-6072	104	6	rn×n	rn×n	PROPN
ejpam-6072	104	7	for	for	ADP
ejpam-6072	104	8	i	i	PRON
ejpam-6072	104	9	=	=	NOUN
ejpam-6072	104	10	1	1	NUM
ejpam-6072	104	11	,	,	PUNCT
ejpam-6072	104	12	.	.	PUNCT
ejpam-6072	104	13	.	.	PUNCT
ejpam-6072	105	1	.	.	PUNCT
ejpam-6072	106	1	,	,	PUNCT
ejpam-6072	106	2	m.	m.	NOUN
ejpam-6072	106	3	we	we	PRON
ejpam-6072	106	4	say	say	VERB
ejpam-6072	106	5	that	that	SCONJ
ejpam-6072	106	6	the	the	DET
ejpam-6072	106	7	family	family	NOUN
ejpam-6072	106	8	of	of	ADP
ejpam-6072	106	9	pairs	pair	NOUN
ejpam-6072	106	10	u	u	NOUN
ejpam-6072	106	11	=	=	X
ejpam-6072	106	12	{	{	PUNCT
ejpam-6072	106	13	(	(	PUNCT
ejpam-6072	106	14	ai	ai	PROPN
ejpam-6072	106	15	,	,	PUNCT
ejpam-6072	106	16	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	106	17	has	have	VERB
ejpam-6072	106	18	common	common	ADJ
ejpam-6072	106	19	riccati	riccati	NOUN
ejpam-6072	106	20	stability	stability	NOUN
ejpam-6072	106	21	if	if	SCONJ
ejpam-6072	106	22	there	there	PRON
ejpam-6072	106	23	exist	exist	VERB
ejpam-6072	106	24	positive	positive	ADJ
ejpam-6072	106	25	definite	definite	ADJ
ejpam-6072	106	26	matrices	matrix	NOUN
ejpam-6072	106	27	p	p	NOUN
ejpam-6072	106	28	,	,	PUNCT
ejpam-6072	106	29	q	q	ADJ
ejpam-6072	106	30	,	,	PUNCT
ejpam-6072	106	31	ri	ri	PROPN
ejpam-6072	106	32	∈	∈	PROPN
ejpam-6072	106	33	rn×n	rn×n	NOUN
ejpam-6072	106	34	such	such	ADJ
ejpam-6072	106	35	that	that	SCONJ
ejpam-6072	106	36	the	the	DET
ejpam-6072	106	37	following	follow	VERB
ejpam-6072	106	38	riccati	riccati	PROPN
ejpam-6072	106	39	equations	equation	NOUN
ejpam-6072	106	40	at	at	ADP
ejpam-6072	106	41	i	i	PROPN
ejpam-6072	106	42	p	p	PROPN
ejpam-6072	107	1	+	+	CCONJ
ejpam-6072	107	2	pai	pai	PROPN
ejpam-6072	107	3	+	+	PROPN
ejpam-6072	107	4	q+	q+	ADP
ejpam-6072	107	5	pbiq	pbiq	PROPN
ejpam-6072	108	1	−1bt	−1bt	ADP
ejpam-6072	108	2	i	i	PRON
ejpam-6072	108	3	p	p	X
ejpam-6072	109	1	+	+	PROPN
ejpam-6072	109	2	ri	ri	NOUN
ejpam-6072	109	3	=	=	SYM
ejpam-6072	109	4	0	0	PROPN
ejpam-6072	109	5	,	,	PUNCT
ejpam-6072	109	6	i	i	PRON
ejpam-6072	109	7	=	=	NOUN
ejpam-6072	109	8	1	1	NUM
ejpam-6072	109	9	,	,	PUNCT
ejpam-6072	109	10	.	.	PUNCT
ejpam-6072	109	11	.	.	PUNCT
ejpam-6072	109	12	.	.	PUNCT
ejpam-6072	110	1	,	,	PUNCT
ejpam-6072	110	2	m	m	PRON
ejpam-6072	110	3	,	,	PUNCT
ejpam-6072	110	4	hold	hold	VERB
ejpam-6072	110	5	.	.	PUNCT
ejpam-6072	111	1	when	when	SCONJ
ejpam-6072	111	2	such	such	ADJ
ejpam-6072	111	3	matrices	matrix	NOUN
ejpam-6072	111	4	p	p	X
ejpam-6072	111	5	,	,	PUNCT
ejpam-6072	111	6	q	q	ADJ
ejpam-6072	111	7	,	,	PUNCT
ejpam-6072	111	8	ri	ri	PROPN
ejpam-6072	111	9	,	,	PUNCT
ejpam-6072	111	10	i	i	NOUN
ejpam-6072	111	11	=	=	NOUN
ejpam-6072	111	12	1	1	NUM
ejpam-6072	111	13	,	,	PUNCT
ejpam-6072	111	14	.	.	PUNCT
ejpam-6072	111	15	.	.	PUNCT
ejpam-6072	111	16	.	.	PUNCT
ejpam-6072	112	1	,	,	PUNCT
ejpam-6072	112	2	m	m	PRON
ejpam-6072	112	3	,	,	PUNCT
ejpam-6072	112	4	exist	exist	VERB
ejpam-6072	112	5	,	,	PUNCT
ejpam-6072	112	6	we	we	PRON
ejpam-6072	112	7	refer	refer	VERB
ejpam-6072	112	8	to	to	ADP
ejpam-6072	112	9	the	the	DET
ejpam-6072	112	10	pair	pair	NOUN
ejpam-6072	112	11	(	(	PUNCT
ejpam-6072	112	12	p	p	X
ejpam-6072	112	13	,	,	PUNCT
ejpam-6072	112	14	q	q	NOUN
ejpam-6072	112	15	)	)	PUNCT
ejpam-6072	112	16	as	as	ADP
ejpam-6072	112	17	a	a	DET
ejpam-6072	112	18	common	common	ADJ
ejpam-6072	112	19	riccati	riccati	NOUN
ejpam-6072	112	20	solution	solution	NOUN
ejpam-6072	112	21	for	for	ADP
ejpam-6072	112	22	the	the	DET
ejpam-6072	112	23	family	family	NOUN
ejpam-6072	112	24	u	u	NOUN
ejpam-6072	112	25	.	.	PUNCT
ejpam-6072	113	1	essentially	essentially	ADV
ejpam-6072	113	2	,	,	PUNCT
ejpam-6072	113	3	common	common	ADJ
ejpam-6072	113	4	riccati	riccati	NOUN
ejpam-6072	113	5	stability	stability	NOUN
ejpam-6072	113	6	represents	represent	VERB
ejpam-6072	113	7	a	a	DET
ejpam-6072	113	8	simultaneous	simultaneous	ADJ
ejpam-6072	113	9	solution	solution	NOUN
ejpam-6072	113	10	to	to	ADP
ejpam-6072	113	11	the	the	DET
ejpam-6072	113	12	riccati	riccati	PROPN
ejpam-6072	113	13	equations	equation	NOUN
ejpam-6072	113	14	associated	associate	VERB
ejpam-6072	113	15	with	with	ADP
ejpam-6072	113	16	each	each	DET
ejpam-6072	113	17	pair	pair	NOUN
ejpam-6072	113	18	(	(	PUNCT
ejpam-6072	113	19	ai	ai	NOUN
ejpam-6072	113	20	,	,	PUNCT
ejpam-6072	113	21	bi	bi	NOUN
ejpam-6072	113	22	)	)	PUNCT
ejpam-6072	113	23	in	in	ADP
ejpam-6072	113	24	u	u	PROPN
ejpam-6072	113	25	.	.	PUNCT
ejpam-6072	114	1	the	the	DET
ejpam-6072	114	2	existence	existence	NOUN
ejpam-6072	114	3	of	of	ADP
ejpam-6072	114	4	a	a	DET
ejpam-6072	114	5	common	common	ADJ
ejpam-6072	114	6	riccati	riccati	NOUN
ejpam-6072	114	7	solution	solution	NOUN
ejpam-6072	114	8	for	for	ADP
ejpam-6072	114	9	the	the	DET
ejpam-6072	114	10	family	family	NOUN
ejpam-6072	114	11	u	u	NOUN
ejpam-6072	114	12	implies	imply	VERB
ejpam-6072	114	13	that	that	SCONJ
ejpam-6072	114	14	v	v	X
ejpam-6072	114	15	(	(	PUNCT
ejpam-6072	114	16	x	x	NOUN
ejpam-6072	114	17	)	)	PUNCT
ejpam-6072	114	18	=	=	SYM
ejpam-6072	115	1	xtpx+	xtpx+	PROPN
ejpam-6072	115	2	∫	∫	PROPN
ejpam-6072	115	3	t	t	PROPN
ejpam-6072	115	4	t−τ	t−τ	PROPN
ejpam-6072	115	5	xt	xt	PROPN
ejpam-6072	115	6	(	(	PUNCT
ejpam-6072	115	7	s)qx(s	s)qx(s	NOUN
ejpam-6072	115	8	)	)	PUNCT
ejpam-6072	115	9	ds	ds	NOUN
ejpam-6072	115	10	serves	serve	VERB
ejpam-6072	115	11	as	as	ADP
ejpam-6072	115	12	a	a	DET
ejpam-6072	115	13	common	common	ADJ
ejpam-6072	115	14	lyapunov	lyapunov	NOUN
ejpam-6072	115	15	-	-	PUNCT
ejpam-6072	115	16	krasovskii	krasovskii	VERB
ejpam-6072	115	17	functional	functional	ADJ
ejpam-6072	115	18	for	for	ADP
ejpam-6072	115	19	all	all	DET
ejpam-6072	115	20	time	time	NOUN
ejpam-6072	115	21	-	-	PUNCT
ejpam-6072	115	22	delay	delay	NOUN
ejpam-6072	115	23	systems	system	NOUN
ejpam-6072	115	24	associated	associate	VERB
ejpam-6072	115	25	with	with	ADP
ejpam-6072	115	26	the	the	DET
ejpam-6072	115	27	pairs	pair	NOUN
ejpam-6072	115	28	in	in	ADP
ejpam-6072	115	29	u	u	PROPN
ejpam-6072	115	30	.	.	PUNCT
ejpam-6072	116	1	the	the	DET
ejpam-6072	116	2	main	main	ADJ
ejpam-6072	116	3	contributions	contribution	NOUN
ejpam-6072	116	4	of	of	ADP
ejpam-6072	116	5	this	this	DET
ejpam-6072	116	6	paper	paper	NOUN
ejpam-6072	116	7	are	be	AUX
ejpam-6072	116	8	organized	organize	VERB
ejpam-6072	116	9	into	into	ADP
ejpam-6072	116	10	two	two	NUM
ejpam-6072	116	11	key	key	ADJ
ejpam-6072	116	12	parts	part	NOUN
ejpam-6072	116	13	.	.	PUNCT
ejpam-6072	117	1	in	in	ADP
ejpam-6072	117	2	the	the	DET
ejpam-6072	117	3	first	first	ADJ
ejpam-6072	117	4	part	part	NOUN
ejpam-6072	117	5	,	,	PUNCT
ejpam-6072	117	6	we	we	PRON
ejpam-6072	117	7	explore	explore	VERB
ejpam-6072	117	8	the	the	DET
ejpam-6072	117	9	connections	connection	NOUN
ejpam-6072	117	10	between	between	ADP
ejpam-6072	117	11	common	common	ADJ
ejpam-6072	117	12	riccati	riccati	NOUN
ejpam-6072	117	13	stability	stability	NOUN
ejpam-6072	117	14	for	for	ADP
ejpam-6072	117	15	a	a	DET
ejpam-6072	117	16	family	family	NOUN
ejpam-6072	117	17	of	of	ADP
ejpam-6072	117	18	matrix	matrix	NOUN
ejpam-6072	117	19	pairs	pair	NOUN
ejpam-6072	117	20	u	u	NOUN
ejpam-6072	117	21	=	=	X
ejpam-6072	117	22	{	{	PUNCT
ejpam-6072	117	23	(	(	PUNCT
ejpam-6072	117	24	ai	ai	PROPN
ejpam-6072	117	25	,	,	PUNCT
ejpam-6072	117	26	bi)}mi=1	bi)}mi=1	PROPN
ejpam-6072	117	27	and	and	CCONJ
ejpam-6072	117	28	the	the	DET
ejpam-6072	117	29	concepts	concept	NOUN
ejpam-6072	117	30	of	of	ADP
ejpam-6072	117	31	common	common	ADJ
ejpam-6072	117	32	lyapunov	lyapunov	ADJ
ejpam-6072	117	33	stability	stability	NOUN
ejpam-6072	117	34	and	and	CCONJ
ejpam-6072	117	35	common	common	ADJ
ejpam-6072	117	36	schur	schur	NOUN
ejpam-6072	117	37	stability	stability	NOUN
ejpam-6072	117	38	.	.	PUNCT
ejpam-6072	118	1	by	by	ADP
ejpam-6072	118	2	investigating	investigate	VERB
ejpam-6072	118	3	these	these	DET
ejpam-6072	118	4	relationships	relationship	NOUN
ejpam-6072	118	5	,	,	PUNCT
ejpam-6072	118	6	we	we	PRON
ejpam-6072	118	7	aim	aim	VERB
ejpam-6072	118	8	to	to	PART
ejpam-6072	118	9	deepen	deepen	VERB
ejpam-6072	118	10	the	the	DET
ejpam-6072	118	11	understanding	understanding	NOUN
ejpam-6072	118	12	of	of	ADP
ejpam-6072	118	13	how	how	SCONJ
ejpam-6072	118	14	these	these	DET
ejpam-6072	118	15	different	different	ADJ
ejpam-6072	118	16	stability	stability	NOUN
ejpam-6072	118	17	notions	notion	NOUN
ejpam-6072	118	18	are	be	AUX
ejpam-6072	118	19	interrelated	interrelate	VERB
ejpam-6072	118	20	within	within	ADP
ejpam-6072	118	21	the	the	DET
ejpam-6072	118	22	context	context	NOUN
ejpam-6072	118	23	of	of	ADP
ejpam-6072	118	24	control	control	NOUN
ejpam-6072	118	25	theory	theory	NOUN
ejpam-6072	118	26	and	and	CCONJ
ejpam-6072	118	27	system	system	NOUN
ejpam-6072	118	28	dynamics	dynamic	NOUN
ejpam-6072	118	29	.	.	PUNCT
ejpam-6072	119	1	a.	a.	PROPN
ejpam-6072	119	2	algefary	algefary	PROPN
ejpam-6072	119	3	,	,	PUNCT
ejpam-6072	119	4	k.	k.	PROPN
ejpam-6072	119	5	a.	a.	PROPN
ejpam-6072	119	6	alqufari	alqufari	PROPN
ejpam-6072	119	7	/	/	SYM
ejpam-6072	119	8	eur	eur	PROPN
ejpam-6072	119	9	.	.	PUNCT
ejpam-6072	120	1	j.	j.	PROPN
ejpam-6072	120	2	pure	pure	PROPN
ejpam-6072	120	3	appl	appl	PROPN
ejpam-6072	120	4	.	.	PROPN
ejpam-6072	120	5	math	math	PROPN
ejpam-6072	120	6	,	,	PUNCT
ejpam-6072	120	7	18	18	NUM
ejpam-6072	120	8	(	(	PUNCT
ejpam-6072	120	9	2	2	NUM
ejpam-6072	120	10	)	)	PUNCT
ejpam-6072	120	11	(	(	PUNCT
ejpam-6072	120	12	2025	2025	NUM
ejpam-6072	120	13	)	)	PUNCT
ejpam-6072	120	14	,	,	PUNCT
ejpam-6072	120	15	6072	6072	NUM
ejpam-6072	120	16	6	6	NUM
ejpam-6072	120	17	of	of	ADP
ejpam-6072	120	18	14	14	NUM
ejpam-6072	120	19	in	in	ADP
ejpam-6072	120	20	the	the	DET
ejpam-6072	120	21	second	second	ADJ
ejpam-6072	120	22	part	part	NOUN
ejpam-6072	120	23	,	,	PUNCT
ejpam-6072	120	24	we	we	PRON
ejpam-6072	120	25	explore	explore	VERB
ejpam-6072	120	26	several	several	ADJ
ejpam-6072	120	27	scaling	scale	VERB
ejpam-6072	120	28	properties	property	NOUN
ejpam-6072	120	29	associated	associate	VERB
ejpam-6072	120	30	with	with	ADP
ejpam-6072	120	31	common	common	ADJ
ejpam-6072	120	32	riccati	riccati	NOUN
ejpam-6072	120	33	stability	stability	NOUN
ejpam-6072	120	34	.	.	PUNCT
ejpam-6072	121	1	analyzing	analyze	VERB
ejpam-6072	121	2	these	these	DET
ejpam-6072	121	3	properties	property	NOUN
ejpam-6072	121	4	is	be	AUX
ejpam-6072	121	5	significant	significant	ADJ
ejpam-6072	121	6	because	because	SCONJ
ejpam-6072	121	7	scaling	scale	VERB
ejpam-6072	121	8	can	can	AUX
ejpam-6072	121	9	affect	affect	VERB
ejpam-6072	121	10	the	the	DET
ejpam-6072	121	11	stability	stability	NOUN
ejpam-6072	121	12	of	of	ADP
ejpam-6072	121	13	systems	system	NOUN
ejpam-6072	121	14	,	,	PUNCT
ejpam-6072	121	15	and	and	CCONJ
ejpam-6072	121	16	understanding	understand	VERB
ejpam-6072	121	17	this	this	DET
ejpam-6072	121	18	impact	impact	NOUN
ejpam-6072	121	19	is	be	AUX
ejpam-6072	121	20	crucial	crucial	ADJ
ejpam-6072	121	21	for	for	ADP
ejpam-6072	121	22	the	the	DET
ejpam-6072	121	23	design	design	NOUN
ejpam-6072	121	24	and	and	CCONJ
ejpam-6072	121	25	analysis	analysis	NOUN
ejpam-6072	121	26	of	of	ADP
ejpam-6072	121	27	robust	robust	ADJ
ejpam-6072	121	28	control	control	NOUN
ejpam-6072	121	29	systems	system	NOUN
ejpam-6072	121	30	.	.	PUNCT
ejpam-6072	122	1	by	by	ADP
ejpam-6072	122	2	identifying	identify	VERB
ejpam-6072	122	3	how	how	SCONJ
ejpam-6072	122	4	scaling	scaling	ADJ
ejpam-6072	122	5	transformations	transformation	NOUN
ejpam-6072	122	6	influence	influence	VERB
ejpam-6072	122	7	common	common	ADJ
ejpam-6072	122	8	riccati	riccati	NOUN
ejpam-6072	122	9	stability	stability	NOUN
ejpam-6072	122	10	,	,	PUNCT
ejpam-6072	122	11	we	we	PRON
ejpam-6072	122	12	provide	provide	VERB
ejpam-6072	122	13	insights	insight	NOUN
ejpam-6072	122	14	that	that	PRON
ejpam-6072	122	15	can	can	AUX
ejpam-6072	122	16	lead	lead	VERB
ejpam-6072	122	17	to	to	ADP
ejpam-6072	122	18	more	more	ADV
ejpam-6072	122	19	efficient	efficient	ADJ
ejpam-6072	122	20	computational	computational	ADJ
ejpam-6072	122	21	methods	method	NOUN
ejpam-6072	122	22	and	and	CCONJ
ejpam-6072	122	23	enhance	enhance	VERB
ejpam-6072	122	24	the	the	DET
ejpam-6072	122	25	applicability	applicability	NOUN
ejpam-6072	122	26	of	of	ADP
ejpam-6072	122	27	stability	stability	NOUN
ejpam-6072	122	28	criteria	criterion	NOUN
ejpam-6072	122	29	to	to	ADP
ejpam-6072	122	30	a	a	DET
ejpam-6072	122	31	broader	broad	ADJ
ejpam-6072	122	32	class	class	NOUN
ejpam-6072	122	33	of	of	ADP
ejpam-6072	122	34	systems	system	NOUN
ejpam-6072	122	35	.	.	PUNCT
ejpam-6072	123	1	2	2	X
ejpam-6072	123	2	.	.	X
ejpam-6072	123	3	common	common	ADJ
ejpam-6072	123	4	lyapunov	lyapunov	PROPN
ejpam-6072	123	5	,	,	PUNCT
ejpam-6072	123	6	schur	schur	NOUN
ejpam-6072	123	7	,	,	PUNCT
ejpam-6072	123	8	and	and	CCONJ
ejpam-6072	123	9	riccati	riccati	PROPN
ejpam-6072	123	10	stability	stability	NOUN
ejpam-6072	123	11	in	in	ADP
ejpam-6072	123	12	this	this	DET
ejpam-6072	123	13	section	section	NOUN
ejpam-6072	123	14	,	,	PUNCT
ejpam-6072	123	15	we	we	PRON
ejpam-6072	123	16	explore	explore	VERB
ejpam-6072	123	17	the	the	DET
ejpam-6072	123	18	foundational	foundational	ADJ
ejpam-6072	123	19	relationships	relationship	NOUN
ejpam-6072	123	20	among	among	ADP
ejpam-6072	123	21	common	common	ADJ
ejpam-6072	123	22	lyapunov	lyapunov	ADJ
ejpam-6072	123	23	stability	stability	NOUN
ejpam-6072	123	24	,	,	PUNCT
ejpam-6072	123	25	common	common	ADJ
ejpam-6072	123	26	schur	schur	NOUN
ejpam-6072	123	27	stability	stability	NOUN
ejpam-6072	123	28	,	,	PUNCT
ejpam-6072	123	29	and	and	CCONJ
ejpam-6072	123	30	common	common	ADJ
ejpam-6072	123	31	riccati	riccati	NOUN
ejpam-6072	123	32	stability	stability	NOUN
ejpam-6072	123	33	for	for	ADP
ejpam-6072	123	34	families	family	NOUN
ejpam-6072	123	35	of	of	ADP
ejpam-6072	123	36	matrices	matrix	NOUN
ejpam-6072	123	37	and	and	CCONJ
ejpam-6072	123	38	matrix	matrix	NOUN
ejpam-6072	123	39	pairs	pair	NOUN
ejpam-6072	123	40	.	.	PUNCT
ejpam-6072	124	1	these	these	DET
ejpam-6072	124	2	stability	stability	NOUN
ejpam-6072	124	3	concepts	concept	NOUN
ejpam-6072	124	4	play	play	VERB
ejpam-6072	124	5	crucial	crucial	ADJ
ejpam-6072	124	6	roles	role	NOUN
ejpam-6072	124	7	in	in	ADP
ejpam-6072	124	8	analyzing	analyze	VERB
ejpam-6072	124	9	and	and	CCONJ
ejpam-6072	124	10	ensuring	ensure	VERB
ejpam-6072	124	11	the	the	DET
ejpam-6072	124	12	robustness	robustness	NOUN
ejpam-6072	124	13	of	of	ADP
ejpam-6072	124	14	complex	complex	ADJ
ejpam-6072	124	15	systems	system	NOUN
ejpam-6072	124	16	,	,	PUNCT
ejpam-6072	124	17	particularly	particularly	ADV
ejpam-6072	124	18	in	in	ADP
ejpam-6072	124	19	control	control	NOUN
ejpam-6072	124	20	theory	theory	NOUN
ejpam-6072	124	21	.	.	PUNCT
ejpam-6072	125	1	by	by	ADP
ejpam-6072	125	2	developing	develop	VERB
ejpam-6072	125	3	these	these	DET
ejpam-6072	125	4	interconnections	interconnection	NOUN
ejpam-6072	125	5	,	,	PUNCT
ejpam-6072	125	6	we	we	PRON
ejpam-6072	125	7	provide	provide	VERB
ejpam-6072	125	8	a	a	DET
ejpam-6072	125	9	unified	unified	ADJ
ejpam-6072	125	10	framework	framework	NOUN
ejpam-6072	125	11	that	that	PRON
ejpam-6072	125	12	simplifies	simplify	VERB
ejpam-6072	125	13	stability	stability	NOUN
ejpam-6072	125	14	analysis	analysis	NOUN
ejpam-6072	125	15	across	across	ADP
ejpam-6072	125	16	various	various	ADJ
ejpam-6072	125	17	system	system	NOUN
ejpam-6072	125	18	structures	structure	NOUN
ejpam-6072	125	19	and	and	CCONJ
ejpam-6072	125	20	enhances	enhance	VERB
ejpam-6072	125	21	our	our	PRON
ejpam-6072	125	22	understanding	understanding	NOUN
ejpam-6072	125	23	of	of	ADP
ejpam-6072	125	24	stability	stability	NOUN
ejpam-6072	125	25	in	in	ADP
ejpam-6072	125	26	both	both	CCONJ
ejpam-6072	125	27	continuous	continuous	ADJ
ejpam-6072	125	28	and	and	CCONJ
ejpam-6072	125	29	discrete	discrete	ADJ
ejpam-6072	125	30	-	-	PUNCT
ejpam-6072	125	31	time	time	NOUN
ejpam-6072	125	32	systems	system	NOUN
ejpam-6072	125	33	.	.	PUNCT
ejpam-6072	126	1	theorem	theorem	NOUN
ejpam-6072	126	2	1	1	NUM
ejpam-6072	126	3	.	.	X
ejpam-6072	127	1	for	for	ADP
ejpam-6072	127	2	i	i	PRON
ejpam-6072	127	3	=	=	NOUN
ejpam-6072	127	4	1	1	NUM
ejpam-6072	127	5	,	,	PUNCT
ejpam-6072	127	6	.	.	PUNCT
ejpam-6072	127	7	.	.	PUNCT
ejpam-6072	128	1	.	.	PUNCT
ejpam-6072	129	1	,	,	PUNCT
ejpam-6072	129	2	m	m	VERB
ejpam-6072	129	3	,	,	PUNCT
ejpam-6072	129	4	suppose	suppose	VERB
ejpam-6072	129	5	that	that	SCONJ
ejpam-6072	129	6	ai	ai	VERB
ejpam-6072	129	7	,	,	PUNCT
ejpam-6072	129	8	bi	bi	NOUN
ejpam-6072	129	9	∈	∈	PROPN
ejpam-6072	129	10	rn×n	rn×n	NOUN
ejpam-6072	129	11	.	.	PUNCT
ejpam-6072	130	1	if	if	SCONJ
ejpam-6072	130	2	the	the	DET
ejpam-6072	130	3	family	family	NOUN
ejpam-6072	130	4	u	u	NOUN
ejpam-6072	130	5	=	=	PRON
ejpam-6072	130	6	{	{	PUNCT
ejpam-6072	130	7	(	(	PUNCT
ejpam-6072	130	8	ai	ai	PROPN
ejpam-6072	130	9	,	,	PUNCT
ejpam-6072	130	10	bi)}mi=1	bi)}mi=1	PROPN
ejpam-6072	130	11	has	have	VERB
ejpam-6072	130	12	a	a	DET
ejpam-6072	130	13	common	common	ADJ
ejpam-6072	130	14	riccati	riccati	NOUN
ejpam-6072	130	15	stability	stability	NOUN
ejpam-6072	130	16	,	,	PUNCT
ejpam-6072	130	17	then	then	ADV
ejpam-6072	130	18	the	the	DET
ejpam-6072	130	19	family	family	NOUN
ejpam-6072	130	20	a	a	X
ejpam-6072	130	21	=	=	X
ejpam-6072	130	22	{	{	PUNCT
ejpam-6072	130	23	ai}mi=1	ai}mi=1	PROPN
ejpam-6072	130	24	has	have	VERB
ejpam-6072	130	25	a	a	DET
ejpam-6072	130	26	common	common	ADJ
ejpam-6072	130	27	lyapunov	lyapunov	ADJ
ejpam-6072	130	28	stability	stability	NOUN
ejpam-6072	130	29	.	.	PUNCT
ejpam-6072	131	1	proof	proof	NOUN
ejpam-6072	131	2	.	.	PUNCT
ejpam-6072	132	1	let	let	VERB
ejpam-6072	132	2	p	p	PRON
ejpam-6072	132	3	,	,	PUNCT
ejpam-6072	132	4	q	q	ADJ
ejpam-6072	132	5	,	,	PUNCT
ejpam-6072	132	6	ri	ri	PROPN
ejpam-6072	132	7	∈	∈	PROPN
ejpam-6072	132	8	rn×n	rn×n	NOUN
ejpam-6072	132	9	,	,	PUNCT
ejpam-6072	132	10	i	i	PRON
ejpam-6072	132	11	=	=	NOUN
ejpam-6072	132	12	1	1	NUM
ejpam-6072	132	13	,	,	PUNCT
ejpam-6072	132	14	.	.	PUNCT
ejpam-6072	132	15	.	.	PUNCT
ejpam-6072	133	1	.	.	PUNCT
ejpam-6072	134	1	,	,	PUNCT
ejpam-6072	134	2	m	m	VERB
ejpam-6072	134	3	be	be	VERB
ejpam-6072	134	4	positive	positive	ADJ
ejpam-6072	134	5	definite	definite	ADJ
ejpam-6072	134	6	matrices	matrix	NOUN
ejpam-6072	134	7	such	such	ADJ
ejpam-6072	134	8	that	that	SCONJ
ejpam-6072	134	9	(	(	PUNCT
ejpam-6072	134	10	p	p	X
ejpam-6072	134	11	,	,	PUNCT
ejpam-6072	134	12	q	q	NOUN
ejpam-6072	134	13	)	)	PUNCT
ejpam-6072	134	14	is	be	AUX
ejpam-6072	134	15	a	a	DET
ejpam-6072	134	16	common	common	ADJ
ejpam-6072	134	17	riccati	riccati	NOUN
ejpam-6072	134	18	solution	solution	NOUN
ejpam-6072	134	19	for	for	ADP
ejpam-6072	134	20	the	the	DET
ejpam-6072	134	21	family	family	NOUN
ejpam-6072	134	22	u	u	NOUN
ejpam-6072	134	23	=	=	PRON
ejpam-6072	134	24	{	{	PUNCT
ejpam-6072	134	25	(	(	PUNCT
ejpam-6072	134	26	ai	ai	NOUN
ejpam-6072	134	27	,	,	PUNCT
ejpam-6072	134	28	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	134	29	.	.	PUNCT
ejpam-6072	135	1	then	then	ADV
ejpam-6072	135	2	,	,	PUNCT
ejpam-6072	135	3	for	for	ADP
ejpam-6072	135	4	each	each	DET
ejpam-6072	135	5	i	i	NOUN
ejpam-6072	135	6	=	=	NOUN
ejpam-6072	135	7	1	1	NUM
ejpam-6072	135	8	,	,	PUNCT
ejpam-6072	135	9	.	.	PUNCT
ejpam-6072	135	10	.	.	PUNCT
ejpam-6072	135	11	.	.	PUNCT
ejpam-6072	136	1	,	,	PUNCT
ejpam-6072	136	2	m	m	PROPN
ejpam-6072	136	3	,	,	PUNCT
ejpam-6072	136	4	the	the	DET
ejpam-6072	136	5	matrices	matrix	NOUN
ejpam-6072	136	6	xi	xi	X
ejpam-6072	136	7	=	=	PUNCT
ejpam-6072	136	8	q+	q+	PUNCT
ejpam-6072	136	9	pbiq	pbiq	PROPN
ejpam-6072	137	1	−1bt	−1bt	ADV
ejpam-6072	137	2	i	i	PRON
ejpam-6072	137	3	p	p	PROPN
ejpam-6072	138	1	+	+	NOUN
ejpam-6072	138	2	ri	ri	PROPN
ejpam-6072	138	3	are	be	AUX
ejpam-6072	138	4	positive	positive	ADJ
ejpam-6072	138	5	definite	definite	ADJ
ejpam-6072	138	6	.	.	PUNCT
ejpam-6072	139	1	consequently	consequently	ADV
ejpam-6072	139	2	,	,	PUNCT
ejpam-6072	139	3	we	we	PRON
ejpam-6072	139	4	have	have	VERB
ejpam-6072	139	5	at	at	ADP
ejpam-6072	139	6	i	i	PRON
ejpam-6072	139	7	p	p	PROPN
ejpam-6072	140	1	+	+	CCONJ
ejpam-6072	140	2	pai	pai	PROPN
ejpam-6072	141	1	+	+	PROPN
ejpam-6072	141	2	xi	xi	X
ejpam-6072	141	3	=	=	NOUN
ejpam-6072	141	4	0	0	NUM
ejpam-6072	141	5	for	for	ADP
ejpam-6072	141	6	every	every	DET
ejpam-6072	141	7	i	i	PROPN
ejpam-6072	141	8	∈	∈	PROPN
ejpam-6072	141	9	{	{	PUNCT
ejpam-6072	141	10	1	1	NUM
ejpam-6072	141	11	,	,	PUNCT
ejpam-6072	141	12	.	.	PUNCT
ejpam-6072	141	13	.	.	PUNCT
ejpam-6072	142	1	.	.	PUNCT
ejpam-6072	143	1	,	,	PUNCT
ejpam-6072	143	2	m	m	VERB
ejpam-6072	143	3	}	}	PUNCT
ejpam-6072	143	4	.	.	PUNCT
ejpam-6072	144	1	thus	thus	ADV
ejpam-6072	144	2	,	,	PUNCT
ejpam-6072	144	3	p	p	PROPN
ejpam-6072	144	4	serves	serve	VERB
ejpam-6072	144	5	as	as	ADP
ejpam-6072	144	6	a	a	DET
ejpam-6072	144	7	common	common	ADJ
ejpam-6072	144	8	lyapunov	lyapunov	ADJ
ejpam-6072	144	9	solution	solution	NOUN
ejpam-6072	144	10	for	for	ADP
ejpam-6072	144	11	the	the	DET
ejpam-6072	144	12	family	family	NOUN
ejpam-6072	144	13	a	a	X
ejpam-6072	144	14	=	=	X
ejpam-6072	144	15	{	{	PUNCT
ejpam-6072	144	16	ai}mi=1	ai}mi=1	PROPN
ejpam-6072	144	17	.	.	PUNCT
ejpam-6072	145	1	theorem	theorem	PROPN
ejpam-6072	145	2	2	2	NUM
ejpam-6072	145	3	.	.	X
ejpam-6072	146	1	for	for	ADP
ejpam-6072	146	2	i	i	PRON
ejpam-6072	146	3	=	=	NOUN
ejpam-6072	146	4	1	1	NUM
ejpam-6072	146	5	,	,	PUNCT
ejpam-6072	146	6	.	.	PUNCT
ejpam-6072	146	7	.	.	PUNCT
ejpam-6072	146	8	.	.	PUNCT
ejpam-6072	147	1	,	,	PUNCT
ejpam-6072	147	2	m	m	VERB
ejpam-6072	147	3	,	,	PUNCT
ejpam-6072	147	4	suppose	suppose	VERB
ejpam-6072	147	5	that	that	SCONJ
ejpam-6072	147	6	ai	ai	VERB
ejpam-6072	147	7	,	,	PUNCT
ejpam-6072	147	8	bi	bi	NOUN
ejpam-6072	147	9	∈	∈	PROPN
ejpam-6072	147	10	rn×n	rn×n	NOUN
ejpam-6072	147	11	.	.	PUNCT
ejpam-6072	148	1	if	if	SCONJ
ejpam-6072	148	2	the	the	DET
ejpam-6072	148	3	family	family	NOUN
ejpam-6072	148	4	u	u	NOUN
ejpam-6072	148	5	=	=	PRON
ejpam-6072	148	6	{	{	PUNCT
ejpam-6072	148	7	(	(	PUNCT
ejpam-6072	148	8	ai	ai	PROPN
ejpam-6072	148	9	,	,	PUNCT
ejpam-6072	148	10	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	148	11	has	have	VERB
ejpam-6072	148	12	common	common	ADJ
ejpam-6072	148	13	riccati	riccati	NOUN
ejpam-6072	148	14	stability	stability	NOUN
ejpam-6072	148	15	,	,	PUNCT
ejpam-6072	148	16	then	then	ADV
ejpam-6072	148	17	the	the	DET
ejpam-6072	148	18	family	family	NOUN
ejpam-6072	148	19	{	{	PUNCT
ejpam-6072	148	20	a−1	a−1	PROPN
ejpam-6072	148	21	i	i	PRON
ejpam-6072	148	22	bi}mi=1	bi}mi=1	PROPN
ejpam-6072	148	23	has	have	VERB
ejpam-6072	148	24	common	common	ADJ
ejpam-6072	148	25	schur	schur	ADJ
ejpam-6072	148	26	stability	stability	NOUN
ejpam-6072	148	27	.	.	PUNCT
ejpam-6072	149	1	proof	proof	NOUN
ejpam-6072	149	2	.	.	PUNCT
ejpam-6072	150	1	let	let	VERB
ejpam-6072	150	2	p	p	PRON
ejpam-6072	150	3	,	,	PUNCT
ejpam-6072	150	4	q	q	ADJ
ejpam-6072	150	5	,	,	PUNCT
ejpam-6072	150	6	ri	ri	PROPN
ejpam-6072	150	7	∈	∈	PROPN
ejpam-6072	150	8	rn×n	rn×n	NOUN
ejpam-6072	150	9	,	,	PUNCT
ejpam-6072	150	10	i	i	PRON
ejpam-6072	150	11	=	=	NOUN
ejpam-6072	150	12	1	1	NUM
ejpam-6072	150	13	,	,	PUNCT
ejpam-6072	150	14	.	.	PUNCT
ejpam-6072	150	15	.	.	PUNCT
ejpam-6072	151	1	.	.	PUNCT
ejpam-6072	152	1	,	,	PUNCT
ejpam-6072	152	2	m	m	VERB
ejpam-6072	152	3	be	be	VERB
ejpam-6072	152	4	positive	positive	ADJ
ejpam-6072	152	5	definite	definite	ADJ
ejpam-6072	152	6	matrices	matrix	NOUN
ejpam-6072	152	7	such	such	ADJ
ejpam-6072	152	8	that	that	SCONJ
ejpam-6072	152	9	(	(	PUNCT
ejpam-6072	152	10	p	p	X
ejpam-6072	152	11	,	,	PUNCT
ejpam-6072	152	12	q	q	NOUN
ejpam-6072	152	13	)	)	PUNCT
ejpam-6072	152	14	is	be	AUX
ejpam-6072	152	15	a	a	DET
ejpam-6072	152	16	common	common	ADJ
ejpam-6072	152	17	riccati	riccati	NOUN
ejpam-6072	152	18	solution	solution	NOUN
ejpam-6072	152	19	for	for	ADP
ejpam-6072	152	20	the	the	DET
ejpam-6072	152	21	family	family	NOUN
ejpam-6072	152	22	u	u	NOUN
ejpam-6072	152	23	=	=	PRON
ejpam-6072	152	24	{	{	PUNCT
ejpam-6072	152	25	(	(	PUNCT
ejpam-6072	152	26	ai	ai	NOUN
ejpam-6072	152	27	,	,	PUNCT
ejpam-6072	152	28	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	152	29	.	.	PUNCT
ejpam-6072	153	1	then	then	ADV
ejpam-6072	153	2	,	,	PUNCT
ejpam-6072	153	3	for	for	ADP
ejpam-6072	153	4	i	i	PROPN
ejpam-6072	153	5	=	=	NOUN
ejpam-6072	153	6	1	1	NUM
ejpam-6072	153	7	,	,	PUNCT
ejpam-6072	153	8	.	.	PUNCT
ejpam-6072	153	9	.	.	PUNCT
ejpam-6072	153	10	.	.	PUNCT
ejpam-6072	154	1	,	,	PUNCT
ejpam-6072	154	2	m	m	PROPN
ejpam-6072	154	3	,	,	PUNCT
ejpam-6072	154	4	the	the	DET
ejpam-6072	154	5	following	follow	VERB
ejpam-6072	154	6	equations	equation	NOUN
ejpam-6072	154	7	hold	hold	VERB
ejpam-6072	154	8	at	at	ADP
ejpam-6072	154	9	i	i	PROPN
ejpam-6072	154	10	p	p	PROPN
ejpam-6072	155	1	+	+	CCONJ
ejpam-6072	155	2	pai	pai	PROPN
ejpam-6072	155	3	+	+	PROPN
ejpam-6072	155	4	q+	q+	ADP
ejpam-6072	155	5	pbiq	pbiq	PROPN
ejpam-6072	156	1	−1bt	−1bt	ADP
ejpam-6072	156	2	i	i	PRON
ejpam-6072	156	3	p	p	X
ejpam-6072	157	1	+	+	PROPN
ejpam-6072	157	2	ri	ri	NOUN
ejpam-6072	157	3	=	=	NOUN
ejpam-6072	157	4	0	0	PROPN
ejpam-6072	157	5	.	.	PUNCT
ejpam-6072	158	1	(	(	PUNCT
ejpam-6072	158	2	6	6	NUM
ejpam-6072	158	3	)	)	PUNCT
ejpam-6072	158	4	according	accord	VERB
ejpam-6072	158	5	to	to	ADP
ejpam-6072	158	6	theorem	theorem	NOUN
ejpam-6072	158	7	1	1	NUM
ejpam-6072	158	8	,	,	PUNCT
ejpam-6072	158	9	the	the	DET
ejpam-6072	158	10	family	family	NOUN
ejpam-6072	158	11	{	{	PUNCT
ejpam-6072	158	12	ai}mi=1	ai}mi=1	PROPN
ejpam-6072	158	13	has	have	VERB
ejpam-6072	158	14	common	common	ADJ
ejpam-6072	158	15	lyapunov	lyapunov	ADJ
ejpam-6072	158	16	stability	stability	NOUN
ejpam-6072	158	17	,	,	PUNCT
ejpam-6072	158	18	and	and	CCONJ
ejpam-6072	158	19	therefore	therefore	ADV
ejpam-6072	158	20	,	,	PUNCT
ejpam-6072	158	21	each	each	PRON
ejpam-6072	158	22	ai	ai	VERB
ejpam-6072	158	23	is	be	AUX
ejpam-6072	158	24	nonsingular	nonsingular	ADJ
ejpam-6072	158	25	.	.	PUNCT
ejpam-6072	159	1	thus	thus	ADV
ejpam-6072	159	2	,	,	PUNCT
ejpam-6072	159	3	the	the	DET
ejpam-6072	159	4	equations	equation	NOUN
ejpam-6072	159	5	in	in	ADP
ejpam-6072	159	6	(	(	PUNCT
ejpam-6072	159	7	6	6	NUM
ejpam-6072	159	8	)	)	PUNCT
ejpam-6072	159	9	can	can	AUX
ejpam-6072	159	10	be	be	AUX
ejpam-6072	159	11	rewritten	rewrite	VERB
ejpam-6072	159	12	as	as	ADP
ejpam-6072	159	13	at	at	ADP
ejpam-6072	159	14	i	i	PRON
ejpam-6072	159	15	p	p	PROPN
ejpam-6072	160	1	+	+	CCONJ
ejpam-6072	160	2	pai	pai	PROPN
ejpam-6072	160	3	+	+	PROPN
ejpam-6072	160	4	q+	q+	ADV
ejpam-6072	160	5	pai	pai	NOUN
ejpam-6072	160	6	[	[	PUNCT
ejpam-6072	160	7	a−1	a−1	PROPN
ejpam-6072	160	8	i	i	PRON
ejpam-6072	160	9	biq	biq	VERB
ejpam-6072	161	1	−1bt	−1bt	ADV
ejpam-6072	161	2	i	i	PRON
ejpam-6072	161	3	a	a	DET
ejpam-6072	161	4	−t	−t	NOUN
ejpam-6072	162	1	i	i	PRON
ejpam-6072	162	2	]	]	PUNCT
ejpam-6072	162	3	at	at	ADP
ejpam-6072	162	4	i	i	PRON
ejpam-6072	162	5	p	p	PROPN
ejpam-6072	163	1	+	+	PROPN
ejpam-6072	163	2	ri	ri	NOUN
ejpam-6072	163	3	=	=	SYM
ejpam-6072	163	4	0	0	NUM
ejpam-6072	163	5	a.	a.	NOUN
ejpam-6072	163	6	algefary	algefary	PROPN
ejpam-6072	163	7	,	,	PUNCT
ejpam-6072	163	8	k.	k.	PROPN
ejpam-6072	163	9	a.	a.	PROPN
ejpam-6072	163	10	alqufari	alqufari	PROPN
ejpam-6072	163	11	/	/	SYM
ejpam-6072	163	12	eur	eur	PROPN
ejpam-6072	163	13	.	.	PUNCT
ejpam-6072	164	1	j.	j.	PROPN
ejpam-6072	164	2	pure	pure	PROPN
ejpam-6072	164	3	appl	appl	PROPN
ejpam-6072	164	4	.	.	PROPN
ejpam-6072	164	5	math	math	PROPN
ejpam-6072	164	6	,	,	PUNCT
ejpam-6072	164	7	18	18	NUM
ejpam-6072	164	8	(	(	PUNCT
ejpam-6072	164	9	2	2	NUM
ejpam-6072	164	10	)	)	PUNCT
ejpam-6072	164	11	(	(	PUNCT
ejpam-6072	164	12	2025	2025	NUM
ejpam-6072	164	13	)	)	PUNCT
ejpam-6072	164	14	,	,	PUNCT
ejpam-6072	164	15	6072	6072	NUM
ejpam-6072	164	16	7	7	NUM
ejpam-6072	164	17	of	of	ADP
ejpam-6072	164	18	14	14	NUM
ejpam-6072	164	19	for	for	ADP
ejpam-6072	164	20	each	each	DET
ejpam-6072	164	21	i.	i.	NOUN
ejpam-6072	164	22	next	next	ADV
ejpam-6072	164	23	,	,	PUNCT
ejpam-6072	164	24	observe	observe	VERB
ejpam-6072	164	25	that	that	SCONJ
ejpam-6072	164	26	for	for	ADP
ejpam-6072	164	27	each	each	DET
ejpam-6072	164	28	i	i	PRON
ejpam-6072	164	29	∈	∈	PROPN
ejpam-6072	164	30	{	{	PUNCT
ejpam-6072	164	31	1	1	NUM
ejpam-6072	164	32	,	,	PUNCT
ejpam-6072	164	33	.	.	PUNCT
ejpam-6072	164	34	.	.	PUNCT
ejpam-6072	164	35	.	.	PUNCT
ejpam-6072	165	1	,	,	PUNCT
ejpam-6072	165	2	m	m	PROPN
ejpam-6072	165	3	}	}	PUNCT
ejpam-6072	165	4	,	,	PUNCT
ejpam-6072	165	5	these	these	DET
ejpam-6072	165	6	equations	equation	NOUN
ejpam-6072	165	7	are	be	AUX
ejpam-6072	165	8	identical	identical	ADJ
ejpam-6072	165	9	to	to	ADP
ejpam-6072	165	10	(	(	PUNCT
ejpam-6072	165	11	paiq	paiq	NOUN
ejpam-6072	165	12	−1	−1	NOUN
ejpam-6072	166	1	+	+	CCONJ
ejpam-6072	166	2	i)q(i	i)q(i	NOUN
ejpam-6072	166	3	+	+	ADJ
ejpam-6072	166	4	q−1at	q−1at	NOUN
ejpam-6072	166	5	i	i	PRON
ejpam-6072	166	6	p	p	NOUN
ejpam-6072	166	7	)	)	PUNCT
ejpam-6072	167	1	+	+	CCONJ
ejpam-6072	167	2	pai	pai	NOUN
ejpam-6072	167	3	[	[	PUNCT
ejpam-6072	167	4	a−1	a−1	PROPN
ejpam-6072	167	5	i	i	PRON
ejpam-6072	167	6	biq	biq	VERB
ejpam-6072	168	1	−1bt	−1bt	ADV
ejpam-6072	168	2	i	i	PRON
ejpam-6072	168	3	a	a	DET
ejpam-6072	168	4	−t	−t	NOUN
ejpam-6072	168	5	i	i	PRON
ejpam-6072	168	6	−q−1	−q−1	NUM
ejpam-6072	168	7	]	]	PUNCT
ejpam-6072	168	8	at	at	ADP
ejpam-6072	168	9	i	i	PRON
ejpam-6072	168	10	p	p	PROPN
ejpam-6072	169	1	+	+	PROPN
ejpam-6072	169	2	ri	ri	NOUN
ejpam-6072	169	3	=	=	NOUN
ejpam-6072	169	4	0	0	PROPN
ejpam-6072	169	5	.	.	PUNCT
ejpam-6072	170	1	(	(	PUNCT
ejpam-6072	170	2	7	7	X
ejpam-6072	170	3	)	)	PUNCT
ejpam-6072	170	4	define	define	VERB
ejpam-6072	170	5	zi	zi	NOUN
ejpam-6072	170	6	=	=	PUNCT
ejpam-6072	170	7	(	(	PUNCT
ejpam-6072	170	8	paiq	paiq	NOUN
ejpam-6072	170	9	−1	−1	NOUN
ejpam-6072	170	10	+	+	CCONJ
ejpam-6072	170	11	i)q(i	i)q(i	NOUN
ejpam-6072	170	12	+	+	ADJ
ejpam-6072	170	13	q−1at	q−1at	NOUN
ejpam-6072	170	14	i	i	PRON
ejpam-6072	170	15	p	p	NOUN
ejpam-6072	170	16	)	)	PUNCT
ejpam-6072	171	1	+	+	PROPN
ejpam-6072	171	2	ri	ri	PROPN
ejpam-6072	171	3	,	,	PUNCT
ejpam-6072	171	4	for	for	ADP
ejpam-6072	171	5	i	i	PRON
ejpam-6072	171	6	∈	∈	PROPN
ejpam-6072	171	7	{	{	PUNCT
ejpam-6072	171	8	1	1	NUM
ejpam-6072	171	9	,	,	PUNCT
ejpam-6072	171	10	.	.	PUNCT
ejpam-6072	171	11	.	.	PUNCT
ejpam-6072	171	12	.	.	PUNCT
ejpam-6072	172	1	,	,	PUNCT
ejpam-6072	172	2	m	m	VERB
ejpam-6072	172	3	}	}	PUNCT
ejpam-6072	172	4	.	.	PUNCT
ejpam-6072	173	1	it	it	PRON
ejpam-6072	173	2	is	be	AUX
ejpam-6072	173	3	evident	evident	ADJ
ejpam-6072	173	4	that	that	SCONJ
ejpam-6072	173	5	each	each	PRON
ejpam-6072	173	6	of	of	ADP
ejpam-6072	173	7	zi	zi	PROPN
ejpam-6072	173	8	is	be	AUX
ejpam-6072	173	9	a	a	DET
ejpam-6072	173	10	positive	positive	ADJ
ejpam-6072	173	11	definite	definite	ADJ
ejpam-6072	173	12	matrix	matrix	NOUN
ejpam-6072	173	13	.	.	PUNCT
ejpam-6072	174	1	by	by	ADP
ejpam-6072	174	2	substituting	substitute	VERB
ejpam-6072	174	3	zi	zi	NOUN
ejpam-6072	174	4	in	in	ADP
ejpam-6072	174	5	(	(	PUNCT
ejpam-6072	174	6	7	7	NUM
ejpam-6072	174	7	)	)	PUNCT
ejpam-6072	174	8	,	,	PUNCT
ejpam-6072	174	9	we	we	PRON
ejpam-6072	174	10	obtain	obtain	VERB
ejpam-6072	174	11	pai	pai	NOUN
ejpam-6072	175	1	[	[	PUNCT
ejpam-6072	175	2	a−1	a−1	PROPN
ejpam-6072	175	3	i	i	PRON
ejpam-6072	175	4	biq	biq	VERB
ejpam-6072	175	5	−1bt	−1bt	ADV
ejpam-6072	175	6	i	i	PRON
ejpam-6072	175	7	a	a	DET
ejpam-6072	175	8	−t	−t	NOUN
ejpam-6072	175	9	i	i	PRON
ejpam-6072	175	10	−q−1	−q−1	NUM
ejpam-6072	175	11	]	]	PUNCT
ejpam-6072	176	1	at	at	ADP
ejpam-6072	176	2	i	i	PRON
ejpam-6072	176	3	p	p	PROPN
ejpam-6072	176	4	+	+	NUM
ejpam-6072	176	5	zi	zi	NOUN
ejpam-6072	176	6	=	=	SYM
ejpam-6072	176	7	0	0	X
ejpam-6072	176	8	.	.	X
ejpam-6072	177	1	for	for	ADP
ejpam-6072	177	2	i	i	PRON
ejpam-6072	177	3	=	=	NOUN
ejpam-6072	177	4	1	1	NUM
ejpam-6072	177	5	,	,	PUNCT
ejpam-6072	177	6	.	.	PUNCT
ejpam-6072	177	7	.	.	PUNCT
ejpam-6072	177	8	.	.	PUNCT
ejpam-6072	178	1	,	,	PUNCT
ejpam-6072	178	2	m	m	X
ejpam-6072	178	3	,	,	PUNCT
ejpam-6072	178	4	note	note	VERB
ejpam-6072	178	5	that	that	SCONJ
ejpam-6072	178	6	ai	ai	VERB
ejpam-6072	178	7	is	be	AUX
ejpam-6072	178	8	nonsingular	nonsingular	ADJ
ejpam-6072	178	9	,	,	PUNCT
ejpam-6072	178	10	and	and	CCONJ
ejpam-6072	178	11	since	since	SCONJ
ejpam-6072	178	12	p	p	NOUN
ejpam-6072	178	13	is	be	AUX
ejpam-6072	178	14	positive	positive	ADJ
ejpam-6072	178	15	definite	definite	ADJ
ejpam-6072	178	16	,	,	PUNCT
ejpam-6072	178	17	it	it	PRON
ejpam-6072	178	18	is	be	AUX
ejpam-6072	178	19	also	also	ADV
ejpam-6072	178	20	nonsingular	nonsingular	ADJ
ejpam-6072	178	21	.	.	PUNCT
ejpam-6072	179	1	therefore	therefore	ADV
ejpam-6072	179	2	,	,	PUNCT
ejpam-6072	179	3	the	the	DET
ejpam-6072	179	4	matrices	matrix	NOUN
ejpam-6072	179	5	pai	pai	PROPN
ejpam-6072	179	6	and	and	CCONJ
ejpam-6072	179	7	(	(	PUNCT
ejpam-6072	179	8	pai	pai	PROPN
ejpam-6072	179	9	)	)	PUNCT
ejpam-6072	179	10	t	t	NOUN
ejpam-6072	179	11	for	for	ADP
ejpam-6072	179	12	i	i	PRON
ejpam-6072	179	13	=	=	NOUN
ejpam-6072	179	14	1	1	NUM
ejpam-6072	179	15	,	,	PUNCT
ejpam-6072	179	16	.	.	PUNCT
ejpam-6072	179	17	.	.	PUNCT
ejpam-6072	179	18	.	.	PUNCT
ejpam-6072	180	1	,	,	PUNCT
ejpam-6072	180	2	m	m	NOUN
ejpam-6072	180	3	are	be	AUX
ejpam-6072	180	4	nonsingular	nonsingular	ADJ
ejpam-6072	180	5	.	.	PUNCT
ejpam-6072	181	1	now	now	ADV
ejpam-6072	181	2	,	,	PUNCT
ejpam-6072	181	3	observe	observe	VERB
ejpam-6072	181	4	that	that	SCONJ
ejpam-6072	181	5	for	for	ADP
ejpam-6072	181	6	i	i	PROPN
ejpam-6072	181	7	=	=	NOUN
ejpam-6072	181	8	1	1	NUM
ejpam-6072	181	9	,	,	PUNCT
ejpam-6072	181	10	.	.	PUNCT
ejpam-6072	181	11	.	.	PUNCT
ejpam-6072	182	1	.	.	PUNCT
ejpam-6072	183	1	,	,	PUNCT
ejpam-6072	183	2	m	m	X
ejpam-6072	183	3	,	,	PUNCT
ejpam-6072	183	4	we	we	PRON
ejpam-6072	183	5	have	have	VERB
ejpam-6072	183	6	(	(	PUNCT
ejpam-6072	183	7	pai	pai	PROPN
ejpam-6072	183	8	)	)	PUNCT
ejpam-6072	183	9	−1	−1	NOUN
ejpam-6072	184	1	=	=	SYM
ejpam-6072	184	2	a−1	a−1	PROPN
ejpam-6072	184	3	i	i	PRON
ejpam-6072	184	4	p−1	p−1	PROPN
ejpam-6072	184	5	and	and	CCONJ
ejpam-6072	184	6	(	(	PUNCT
ejpam-6072	184	7	pai	pai	PROPN
ejpam-6072	184	8	)	)	PUNCT
ejpam-6072	184	9	−t	−t	NOUN
ejpam-6072	184	10	=	=	SYM
ejpam-6072	184	11	p−1a−t	p−1a−t	PROPN
ejpam-6072	185	1	i	i	PRON
ejpam-6072	185	2	.	.	PUNCT
ejpam-6072	186	1	consequently	consequently	ADV
ejpam-6072	186	2	,	,	PUNCT
ejpam-6072	186	3	for	for	ADP
ejpam-6072	186	4	each	each	DET
ejpam-6072	186	5	i	i	PRON
ejpam-6072	186	6	∈	∈	PROPN
ejpam-6072	186	7	{	{	PUNCT
ejpam-6072	186	8	1	1	NUM
ejpam-6072	186	9	,	,	PUNCT
ejpam-6072	186	10	.	.	PUNCT
ejpam-6072	186	11	.	.	PUNCT
ejpam-6072	186	12	.	.	PUNCT
ejpam-6072	187	1	,	,	PUNCT
ejpam-6072	187	2	m	m	PROPN
ejpam-6072	187	3	}	}	PUNCT
ejpam-6072	187	4	,	,	PUNCT
ejpam-6072	187	5	we	we	PRON
ejpam-6072	187	6	can	can	AUX
ejpam-6072	187	7	pre	pre	VERB
ejpam-6072	187	8	-	-	VERB
ejpam-6072	187	9	multiply	multiply	VERB
ejpam-6072	187	10	the	the	DET
ejpam-6072	187	11	ith	ith	NOUN
ejpam-6072	187	12	equation	equation	NOUN
ejpam-6072	187	13	in	in	ADP
ejpam-6072	187	14	(	(	PUNCT
ejpam-6072	187	15	7	7	NUM
ejpam-6072	187	16	)	)	PUNCT
ejpam-6072	187	17	by	by	ADP
ejpam-6072	187	18	(	(	PUNCT
ejpam-6072	187	19	pai	pai	PROPN
ejpam-6072	187	20	)	)	PUNCT
ejpam-6072	187	21	−1	−1	NOUN
ejpam-6072	187	22	and	and	CCONJ
ejpam-6072	187	23	post	post	ADJ
ejpam-6072	187	24	-	-	ADJ
ejpam-6072	187	25	multiply	multiply	VERB
ejpam-6072	187	26	it	it	PRON
ejpam-6072	187	27	by	by	ADP
ejpam-6072	187	28	(	(	PUNCT
ejpam-6072	187	29	pai	pai	PROPN
ejpam-6072	187	30	)	)	PUNCT
ejpam-6072	187	31	−t	−t	NOUN
ejpam-6072	187	32	.	.	PUNCT
ejpam-6072	188	1	thus	thus	ADV
ejpam-6072	188	2	,	,	PUNCT
ejpam-6072	188	3	the	the	DET
ejpam-6072	188	4	equations	equation	NOUN
ejpam-6072	188	5	in	in	ADP
ejpam-6072	188	6	(	(	PUNCT
ejpam-6072	188	7	7	7	X
ejpam-6072	188	8	)	)	PUNCT
ejpam-6072	188	9	become	become	VERB
ejpam-6072	188	10	a−1	a−1	PROPN
ejpam-6072	189	1	i	i	PRON
ejpam-6072	189	2	biq	biq	VERB
ejpam-6072	190	1	−1bt	−1bt	ADV
ejpam-6072	190	2	i	i	PRON
ejpam-6072	190	3	a	a	DET
ejpam-6072	190	4	−t	−t	NOUN
ejpam-6072	190	5	i	i	PRON
ejpam-6072	190	6	−q−1	−q−1	NUM
ejpam-6072	190	7	+	+	CCONJ
ejpam-6072	190	8	(	(	PUNCT
ejpam-6072	190	9	pai	pai	NOUN
ejpam-6072	190	10	)	)	PUNCT
ejpam-6072	190	11	−1zi(pai	−1zi(pai	NOUN
ejpam-6072	190	12	)	)	PUNCT
ejpam-6072	190	13	−t	−t	NOUN
ejpam-6072	190	14	=	=	SYM
ejpam-6072	190	15	0	0	NUM
ejpam-6072	190	16	,	,	PUNCT
ejpam-6072	190	17	(	(	PUNCT
ejpam-6072	190	18	8)	8)	NUM
ejpam-6072	190	19	for	for	ADP
ejpam-6072	190	20	i	i	PRON
ejpam-6072	190	21	=	=	NOUN
ejpam-6072	190	22	1	1	NUM
ejpam-6072	190	23	,	,	PUNCT
ejpam-6072	190	24	.	.	PUNCT
ejpam-6072	190	25	.	.	PUNCT
ejpam-6072	190	26	.	.	PUNCT
ejpam-6072	191	1	,	,	PUNCT
ejpam-6072	191	2	m.	m.	NOUN
ejpam-6072	191	3	next	next	ADV
ejpam-6072	191	4	,	,	PUNCT
ejpam-6072	191	5	let	let	VERB
ejpam-6072	191	6	yi	yi	X
ejpam-6072	191	7	=	=	SYM
ejpam-6072	191	8	(	(	PUNCT
ejpam-6072	191	9	pai	pai	PROPN
ejpam-6072	191	10	)	)	PUNCT
ejpam-6072	191	11	−1zi(pai	−1zi(pai	NOUN
ejpam-6072	191	12	)	)	PUNCT
ejpam-6072	191	13	−t	−t	NOUN
ejpam-6072	191	14	,	,	PUNCT
ejpam-6072	191	15	for	for	ADP
ejpam-6072	191	16	i	i	PROPN
ejpam-6072	191	17	=	=	NOUN
ejpam-6072	191	18	1	1	NUM
ejpam-6072	191	19	,	,	PUNCT
ejpam-6072	191	20	.	.	PUNCT
ejpam-6072	191	21	.	.	PUNCT
ejpam-6072	192	1	.	.	PUNCT
ejpam-6072	193	1	,	,	PUNCT
ejpam-6072	193	2	m.	m.	NOUN
ejpam-6072	193	3	recall	recall	VERB
ejpam-6072	193	4	that	that	PRON
ejpam-6072	193	5	each	each	DET
ejpam-6072	193	6	zi	zi	NOUN
ejpam-6072	193	7	is	be	AUX
ejpam-6072	193	8	positive	positive	ADJ
ejpam-6072	193	9	definite	definite	ADJ
ejpam-6072	193	10	;	;	PUNCT
ejpam-6072	193	11	consequently	consequently	ADV
ejpam-6072	193	12	,	,	PUNCT
ejpam-6072	193	13	yi	yi	PROPN
ejpam-6072	193	14	is	be	AUX
ejpam-6072	193	15	positive	positive	ADJ
ejpam-6072	193	16	definite	definite	ADJ
ejpam-6072	193	17	for	for	ADP
ejpam-6072	193	18	each	each	DET
ejpam-6072	193	19	i	i	PRON
ejpam-6072	193	20	∈	∈	PROPN
ejpam-6072	193	21	{	{	PUNCT
ejpam-6072	193	22	1	1	NUM
ejpam-6072	193	23	,	,	PUNCT
ejpam-6072	193	24	.	.	PUNCT
ejpam-6072	193	25	.	.	PUNCT
ejpam-6072	194	1	.	.	PUNCT
ejpam-6072	195	1	,	,	PUNCT
ejpam-6072	195	2	m	m	VERB
ejpam-6072	195	3	}	}	PUNCT
ejpam-6072	195	4	.	.	PUNCT
ejpam-6072	196	1	hence	hence	ADV
ejpam-6072	196	2	,	,	PUNCT
ejpam-6072	196	3	the	the	DET
ejpam-6072	196	4	equations	equation	NOUN
ejpam-6072	196	5	in	in	ADP
ejpam-6072	196	6	(	(	PUNCT
ejpam-6072	196	7	8)	8)	NUM
ejpam-6072	196	8	reduce	reduce	VERB
ejpam-6072	196	9	to	to	ADP
ejpam-6072	196	10	the	the	DET
ejpam-6072	196	11	following	follow	VERB
ejpam-6072	196	12	(	(	PUNCT
ejpam-6072	196	13	a−1	a−1	PROPN
ejpam-6072	196	14	i	i	PRON
ejpam-6072	196	15	bi)q	bi)q	PROPN
ejpam-6072	196	16	−1(a−1	−1(a−1	PROPN
ejpam-6072	196	17	i	i	PRON
ejpam-6072	196	18	bi	bi	PROPN
ejpam-6072	196	19	)	)	PUNCT
ejpam-6072	196	20	t	t	NOUN
ejpam-6072	196	21	−q−1	−q−1	NUM
ejpam-6072	196	22	+	+	CCONJ
ejpam-6072	196	23	yi	yi	X
ejpam-6072	196	24	=	=	SYM
ejpam-6072	196	25	0	0	NUM
ejpam-6072	196	26	,	,	PUNCT
ejpam-6072	196	27	for	for	ADP
ejpam-6072	196	28	i	i	PROPN
ejpam-6072	196	29	=	=	NOUN
ejpam-6072	196	30	1	1	NUM
ejpam-6072	196	31	,	,	PUNCT
ejpam-6072	196	32	.	.	PUNCT
ejpam-6072	196	33	.	.	PUNCT
ejpam-6072	196	34	.	.	PUNCT
ejpam-6072	197	1	,	,	PUNCT
ejpam-6072	197	2	m.	m.	NOUN
ejpam-6072	197	3	by	by	ADP
ejpam-6072	197	4	the	the	DET
ejpam-6072	197	5	definition	definition	NOUN
ejpam-6072	197	6	of	of	ADP
ejpam-6072	197	7	common	common	ADJ
ejpam-6072	197	8	schur	schur	PROPN
ejpam-6072	197	9	stability	stability	NOUN
ejpam-6072	197	10	,	,	PUNCT
ejpam-6072	197	11	this	this	PRON
ejpam-6072	197	12	implies	imply	VERB
ejpam-6072	197	13	that	that	SCONJ
ejpam-6072	197	14	the	the	DET
ejpam-6072	197	15	family	family	NOUN
ejpam-6072	197	16	{	{	PUNCT
ejpam-6072	197	17	a−1	a−1	PROPN
ejpam-6072	197	18	i	i	PRON
ejpam-6072	197	19	bi}mi=1	bi}mi=1	PROPN
ejpam-6072	197	20	has	have	VERB
ejpam-6072	197	21	common	common	ADJ
ejpam-6072	197	22	schur	schur	ADJ
ejpam-6072	197	23	stability	stability	NOUN
ejpam-6072	197	24	.	.	PUNCT
ejpam-6072	198	1	having	having	AUX
ejpam-6072	198	2	established	establish	VERB
ejpam-6072	198	3	that	that	DET
ejpam-6072	198	4	common	common	ADJ
ejpam-6072	198	5	riccati	riccati	NOUN
ejpam-6072	198	6	stability	stability	NOUN
ejpam-6072	198	7	implies	imply	VERB
ejpam-6072	198	8	both	both	PRON
ejpam-6072	198	9	common	common	ADJ
ejpam-6072	198	10	lyapunov	lyapunov	NOUN
ejpam-6072	198	11	and	and	CCONJ
ejpam-6072	198	12	schur	schur	PROPN
ejpam-6072	198	13	stability	stability	PROPN
ejpam-6072	198	14	,	,	PUNCT
ejpam-6072	198	15	we	we	PRON
ejpam-6072	198	16	now	now	ADV
ejpam-6072	198	17	examine	examine	VERB
ejpam-6072	198	18	the	the	DET
ejpam-6072	198	19	reverse	reverse	ADJ
ejpam-6072	198	20	relationship	relationship	NOUN
ejpam-6072	198	21	in	in	ADP
ejpam-6072	198	22	theorems	theorem	NOUN
ejpam-6072	198	23	3	3	NUM
ejpam-6072	198	24	and	and	CCONJ
ejpam-6072	198	25	4	4	NUM
ejpam-6072	198	26	.	.	PUNCT
ejpam-6072	198	27	specifically	specifically	ADV
ejpam-6072	198	28	,	,	PUNCT
ejpam-6072	198	29	in	in	ADP
ejpam-6072	198	30	theorem	theorem	NOUN
ejpam-6072	198	31	3	3	NUM
ejpam-6072	198	32	,	,	PUNCT
ejpam-6072	198	33	we	we	PRON
ejpam-6072	198	34	show	show	VERB
ejpam-6072	198	35	that	that	SCONJ
ejpam-6072	198	36	if	if	SCONJ
ejpam-6072	198	37	the	the	DET
ejpam-6072	198	38	family	family	NOUN
ejpam-6072	198	39	{	{	PUNCT
ejpam-6072	198	40	a−1	a−1	PROPN
ejpam-6072	198	41	i	i	PRON
ejpam-6072	198	42	bi	bi	VERB
ejpam-6072	198	43	}	}	PUNCT
ejpam-6072	198	44	m	m	VERB
ejpam-6072	198	45	i=1	i=1	PROPN
ejpam-6072	198	46	possesses	possess	VERB
ejpam-6072	198	47	common	common	ADJ
ejpam-6072	198	48	schur	schur	PROPN
ejpam-6072	198	49	stability	stability	NOUN
ejpam-6072	198	50	,	,	PUNCT
ejpam-6072	198	51	then	then	ADV
ejpam-6072	198	52	there	there	PRON
ejpam-6072	198	53	exist	exist	VERB
ejpam-6072	198	54	orthogonal	orthogonal	ADJ
ejpam-6072	198	55	transformations	transformation	NOUN
ejpam-6072	198	56	of	of	ADP
ejpam-6072	198	57	the	the	DET
ejpam-6072	198	58	matrices	matrix	NOUN
ejpam-6072	198	59	ai	ai	VERB
ejpam-6072	198	60	that	that	PRON
ejpam-6072	198	61	ensure	ensure	VERB
ejpam-6072	198	62	each	each	DET
ejpam-6072	198	63	transformed	transform	VERB
ejpam-6072	198	64	matrix	matrix	NOUN
ejpam-6072	198	65	is	be	AUX
ejpam-6072	198	66	hurwitz	hurwitz	PROPN
ejpam-6072	198	67	.	.	PUNCT
ejpam-6072	199	1	furthermore	furthermore	ADV
ejpam-6072	199	2	,	,	PUNCT
ejpam-6072	199	3	under	under	ADP
ejpam-6072	199	4	these	these	DET
ejpam-6072	199	5	transformations	transformation	NOUN
ejpam-6072	199	6	,	,	PUNCT
ejpam-6072	199	7	the	the	DET
ejpam-6072	199	8	pairs	pair	NOUN
ejpam-6072	199	9	(	(	PUNCT
ejpam-6072	199	10	∆iai,∆ibi	∆iai,∆ibi	PROPN
ejpam-6072	199	11	)	)	PUNCT
ejpam-6072	199	12	maintain	maintain	VERB
ejpam-6072	199	13	a	a	DET
ejpam-6072	199	14	riccati	riccati	NOUN
ejpam-6072	199	15	solution	solution	NOUN
ejpam-6072	199	16	that	that	PRON
ejpam-6072	199	17	shares	share	VERB
ejpam-6072	199	18	a	a	DET
ejpam-6072	199	19	common	common	ADJ
ejpam-6072	199	20	matrix	matrix	NOUN
ejpam-6072	199	21	.	.	PUNCT
ejpam-6072	200	1	theorem	theorem	NOUN
ejpam-6072	200	2	3	3	NUM
ejpam-6072	200	3	.	.	X
ejpam-6072	201	1	for	for	ADP
ejpam-6072	201	2	i	i	PRON
ejpam-6072	201	3	=	=	NOUN
ejpam-6072	201	4	1	1	NUM
ejpam-6072	201	5	,	,	PUNCT
ejpam-6072	201	6	.	.	PUNCT
ejpam-6072	201	7	.	.	PUNCT
ejpam-6072	202	1	.	.	PUNCT
ejpam-6072	203	1	,	,	PUNCT
ejpam-6072	203	2	m	m	VERB
ejpam-6072	203	3	,	,	PUNCT
ejpam-6072	203	4	suppose	suppose	VERB
ejpam-6072	203	5	that	that	SCONJ
ejpam-6072	203	6	ai	ai	VERB
ejpam-6072	203	7	,	,	PUNCT
ejpam-6072	203	8	bi	bi	NOUN
ejpam-6072	203	9	∈	∈	PROPN
ejpam-6072	203	10	rn×n	rn×n	NOUN
ejpam-6072	203	11	.	.	PUNCT
ejpam-6072	204	1	if	if	SCONJ
ejpam-6072	204	2	the	the	DET
ejpam-6072	204	3	family	family	NOUN
ejpam-6072	204	4	{	{	PUNCT
ejpam-6072	204	5	a−1	a−1	PROPN
ejpam-6072	204	6	i	i	PRON
ejpam-6072	204	7	bi}mi=1	bi}mi=1	PROPN
ejpam-6072	204	8	has	have	VERB
ejpam-6072	204	9	common	common	ADJ
ejpam-6072	204	10	schur	schur	ADJ
ejpam-6072	204	11	stability	stability	NOUN
ejpam-6072	204	12	,	,	PUNCT
ejpam-6072	204	13	then	then	ADV
ejpam-6072	204	14	there	there	PRON
ejpam-6072	204	15	exist	exist	VERB
ejpam-6072	204	16	orthogonal	orthogonal	ADJ
ejpam-6072	204	17	matrices	matrix	NOUN
ejpam-6072	204	18	∆i	∆i	PROPN
ejpam-6072	204	19	,	,	PUNCT
ejpam-6072	204	20	i	i	PRON
ejpam-6072	204	21	=	=	NOUN
ejpam-6072	204	22	1	1	NUM
ejpam-6072	204	23	,	,	PUNCT
ejpam-6072	204	24	.	.	PUNCT
ejpam-6072	204	25	.	.	PUNCT
ejpam-6072	205	1	.	.	PUNCT
ejpam-6072	206	1	,	,	PUNCT
ejpam-6072	206	2	m	m	PROPN
ejpam-6072	206	3	,	,	PUNCT
ejpam-6072	206	4	such	such	ADJ
ejpam-6072	206	5	that	that	SCONJ
ejpam-6072	206	6	for	for	ADP
ejpam-6072	206	7	each	each	DET
ejpam-6072	206	8	i	i	PRON
ejpam-6072	206	9	,	,	PUNCT
ejpam-6072	206	10	∆iai	∆iai	PROPN
ejpam-6072	206	11	is	be	AUX
ejpam-6072	206	12	hurwitz	hurwitz	PROPN
ejpam-6072	206	13	,	,	PUNCT
ejpam-6072	206	14	and	and	CCONJ
ejpam-6072	206	15	for	for	ADP
ejpam-6072	206	16	each	each	DET
ejpam-6072	206	17	i	i	PRON
ejpam-6072	206	18	,	,	PUNCT
ejpam-6072	206	19	the	the	DET
ejpam-6072	206	20	pair	pair	NOUN
ejpam-6072	206	21	(	(	PUNCT
ejpam-6072	206	22	∆iai,∆ibi	∆iai,∆ibi	PROPN
ejpam-6072	206	23	)	)	PUNCT
ejpam-6072	206	24	has	have	VERB
ejpam-6072	206	25	a	a	DET
ejpam-6072	206	26	riccati	riccati	NOUN
ejpam-6072	206	27	solution	solution	NOUN
ejpam-6072	206	28	(	(	PUNCT
ejpam-6072	206	29	xi	xi	PROPN
ejpam-6072	206	30	,	,	PUNCT
ejpam-6072	206	31	y	y	PROPN
ejpam-6072	206	32	)	)	PUNCT
ejpam-6072	206	33	,	,	PUNCT
ejpam-6072	206	34	i.e.	i.e.	X
ejpam-6072	206	35	all	all	DET
ejpam-6072	206	36	the	the	DET
ejpam-6072	206	37	pairs	pair	NOUN
ejpam-6072	206	38	share	share	VERB
ejpam-6072	206	39	the	the	DET
ejpam-6072	206	40	same	same	ADJ
ejpam-6072	206	41	y	y	NOUN
ejpam-6072	206	42	in	in	ADP
ejpam-6072	206	43	their	their	PRON
ejpam-6072	206	44	riccati	riccati	NOUN
ejpam-6072	206	45	solution	solution	NOUN
ejpam-6072	206	46	.	.	PUNCT
ejpam-6072	207	1	proof	proof	NOUN
ejpam-6072	207	2	.	.	PUNCT
ejpam-6072	208	1	as	as	SCONJ
ejpam-6072	208	2	{	{	PUNCT
ejpam-6072	208	3	a−1	a−1	PROPN
ejpam-6072	208	4	i	i	PRON
ejpam-6072	208	5	bi}mi=1	bi}mi=1	PROPN
ejpam-6072	208	6	has	have	VERB
ejpam-6072	208	7	common	common	ADJ
ejpam-6072	208	8	schur	schur	ADJ
ejpam-6072	208	9	stability	stability	NOUN
ejpam-6072	208	10	,	,	PUNCT
ejpam-6072	208	11	there	there	PRON
ejpam-6072	208	12	are	be	VERB
ejpam-6072	208	13	positive	positive	ADJ
ejpam-6072	208	14	definite	definite	ADJ
ejpam-6072	208	15	matrices	matrix	NOUN
ejpam-6072	208	16	p	p	NOUN
ejpam-6072	208	17	,	,	PUNCT
ejpam-6072	208	18	q1	q1	PROPN
ejpam-6072	208	19	,	,	PUNCT
ejpam-6072	208	20	.	.	PUNCT
ejpam-6072	208	21	.	.	PUNCT
ejpam-6072	209	1	.	.	PUNCT
ejpam-6072	210	1	,	,	PUNCT
ejpam-6072	210	2	qm	qm	PROPN
ejpam-6072	210	3	such	such	ADJ
ejpam-6072	210	4	that	that	PRON
ejpam-6072	210	5	(	(	PUNCT
ejpam-6072	210	6	a−1	a−1	PROPN
ejpam-6072	210	7	i	i	PRON
ejpam-6072	210	8	bi)p	bi)p	PROPN
ejpam-6072	210	9	(	(	PUNCT
ejpam-6072	210	10	a−1	a−1	PROPN
ejpam-6072	210	11	i	i	NOUN
ejpam-6072	210	12	bi	bi	NOUN
ejpam-6072	210	13	)	)	PUNCT
ejpam-6072	210	14	t	t	PROPN
ejpam-6072	210	15	+	+	NOUN
ejpam-6072	210	16	qi	qi	X
ejpam-6072	210	17	=	=	SYM
ejpam-6072	210	18	p	p	X
ejpam-6072	210	19	,	,	PUNCT
ejpam-6072	210	20	(	(	PUNCT
ejpam-6072	210	21	9	9	X
ejpam-6072	210	22	)	)	PUNCT
ejpam-6072	210	23	a.	a.	NOUN
ejpam-6072	210	24	algefary	algefary	PROPN
ejpam-6072	210	25	,	,	PUNCT
ejpam-6072	210	26	k.	k.	PROPN
ejpam-6072	210	27	a.	a.	PROPN
ejpam-6072	210	28	alqufari	alqufari	PROPN
ejpam-6072	210	29	/	/	SYM
ejpam-6072	210	30	eur	eur	PROPN
ejpam-6072	210	31	.	.	PUNCT
ejpam-6072	211	1	j.	j.	PROPN
ejpam-6072	211	2	pure	pure	PROPN
ejpam-6072	211	3	appl	appl	PROPN
ejpam-6072	211	4	.	.	PROPN
ejpam-6072	211	5	math	math	PROPN
ejpam-6072	211	6	,	,	PUNCT
ejpam-6072	211	7	18	18	NUM
ejpam-6072	211	8	(	(	PUNCT
ejpam-6072	211	9	2	2	NUM
ejpam-6072	211	10	)	)	PUNCT
ejpam-6072	211	11	(	(	PUNCT
ejpam-6072	211	12	2025	2025	NUM
ejpam-6072	211	13	)	)	PUNCT
ejpam-6072	211	14	,	,	PUNCT
ejpam-6072	211	15	6072	6072	NUM
ejpam-6072	211	16	8	8	NUM
ejpam-6072	211	17	of	of	ADP
ejpam-6072	211	18	14	14	NUM
ejpam-6072	211	19	for	for	ADP
ejpam-6072	211	20	i	i	PRON
ejpam-6072	211	21	=	=	NOUN
ejpam-6072	211	22	1	1	NUM
ejpam-6072	211	23	,	,	PUNCT
ejpam-6072	211	24	.	.	PUNCT
ejpam-6072	211	25	.	.	PUNCT
ejpam-6072	211	26	.	.	PUNCT
ejpam-6072	212	1	,	,	PUNCT
ejpam-6072	212	2	m.	m.	NOUN
ejpam-6072	212	3	additionally	additionally	ADV
ejpam-6072	212	4	,	,	PUNCT
ejpam-6072	212	5	the	the	DET
ejpam-6072	212	6	existence	existence	NOUN
ejpam-6072	212	7	of	of	ADP
ejpam-6072	212	8	the	the	DET
ejpam-6072	212	9	family	family	NOUN
ejpam-6072	212	10	{	{	PUNCT
ejpam-6072	212	11	a−1	a−1	PROPN
ejpam-6072	212	12	i	i	PRON
ejpam-6072	212	13	bi}mi=1	bi}mi=1	PROPN
ejpam-6072	212	14	means	mean	VERB
ejpam-6072	212	15	that	that	SCONJ
ejpam-6072	212	16	for	for	ADP
ejpam-6072	212	17	each	each	DET
ejpam-6072	212	18	i	i	PRON
ejpam-6072	212	19	,	,	PUNCT
ejpam-6072	212	20	the	the	DET
ejpam-6072	212	21	matrices	matrix	NOUN
ejpam-6072	212	22	a−1	a−1	PROPN
ejpam-6072	212	23	i	i	PRON
ejpam-6072	212	24	exist	exist	VERB
ejpam-6072	212	25	.	.	PUNCT
ejpam-6072	213	1	now	now	ADV
ejpam-6072	213	2	,	,	PUNCT
ejpam-6072	213	3	let	let	VERB
ejpam-6072	213	4	y	y	PROPN
ejpam-6072	213	5	=	=	PROPN
ejpam-6072	213	6	p−1	p−1	PROPN
ejpam-6072	213	7	≻	≻	PROPN
ejpam-6072	213	8	0	0	NUM
ejpam-6072	213	9	and	and	CCONJ
ejpam-6072	213	10	suppose	suppose	VERB
ejpam-6072	213	11	that	that	SCONJ
ejpam-6072	213	12	the	the	DET
ejpam-6072	213	13	matrices	matrix	NOUN
ejpam-6072	213	14	y	y	PROPN
ejpam-6072	213	15	a−1	a−1	PROPN
ejpam-6072	213	16	i	i	PROPN
ejpam-6072	213	17	for	for	ADP
ejpam-6072	213	18	all	all	PRON
ejpam-6072	213	19	i	i	PRON
ejpam-6072	213	20	∈	∈	PROPN
ejpam-6072	213	21	{	{	PUNCT
ejpam-6072	213	22	1	1	NUM
ejpam-6072	213	23	,	,	PUNCT
ejpam-6072	213	24	.	.	PUNCT
ejpam-6072	213	25	.	.	PUNCT
ejpam-6072	214	1	.	.	PUNCT
ejpam-6072	215	1	,	,	PUNCT
ejpam-6072	215	2	m	m	AUX
ejpam-6072	215	3	}	}	PUNCT
ejpam-6072	215	4	have	have	VERB
ejpam-6072	215	5	singular	singular	ADJ
ejpam-6072	215	6	value	value	NOUN
ejpam-6072	215	7	decomposition	decomposition	NOUN
ejpam-6072	215	8	y	y	PROPN
ejpam-6072	215	9	a−1	a−1	PROPN
ejpam-6072	216	1	i	i	PROPN
ejpam-6072	216	2	=	=	VERB
ejpam-6072	217	1	uiσiv	uiσiv	PROPN
ejpam-6072	217	2	t	t	X
ejpam-6072	218	1	i	i	PRON
ejpam-6072	218	2	,	,	PUNCT
ejpam-6072	218	3	where	where	SCONJ
ejpam-6072	218	4	uiu	uiu	PROPN
ejpam-6072	218	5	t	t	PROPN
ejpam-6072	219	1	i	i	PRON
ejpam-6072	220	1	=	=	PROPN
ejpam-6072	221	1	i	i	PROPN
ejpam-6072	221	2	,	,	PUNCT
ejpam-6072	221	3	viv	viv	PROPN
ejpam-6072	221	4	t	t	PROPN
ejpam-6072	222	1	i	i	PRON
ejpam-6072	222	2	=	=	PROPN
ejpam-6072	222	3	i	i	PROPN
ejpam-6072	222	4	,	,	PUNCT
ejpam-6072	222	5	and	and	CCONJ
ejpam-6072	222	6	the	the	DET
ejpam-6072	222	7	diagonal	diagonal	ADJ
ejpam-6072	222	8	matrices	matrix	NOUN
ejpam-6072	222	9	σi	σi	PRON
ejpam-6072	222	10	are	be	AUX
ejpam-6072	222	11	positive	positive	ADJ
ejpam-6072	222	12	definite	definite	ADJ
ejpam-6072	222	13	.	.	PUNCT
ejpam-6072	223	1	next	next	ADV
ejpam-6072	223	2	,	,	PUNCT
ejpam-6072	223	3	for	for	ADP
ejpam-6072	223	4	each	each	DET
ejpam-6072	223	5	i	i	PRON
ejpam-6072	223	6	,	,	PUNCT
ejpam-6072	223	7	define	define	VERB
ejpam-6072	223	8	∆i	∆i	PROPN
ejpam-6072	223	9	=	=	PUNCT
ejpam-6072	223	10	−uiv	−uiv	PROPN
ejpam-6072	223	11	t	t	PROPN
ejpam-6072	224	1	i	i	PRON
ejpam-6072	224	2	.	.	PUNCT
ejpam-6072	225	1	thus	thus	ADV
ejpam-6072	225	2	,	,	PUNCT
ejpam-6072	225	3	we	we	PRON
ejpam-6072	225	4	have	have	VERB
ejpam-6072	225	5	y	y	PROPN
ejpam-6072	225	6	a−1	a−1	PROPN
ejpam-6072	225	7	i	i	PRON
ejpam-6072	225	8	∆t	∆t	VERB
ejpam-6072	225	9	i	i	PRON
ejpam-6072	225	10	=	=	PUNCT
ejpam-6072	225	11	−uiσiu	−uiσiu	NOUN
ejpam-6072	225	12	t	t	X
ejpam-6072	226	1	i	i	PRON
ejpam-6072	226	2	=	=	SYM
ejpam-6072	226	3	−xi	−xi	PRON
ejpam-6072	226	4	.	.	PUNCT
ejpam-6072	227	1	(	(	PUNCT
ejpam-6072	227	2	10	10	NUM
ejpam-6072	227	3	)	)	PUNCT
ejpam-6072	227	4	clearly	clearly	ADV
ejpam-6072	227	5	,	,	PUNCT
ejpam-6072	227	6	each	each	PRON
ejpam-6072	227	7	xi	xi	ADP
ejpam-6072	227	8	is	be	AUX
ejpam-6072	227	9	a	a	DET
ejpam-6072	227	10	positive	positive	ADJ
ejpam-6072	227	11	definite	definite	ADJ
ejpam-6072	227	12	matrix	matrix	NOUN
ejpam-6072	227	13	.	.	PUNCT
ejpam-6072	228	1	now	now	ADV
ejpam-6072	228	2	,	,	PUNCT
ejpam-6072	228	3	for	for	ADP
ejpam-6072	228	4	each	each	DET
ejpam-6072	228	5	i	i	PRON
ejpam-6072	228	6	,	,	PUNCT
ejpam-6072	228	7	observe	observe	VERB
ejpam-6072	228	8	that	that	SCONJ
ejpam-6072	228	9	y	y	PROPN
ejpam-6072	228	10	=	=	PUNCT
ejpam-6072	228	11	−xi∆iai	−xi∆iai	NOUN
ejpam-6072	229	1	=	=	PUNCT
ejpam-6072	229	2	−at	−at	NUM
ejpam-6072	230	1	i	i	PRON
ejpam-6072	230	2	∆	∆	VERB
ejpam-6072	231	1	t	t	NOUN
ejpam-6072	231	2	i	i	PRON
ejpam-6072	231	3	xi	xi	PROPN
ejpam-6072	231	4	,	,	PUNCT
ejpam-6072	231	5	i.e.	i.e.	X
ejpam-6072	231	6	,	,	PUNCT
ejpam-6072	231	7	y	y	PROPN
ejpam-6072	231	8	+	+	PROPN
ejpam-6072	231	9	xi∆iai	xi∆iai	X
ejpam-6072	231	10	=	=	SYM
ejpam-6072	231	11	0	0	NUM
ejpam-6072	231	12	and	and	CCONJ
ejpam-6072	231	13	y	y	PROPN
ejpam-6072	232	1	+	+	PROPN
ejpam-6072	232	2	at	at	ADP
ejpam-6072	232	3	i	i	NOUN
ejpam-6072	232	4	∆	∆	PROPN
ejpam-6072	233	1	t	t	NOUN
ejpam-6072	234	1	i	i	PRON
ejpam-6072	234	2	xi	xi	PROPN
ejpam-6072	235	1	=	=	NOUN
ejpam-6072	235	2	0	0	X
ejpam-6072	235	3	.	.	PUNCT
ejpam-6072	236	1	adding	add	VERB
ejpam-6072	236	2	these	these	DET
ejpam-6072	236	3	two	two	NUM
ejpam-6072	236	4	equations	equation	NOUN
ejpam-6072	236	5	together	together	ADV
ejpam-6072	236	6	,	,	PUNCT
ejpam-6072	236	7	we	we	PRON
ejpam-6072	236	8	obtain	obtain	VERB
ejpam-6072	236	9	(	(	PUNCT
ejpam-6072	236	10	∆iai	∆iai	X
ejpam-6072	236	11	)	)	PUNCT
ejpam-6072	236	12	txi	txi	PUNCT
ejpam-6072	237	1	+	+	PROPN
ejpam-6072	237	2	xi(∆iai	xi(∆iai	PROPN
ejpam-6072	237	3	)	)	PUNCT
ejpam-6072	238	1	+	+	NUM
ejpam-6072	238	2	2y	2y	NUM
ejpam-6072	238	3	=	=	SYM
ejpam-6072	238	4	0	0	NUM
ejpam-6072	238	5	,	,	PUNCT
ejpam-6072	238	6	(	(	PUNCT
ejpam-6072	238	7	11	11	NUM
ejpam-6072	238	8	)	)	PUNCT
ejpam-6072	238	9	for	for	ADP
ejpam-6072	238	10	i	i	PROPN
ejpam-6072	238	11	=	=	NOUN
ejpam-6072	238	12	1	1	NUM
ejpam-6072	238	13	,	,	PUNCT
ejpam-6072	238	14	.	.	PUNCT
ejpam-6072	238	15	.	.	PUNCT
ejpam-6072	238	16	.	.	PUNCT
ejpam-6072	239	1	,	,	PUNCT
ejpam-6072	239	2	m.	m.	NOUN
ejpam-6072	239	3	this	this	PRON
ejpam-6072	239	4	implies	imply	VERB
ejpam-6072	239	5	that	that	SCONJ
ejpam-6072	239	6	for	for	ADP
ejpam-6072	239	7	every	every	DET
ejpam-6072	239	8	i	i	PROPN
ejpam-6072	239	9	∈	∈	PROPN
ejpam-6072	239	10	{	{	PUNCT
ejpam-6072	239	11	1	1	NUM
ejpam-6072	239	12	,	,	PUNCT
ejpam-6072	239	13	.	.	PUNCT
ejpam-6072	239	14	.	.	PUNCT
ejpam-6072	240	1	.	.	PUNCT
ejpam-6072	241	1	,	,	PUNCT
ejpam-6072	241	2	m	m	VERB
ejpam-6072	241	3	}	}	PUNCT
ejpam-6072	241	4	,	,	PUNCT
ejpam-6072	241	5	∆iai	∆iai	PROPN
ejpam-6072	241	6	is	be	AUX
ejpam-6072	241	7	hurwitz	hurwitz	PROPN
ejpam-6072	241	8	.	.	PUNCT
ejpam-6072	242	1	now	now	ADV
ejpam-6072	242	2	,	,	PUNCT
ejpam-6072	242	3	from	from	ADP
ejpam-6072	242	4	(	(	PUNCT
ejpam-6072	242	5	9	9	NUM
ejpam-6072	242	6	)	)	PUNCT
ejpam-6072	242	7	,	,	PUNCT
ejpam-6072	242	8	it	it	PRON
ejpam-6072	242	9	follows	follow	VERB
ejpam-6072	242	10	that	that	SCONJ
ejpam-6072	242	11	a−1	a−1	PROPN
ejpam-6072	242	12	i	i	PRON
ejpam-6072	242	13	∆t	∆t	VERB
ejpam-6072	242	14	i	i	PRON
ejpam-6072	242	15	∆ibiy	∆ibiy	VERB
ejpam-6072	243	1	−1bt	−1bt	ADP
ejpam-6072	243	2	i	i	PRON
ejpam-6072	243	3	∆	∆	VERB
ejpam-6072	243	4	t	t	NOUN
ejpam-6072	244	1	i	i	PRON
ejpam-6072	244	2	∆ia	∆ia	VERB
ejpam-6072	244	3	−t	−t	VERB
ejpam-6072	244	4	i	i	PROPN
ejpam-6072	244	5	+	+	PROPN
ejpam-6072	244	6	qi	qi	X
ejpam-6072	244	7	=	=	SYM
ejpam-6072	244	8	y	y	PROPN
ejpam-6072	244	9	−1	−1	NOUN
ejpam-6072	244	10	.	.	PUNCT
ejpam-6072	245	1	by	by	ADP
ejpam-6072	245	2	pre	pre	VERB
ejpam-6072	245	3	-	-	ADJ
ejpam-6072	245	4	multiplying	multiply	VERB
ejpam-6072	245	5	this	this	DET
ejpam-6072	245	6	last	last	ADJ
ejpam-6072	245	7	equation	equation	NOUN
ejpam-6072	245	8	by	by	ADP
ejpam-6072	245	9	y	y	PROPN
ejpam-6072	245	10	and	and	CCONJ
ejpam-6072	245	11	post	post	ADJ
ejpam-6072	245	12	-	-	ADJ
ejpam-6072	245	13	multiplying	multiply	VERB
ejpam-6072	245	14	it	it	PRON
ejpam-6072	245	15	by	by	ADP
ejpam-6072	245	16	y	y	PROPN
ejpam-6072	245	17	t	t	PROPN
ejpam-6072	245	18	,	,	PUNCT
ejpam-6072	245	19	we	we	PRON
ejpam-6072	245	20	get	get	VERB
ejpam-6072	245	21	y	y	PROPN
ejpam-6072	245	22	a−1	a−1	PROPN
ejpam-6072	245	23	i	i	PRON
ejpam-6072	245	24	∆t	∆t	VERB
ejpam-6072	246	1	i	i	PRON
ejpam-6072	246	2	(	(	PUNCT
ejpam-6072	246	3	∆ibi)y	∆ibi)y	NOUN
ejpam-6072	246	4	−1(bt	−1(bt	NOUN
ejpam-6072	246	5	i	i	NOUN
ejpam-6072	246	6	∆	∆	PROPN
ejpam-6072	246	7	t	t	PROPN
ejpam-6072	246	8	i	i	PRON
ejpam-6072	246	9	)	)	PUNCT
ejpam-6072	246	10	∆ia	∆ia	VERB
ejpam-6072	246	11	−t	−t	VERB
ejpam-6072	247	1	i	i	PRON
ejpam-6072	247	2	y	y	PROPN
ejpam-6072	247	3	t	t	PROPN
ejpam-6072	248	1	+	+	CCONJ
ejpam-6072	248	2	y	y	PROPN
ejpam-6072	248	3	qiy	qiy	PROPN
ejpam-6072	248	4	t	t	PROPN
ejpam-6072	248	5	=	=	SYM
ejpam-6072	248	6	y	y	PROPN
ejpam-6072	248	7	,	,	PUNCT
ejpam-6072	248	8	i	i	PRON
ejpam-6072	248	9	=	=	NOUN
ejpam-6072	248	10	1	1	NUM
ejpam-6072	248	11	,	,	PUNCT
ejpam-6072	248	12	.	.	PUNCT
ejpam-6072	248	13	.	.	PUNCT
ejpam-6072	248	14	.	.	PUNCT
ejpam-6072	249	1	,	,	PUNCT
ejpam-6072	249	2	m.	m.	NOUN
ejpam-6072	249	3	this	this	PRON
ejpam-6072	249	4	,	,	PUNCT
ejpam-6072	249	5	by	by	ADP
ejpam-6072	249	6	(	(	PUNCT
ejpam-6072	249	7	10	10	NUM
ejpam-6072	249	8	)	)	PUNCT
ejpam-6072	249	9	,	,	PUNCT
ejpam-6072	249	10	is	be	AUX
ejpam-6072	249	11	equivalent	equivalent	ADJ
ejpam-6072	249	12	to	to	ADP
ejpam-6072	249	13	xi(∆ibi)y	xi(∆ibi)y	ADP
ejpam-6072	249	14	−1(∆ibi	−1(∆ibi	NOUN
ejpam-6072	249	15	)	)	PUNCT
ejpam-6072	249	16	txi	txi	NOUN
ejpam-6072	250	1	+	+	CCONJ
ejpam-6072	250	2	y	y	PROPN
ejpam-6072	250	3	qiy	qiy	PROPN
ejpam-6072	250	4	t	t	PROPN
ejpam-6072	250	5	=	=	SYM
ejpam-6072	250	6	y	y	PROPN
ejpam-6072	250	7	,	,	PUNCT
ejpam-6072	250	8	(	(	PUNCT
ejpam-6072	250	9	12	12	NUM
ejpam-6072	250	10	)	)	PUNCT
ejpam-6072	250	11	i	i	NOUN
ejpam-6072	250	12	=	=	NOUN
ejpam-6072	250	13	1	1	NUM
ejpam-6072	250	14	,	,	PUNCT
ejpam-6072	250	15	.	.	PUNCT
ejpam-6072	250	16	.	.	PUNCT
ejpam-6072	250	17	.	.	PUNCT
ejpam-6072	251	1	,	,	PUNCT
ejpam-6072	251	2	m.	m.	NOUN
ejpam-6072	251	3	combining	combine	VERB
ejpam-6072	251	4	(	(	PUNCT
ejpam-6072	251	5	11	11	NUM
ejpam-6072	251	6	)	)	PUNCT
ejpam-6072	251	7	and	and	CCONJ
ejpam-6072	251	8	(	(	PUNCT
ejpam-6072	251	9	12	12	NUM
ejpam-6072	251	10	)	)	PUNCT
ejpam-6072	251	11	gives	give	VERB
ejpam-6072	251	12	(	(	PUNCT
ejpam-6072	251	13	∆iai	∆iai	PROPN
ejpam-6072	251	14	)	)	PUNCT
ejpam-6072	251	15	txi	txi	PUNCT
ejpam-6072	252	1	+	+	PROPN
ejpam-6072	252	2	xi(∆iai	xi(∆iai	PROPN
ejpam-6072	252	3	)	)	PUNCT
ejpam-6072	253	1	+	+	CCONJ
ejpam-6072	253	2	y	y	PROPN
ejpam-6072	253	3	+	+	NOUN
ejpam-6072	253	4	xi(∆ibi)y	xi(∆ibi)y	NOUN
ejpam-6072	253	5	−1(∆ibi	−1(∆ibi	NOUN
ejpam-6072	253	6	)	)	PUNCT
ejpam-6072	253	7	txi	txi	NOUN
ejpam-6072	254	1	+	+	CCONJ
ejpam-6072	254	2	zi	zi	NOUN
ejpam-6072	254	3	=	=	SYM
ejpam-6072	254	4	0	0	NUM
ejpam-6072	254	5	,	,	PUNCT
ejpam-6072	254	6	i	i	PRON
ejpam-6072	254	7	=	=	NOUN
ejpam-6072	254	8	1	1	NUM
ejpam-6072	254	9	,	,	PUNCT
ejpam-6072	254	10	.	.	PUNCT
ejpam-6072	254	11	.	.	PUNCT
ejpam-6072	254	12	.	.	PUNCT
ejpam-6072	255	1	,	,	PUNCT
ejpam-6072	255	2	m	m	PROPN
ejpam-6072	255	3	,	,	PUNCT
ejpam-6072	255	4	where	where	SCONJ
ejpam-6072	255	5	zi	zi	NOUN
ejpam-6072	255	6	=	=	PUNCT
ejpam-6072	256	1	y	y	PROPN
ejpam-6072	256	2	qiy	qiy	PROPN
ejpam-6072	256	3	t	t	PROPN
ejpam-6072	256	4	.	.	PUNCT
ejpam-6072	257	1	thus	thus	ADV
ejpam-6072	257	2	,	,	PUNCT
ejpam-6072	257	3	the	the	DET
ejpam-6072	257	4	conclusion	conclusion	NOUN
ejpam-6072	257	5	of	of	ADP
ejpam-6072	257	6	the	the	DET
ejpam-6072	257	7	theorem	theorem	NOUN
ejpam-6072	257	8	holds	hold	VERB
ejpam-6072	257	9	.	.	PUNCT
ejpam-6072	258	1	next	next	ADV
ejpam-6072	258	2	,	,	PUNCT
ejpam-6072	258	3	we	we	PRON
ejpam-6072	258	4	extend	extend	VERB
ejpam-6072	258	5	the	the	DET
ejpam-6072	258	6	results	result	NOUN
ejpam-6072	258	7	on	on	ADP
ejpam-6072	258	8	common	common	ADJ
ejpam-6072	258	9	lyapunov	lyapunov	ADJ
ejpam-6072	258	10	solutions	solution	NOUN
ejpam-6072	258	11	to	to	PART
ejpam-6072	258	12	demonstrate	demonstrate	VERB
ejpam-6072	258	13	that	that	SCONJ
ejpam-6072	258	14	,	,	PUNCT
ejpam-6072	258	15	given	give	VERB
ejpam-6072	258	16	a	a	DET
ejpam-6072	258	17	family	family	NOUN
ejpam-6072	258	18	of	of	ADP
ejpam-6072	258	19	matrices	matrix	NOUN
ejpam-6072	258	20	with	with	ADP
ejpam-6072	258	21	a	a	DET
ejpam-6072	258	22	common	common	ADJ
ejpam-6072	258	23	lyapunov	lyapunov	ADJ
ejpam-6072	258	24	solution	solution	NOUN
ejpam-6072	258	25	,	,	PUNCT
ejpam-6072	258	26	we	we	PRON
ejpam-6072	258	27	can	can	AUX
ejpam-6072	258	28	construct	construct	VERB
ejpam-6072	258	29	a	a	DET
ejpam-6072	258	30	corresponding	correspond	VERB
ejpam-6072	258	31	family	family	NOUN
ejpam-6072	258	32	of	of	ADP
ejpam-6072	258	33	matrix	matrix	NOUN
ejpam-6072	258	34	pairs	pair	NOUN
ejpam-6072	258	35	{	{	PUNCT
ejpam-6072	258	36	(	(	PUNCT
ejpam-6072	258	37	ai	ai	NOUN
ejpam-6072	258	38	,	,	PUNCT
ejpam-6072	258	39	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	258	40	that	that	PRON
ejpam-6072	258	41	shares	share	VERB
ejpam-6072	258	42	a	a	DET
ejpam-6072	258	43	common	common	ADJ
ejpam-6072	258	44	riccati	riccati	NOUN
ejpam-6072	258	45	solution	solution	NOUN
ejpam-6072	258	46	.	.	PUNCT
ejpam-6072	259	1	this	this	DET
ejpam-6072	259	2	result	result	NOUN
ejpam-6072	259	3	a.	a.	PROPN
ejpam-6072	259	4	algefary	algefary	PROPN
ejpam-6072	259	5	,	,	PUNCT
ejpam-6072	259	6	k.	k.	PROPN
ejpam-6072	259	7	a.	a.	PROPN
ejpam-6072	259	8	alqufari	alqufari	PROPN
ejpam-6072	259	9	/	/	SYM
ejpam-6072	259	10	eur	eur	PROPN
ejpam-6072	259	11	.	.	PUNCT
ejpam-6072	260	1	j.	j.	PROPN
ejpam-6072	260	2	pure	pure	PROPN
ejpam-6072	260	3	appl	appl	PROPN
ejpam-6072	260	4	.	.	PROPN
ejpam-6072	260	5	math	math	PROPN
ejpam-6072	260	6	,	,	PUNCT
ejpam-6072	260	7	18	18	NUM
ejpam-6072	260	8	(	(	PUNCT
ejpam-6072	260	9	2	2	NUM
ejpam-6072	260	10	)	)	PUNCT
ejpam-6072	260	11	(	(	PUNCT
ejpam-6072	260	12	2025	2025	NUM
ejpam-6072	260	13	)	)	PUNCT
ejpam-6072	260	14	,	,	PUNCT
ejpam-6072	260	15	6072	6072	NUM
ejpam-6072	260	16	9	9	NUM
ejpam-6072	260	17	of	of	ADP
ejpam-6072	260	18	14	14	NUM
ejpam-6072	260	19	bridges	bridge	NOUN
ejpam-6072	260	20	the	the	DET
ejpam-6072	260	21	gap	gap	NOUN
ejpam-6072	260	22	between	between	ADP
ejpam-6072	260	23	lyapunov	lyapunov	ADJ
ejpam-6072	260	24	stability	stability	NOUN
ejpam-6072	260	25	for	for	ADP
ejpam-6072	260	26	a	a	DET
ejpam-6072	260	27	family	family	NOUN
ejpam-6072	260	28	of	of	ADP
ejpam-6072	260	29	matrices	matrix	NOUN
ejpam-6072	260	30	and	and	CCONJ
ejpam-6072	260	31	riccati	riccati	NOUN
ejpam-6072	260	32	stability	stability	NOUN
ejpam-6072	260	33	for	for	ADP
ejpam-6072	260	34	pairs	pair	NOUN
ejpam-6072	260	35	of	of	ADP
ejpam-6072	260	36	matrices	matrix	NOUN
ejpam-6072	260	37	,	,	PUNCT
ejpam-6072	260	38	highlighting	highlight	VERB
ejpam-6072	260	39	how	how	SCONJ
ejpam-6072	260	40	solutions	solution	NOUN
ejpam-6072	260	41	in	in	ADP
ejpam-6072	260	42	one	one	NUM
ejpam-6072	260	43	framework	framework	NOUN
ejpam-6072	260	44	can	can	AUX
ejpam-6072	260	45	lead	lead	VERB
ejpam-6072	260	46	to	to	ADP
ejpam-6072	260	47	stability	stability	NOUN
ejpam-6072	260	48	in	in	ADP
ejpam-6072	260	49	the	the	DET
ejpam-6072	260	50	other	other	ADJ
ejpam-6072	260	51	.	.	PUNCT
ejpam-6072	261	1	by	by	ADP
ejpam-6072	261	2	constructing	construct	VERB
ejpam-6072	261	3	appropriate	appropriate	ADJ
ejpam-6072	261	4	matrices	matrix	NOUN
ejpam-6072	261	5	bi	bi	NOUN
ejpam-6072	261	6	,	,	PUNCT
ejpam-6072	261	7	we	we	PRON
ejpam-6072	261	8	show	show	VERB
ejpam-6072	261	9	that	that	SCONJ
ejpam-6072	261	10	a	a	DET
ejpam-6072	261	11	single	single	ADJ
ejpam-6072	261	12	lyapunov	lyapunov	ADJ
ejpam-6072	261	13	matrix	matrix	NOUN
ejpam-6072	261	14	can	can	AUX
ejpam-6072	261	15	satisfy	satisfy	VERB
ejpam-6072	261	16	the	the	DET
ejpam-6072	261	17	riccati	riccati	PROPN
ejpam-6072	261	18	equations	equation	NOUN
ejpam-6072	261	19	across	across	ADP
ejpam-6072	261	20	the	the	DET
ejpam-6072	261	21	family	family	NOUN
ejpam-6072	261	22	,	,	PUNCT
ejpam-6072	261	23	establishing	establish	VERB
ejpam-6072	261	24	a	a	DET
ejpam-6072	261	25	unified	unified	ADJ
ejpam-6072	261	26	stability	stability	NOUN
ejpam-6072	261	27	criterion	criterion	NOUN
ejpam-6072	261	28	.	.	PUNCT
ejpam-6072	262	1	theorem	theorem	ADJ
ejpam-6072	262	2	4	4	NUM
ejpam-6072	262	3	.	.	X
ejpam-6072	263	1	for	for	ADP
ejpam-6072	263	2	i	i	PRON
ejpam-6072	263	3	=	=	NOUN
ejpam-6072	263	4	1	1	NUM
ejpam-6072	263	5	,	,	PUNCT
ejpam-6072	263	6	.	.	PUNCT
ejpam-6072	263	7	.	.	PUNCT
ejpam-6072	264	1	.	.	PUNCT
ejpam-6072	265	1	,	,	PUNCT
ejpam-6072	265	2	m	m	VERB
ejpam-6072	265	3	,	,	PUNCT
ejpam-6072	265	4	suppose	suppose	VERB
ejpam-6072	265	5	that	that	SCONJ
ejpam-6072	265	6	ai	ai	VERB
ejpam-6072	265	7	∈	∈	PROPN
ejpam-6072	265	8	rn×n	rn×n	NOUN
ejpam-6072	265	9	.	.	PUNCT
ejpam-6072	266	1	if	if	SCONJ
ejpam-6072	266	2	the	the	DET
ejpam-6072	266	3	family	family	NOUN
ejpam-6072	266	4	a	a	X
ejpam-6072	266	5	=	=	X
ejpam-6072	266	6	{	{	PUNCT
ejpam-6072	266	7	ai}mi=1	ai}mi=1	PROPN
ejpam-6072	266	8	has	have	VERB
ejpam-6072	266	9	a	a	DET
ejpam-6072	266	10	common	common	ADJ
ejpam-6072	266	11	lyapunov	lyapunov	ADJ
ejpam-6072	266	12	solution	solution	NOUN
ejpam-6072	266	13	,	,	PUNCT
ejpam-6072	266	14	then	then	ADV
ejpam-6072	266	15	there	there	PRON
ejpam-6072	266	16	exist	exist	VERB
ejpam-6072	266	17	matrices	matrix	NOUN
ejpam-6072	266	18	bi	bi	NOUN
ejpam-6072	266	19	,	,	PUNCT
ejpam-6072	266	20	i	i	NOUN
ejpam-6072	266	21	=	=	NOUN
ejpam-6072	266	22	1	1	NUM
ejpam-6072	266	23	,	,	PUNCT
ejpam-6072	266	24	.	.	PUNCT
ejpam-6072	266	25	.	.	PUNCT
ejpam-6072	267	1	.	.	PUNCT
ejpam-6072	268	1	,	,	PUNCT
ejpam-6072	268	2	m	m	PROPN
ejpam-6072	268	3	,	,	PUNCT
ejpam-6072	268	4	such	such	ADJ
ejpam-6072	268	5	that	that	SCONJ
ejpam-6072	268	6	for	for	ADP
ejpam-6072	268	7	each	each	DET
ejpam-6072	268	8	i	i	PRON
ejpam-6072	268	9	,	,	PUNCT
ejpam-6072	268	10	the	the	DET
ejpam-6072	268	11	pair	pair	NOUN
ejpam-6072	268	12	(	(	PUNCT
ejpam-6072	268	13	ai	ai	NOUN
ejpam-6072	268	14	,	,	PUNCT
ejpam-6072	268	15	bi	bi	NOUN
ejpam-6072	268	16	)	)	PUNCT
ejpam-6072	268	17	has	have	VERB
ejpam-6072	268	18	a	a	DET
ejpam-6072	268	19	riccati	riccati	NOUN
ejpam-6072	268	20	solution	solution	NOUN
ejpam-6072	268	21	(	(	PUNCT
ejpam-6072	268	22	p	p	X
ejpam-6072	268	23	,	,	PUNCT
ejpam-6072	268	24	q̂i	q̂i	NUM
ejpam-6072	268	25	)	)	PUNCT
ejpam-6072	268	26	,	,	PUNCT
ejpam-6072	268	27	i.e.	i.e.	X
ejpam-6072	268	28	all	all	DET
ejpam-6072	268	29	the	the	DET
ejpam-6072	268	30	pairs	pair	NOUN
ejpam-6072	268	31	share	share	VERB
ejpam-6072	268	32	the	the	DET
ejpam-6072	268	33	same	same	ADJ
ejpam-6072	268	34	p	p	NOUN
ejpam-6072	268	35	in	in	ADP
ejpam-6072	268	36	their	their	PRON
ejpam-6072	268	37	riccati	riccati	NOUN
ejpam-6072	268	38	solution	solution	NOUN
ejpam-6072	268	39	.	.	PUNCT
ejpam-6072	269	1	proof	proof	NOUN
ejpam-6072	269	2	.	.	PUNCT
ejpam-6072	270	1	let	let	VERB
ejpam-6072	270	2	us	we	PRON
ejpam-6072	270	3	assume	assume	VERB
ejpam-6072	270	4	that	that	SCONJ
ejpam-6072	270	5	the	the	DET
ejpam-6072	270	6	family	family	NOUN
ejpam-6072	270	7	a	a	PRON
ejpam-6072	270	8	has	have	VERB
ejpam-6072	270	9	a	a	DET
ejpam-6072	270	10	common	common	ADJ
ejpam-6072	270	11	lyapunov	lyapunov	ADJ
ejpam-6072	270	12	solution	solution	NOUN
ejpam-6072	270	13	.	.	PUNCT
ejpam-6072	271	1	then	then	ADV
ejpam-6072	271	2	,	,	PUNCT
ejpam-6072	271	3	there	there	PRON
ejpam-6072	271	4	exist	exist	VERB
ejpam-6072	271	5	positive	positive	ADJ
ejpam-6072	271	6	definite	definite	ADJ
ejpam-6072	271	7	matrices	matrix	NOUN
ejpam-6072	271	8	p	p	NOUN
ejpam-6072	271	9	,	,	PUNCT
ejpam-6072	271	10	q1	q1	PROPN
ejpam-6072	271	11	,	,	PUNCT
ejpam-6072	271	12	.	.	PUNCT
ejpam-6072	271	13	.	.	PUNCT
ejpam-6072	272	1	.	.	PUNCT
ejpam-6072	273	1	,	,	PUNCT
ejpam-6072	273	2	qm	qm	PROPN
ejpam-6072	273	3	such	such	ADJ
ejpam-6072	273	4	that	that	SCONJ
ejpam-6072	273	5	at	at	ADP
ejpam-6072	273	6	i	i	PRON
ejpam-6072	273	7	p	p	PROPN
ejpam-6072	274	1	+	+	CCONJ
ejpam-6072	274	2	pai	pai	PROPN
ejpam-6072	274	3	+	+	PROPN
ejpam-6072	274	4	qi	qi	X
ejpam-6072	274	5	=	=	SYM
ejpam-6072	274	6	0	0	NUM
ejpam-6072	274	7	,	,	PUNCT
ejpam-6072	274	8	i	i	PRON
ejpam-6072	274	9	=	=	NOUN
ejpam-6072	274	10	1	1	NUM
ejpam-6072	274	11	,	,	PUNCT
ejpam-6072	274	12	.	.	PUNCT
ejpam-6072	274	13	.	.	PUNCT
ejpam-6072	275	1	.	.	PUNCT
ejpam-6072	276	1	,	,	PUNCT
ejpam-6072	276	2	m.	m.	NOUN
ejpam-6072	276	3	now	now	ADV
ejpam-6072	276	4	,	,	PUNCT
ejpam-6072	276	5	consider	consider	VERB
ejpam-6072	276	6	arbitrary	arbitrary	ADJ
ejpam-6072	276	7	scalars	scalar	NOUN
ejpam-6072	276	8	α	α	PROPN
ejpam-6072	276	9	>	>	X
ejpam-6072	276	10	0	0	PUNCT
ejpam-6072	276	11	and	and	CCONJ
ejpam-6072	276	12	β	β	X
ejpam-6072	276	13	>	>	X
ejpam-6072	276	14	0	0	PUNCT
ejpam-6072	276	15	with	with	ADP
ejpam-6072	276	16	α2	α2	PROPN
ejpam-6072	276	17	+	+	CCONJ
ejpam-6072	276	18	β2	β2	VERB
ejpam-6072	276	19	<	<	X
ejpam-6072	276	20	1	1	NUM
ejpam-6072	276	21	.	.	PUNCT
ejpam-6072	277	1	therefore	therefore	ADV
ejpam-6072	277	2	,	,	PUNCT
ejpam-6072	277	3	it	it	PRON
ejpam-6072	277	4	follows	follow	VERB
ejpam-6072	277	5	that	that	SCONJ
ejpam-6072	277	6	at	at	ADP
ejpam-6072	277	7	i	i	PRON
ejpam-6072	277	8	p+pai+α2qi+(1−α2−β2)qi+p	p+pai+α2qi+(1−α2−β2)qi+p	INTJ
ejpam-6072	277	9	(	(	PUNCT
ejpam-6072	277	10	p−1αβqi	p−1αβqi	ADJ
ejpam-6072	278	1	)	)	PUNCT
ejpam-6072	278	2	q−1	q−1	PROPN
ejpam-6072	279	1	i	i	PRON
ejpam-6072	279	2	α−2	α−2	PROPN
ejpam-6072	279	3	(	(	PUNCT
ejpam-6072	279	4	qiαβp	qiαβp	NOUN
ejpam-6072	279	5	−1	−1	NOUN
ejpam-6072	279	6	)	)	PUNCT
ejpam-6072	280	1	p	p	X
ejpam-6072	281	1	=	=	NOUN
ejpam-6072	281	2	0	0	NUM
ejpam-6072	281	3	,	,	PUNCT
ejpam-6072	281	4	i	i	PRON
ejpam-6072	281	5	=	=	NOUN
ejpam-6072	281	6	1	1	NUM
ejpam-6072	281	7	,	,	PUNCT
ejpam-6072	281	8	.	.	PUNCT
ejpam-6072	281	9	.	.	PUNCT
ejpam-6072	281	10	.	.	PUNCT
ejpam-6072	282	1	,	,	PUNCT
ejpam-6072	282	2	m.	m.	NOUN
ejpam-6072	282	3	(	(	PUNCT
ejpam-6072	282	4	13	13	NUM
ejpam-6072	282	5	)	)	PUNCT
ejpam-6072	282	6	define	define	VERB
ejpam-6072	282	7	bi	bi	NOUN
ejpam-6072	282	8	=	=	PROPN
ejpam-6072	282	9	αβp−1qi	αβp−1qi	PROPN
ejpam-6072	282	10	,	,	PUNCT
ejpam-6072	282	11	and	and	CCONJ
ejpam-6072	282	12	si	si	X
ejpam-6072	282	13	=	=	SYM
ejpam-6072	282	14	(	(	PUNCT
ejpam-6072	282	15	1−	1−	NUM
ejpam-6072	282	16	α2	α2	PROPN
ejpam-6072	282	17	−	−	PROPN
ejpam-6072	282	18	β2)qi	β2)qi	PROPN
ejpam-6072	282	19	,	,	PUNCT
ejpam-6072	282	20	i	i	NOUN
ejpam-6072	282	21	=	=	NOUN
ejpam-6072	282	22	1	1	NUM
ejpam-6072	282	23	,	,	PUNCT
ejpam-6072	282	24	.	.	PUNCT
ejpam-6072	282	25	.	.	PUNCT
ejpam-6072	283	1	.	.	PUNCT
ejpam-6072	284	1	,	,	PUNCT
ejpam-6072	284	2	m.	m.	NOUN
ejpam-6072	284	3	then	then	ADV
ejpam-6072	284	4	,	,	PUNCT
ejpam-6072	284	5	equation	equation	NOUN
ejpam-6072	284	6	(	(	PUNCT
ejpam-6072	284	7	13	13	NUM
ejpam-6072	284	8	)	)	PUNCT
ejpam-6072	284	9	reduces	reduce	VERB
ejpam-6072	284	10	to	to	ADP
ejpam-6072	284	11	at	at	ADP
ejpam-6072	284	12	i	i	PROPN
ejpam-6072	284	13	p	p	PROPN
ejpam-6072	285	1	+	+	CCONJ
ejpam-6072	285	2	pai	pai	NOUN
ejpam-6072	285	3	+	+	CCONJ
ejpam-6072	285	4	α2qi	α2qi	NUM
ejpam-6072	286	1	+	+	CCONJ
ejpam-6072	286	2	si	si	X
ejpam-6072	286	3	+	+	NUM
ejpam-6072	286	4	pbiq	pbiq	NOUN
ejpam-6072	286	5	−1	−1	NOUN
ejpam-6072	287	1	i	i	PRON
ejpam-6072	287	2	α−2bt	α−2bt	VERB
ejpam-6072	288	1	i	i	PRON
ejpam-6072	288	2	p	p	NOUN
ejpam-6072	289	1	=	=	ADJ
ejpam-6072	289	2	0	0	NUM
ejpam-6072	289	3	,	,	PUNCT
ejpam-6072	289	4	i	i	PRON
ejpam-6072	289	5	=	=	NOUN
ejpam-6072	289	6	1	1	NUM
ejpam-6072	289	7	,	,	PUNCT
ejpam-6072	289	8	.	.	PUNCT
ejpam-6072	289	9	.	.	PUNCT
ejpam-6072	289	10	.	.	PUNCT
ejpam-6072	290	1	,	,	PUNCT
ejpam-6072	290	2	m.	m.	NOUN
ejpam-6072	290	3	on	on	ADP
ejpam-6072	290	4	letting	let	VERB
ejpam-6072	290	5	q̂i	q̂i	NOUN
ejpam-6072	290	6	=	=	NOUN
ejpam-6072	290	7	α2qi	α2qi	NUM
ejpam-6072	290	8	,	,	PUNCT
ejpam-6072	290	9	this	this	PRON
ejpam-6072	290	10	implies	imply	VERB
ejpam-6072	290	11	that	that	SCONJ
ejpam-6072	290	12	for	for	ADP
ejpam-6072	290	13	each	each	DET
ejpam-6072	290	14	i	i	PRON
ejpam-6072	290	15	∈	∈	PROPN
ejpam-6072	290	16	{	{	PUNCT
ejpam-6072	290	17	1	1	NUM
ejpam-6072	290	18	,	,	PUNCT
ejpam-6072	290	19	.	.	PUNCT
ejpam-6072	290	20	.	.	PUNCT
ejpam-6072	291	1	.	.	PUNCT
ejpam-6072	292	1	,	,	PUNCT
ejpam-6072	292	2	m	m	PROPN
ejpam-6072	292	3	}	}	PUNCT
ejpam-6072	292	4	,	,	PUNCT
ejpam-6072	292	5	the	the	DET
ejpam-6072	292	6	pair	pair	NOUN
ejpam-6072	292	7	(	(	PUNCT
ejpam-6072	292	8	ai	ai	NOUN
ejpam-6072	292	9	,	,	PUNCT
ejpam-6072	292	10	bi	bi	NOUN
ejpam-6072	292	11	)	)	PUNCT
ejpam-6072	292	12	has	have	VERB
ejpam-6072	292	13	(	(	PUNCT
ejpam-6072	292	14	p	p	X
ejpam-6072	292	15	,	,	PUNCT
ejpam-6072	292	16	q̂i	q̂i	CCONJ
ejpam-6072	292	17	)	)	PUNCT
ejpam-6072	292	18	as	as	ADP
ejpam-6072	292	19	a	a	DET
ejpam-6072	292	20	riccati	riccati	NOUN
ejpam-6072	292	21	solution	solution	NOUN
ejpam-6072	292	22	.	.	PUNCT
ejpam-6072	293	1	this	this	PRON
ejpam-6072	293	2	completes	complete	VERB
ejpam-6072	293	3	the	the	DET
ejpam-6072	293	4	proof	proof	NOUN
ejpam-6072	293	5	.	.	PUNCT
ejpam-6072	294	1	this	this	DET
ejpam-6072	294	2	section	section	NOUN
ejpam-6072	294	3	establishes	establish	VERB
ejpam-6072	294	4	the	the	DET
ejpam-6072	294	5	foundational	foundational	ADJ
ejpam-6072	294	6	relationships	relationship	NOUN
ejpam-6072	294	7	between	between	ADP
ejpam-6072	294	8	common	common	ADJ
ejpam-6072	294	9	riccati	riccati	NOUN
ejpam-6072	294	10	,	,	PUNCT
ejpam-6072	294	11	lyapunov	lyapunov	NOUN
ejpam-6072	294	12	,	,	PUNCT
ejpam-6072	294	13	and	and	CCONJ
ejpam-6072	294	14	schur	schur	ADJ
ejpam-6072	294	15	stability	stability	NOUN
ejpam-6072	294	16	.	.	PUNCT
ejpam-6072	295	1	theorems	theorem	VERB
ejpam-6072	295	2	2.1	2.1	NUM
ejpam-6072	295	3	and	and	CCONJ
ejpam-6072	295	4	2.2	2.2	NUM
ejpam-6072	295	5	demonstrate	demonstrate	NOUN
ejpam-6072	295	6	that	that	SCONJ
ejpam-6072	295	7	common	common	ADJ
ejpam-6072	295	8	riccati	riccati	NOUN
ejpam-6072	295	9	stability	stability	NOUN
ejpam-6072	295	10	implies	imply	VERB
ejpam-6072	295	11	both	both	PRON
ejpam-6072	295	12	common	common	ADJ
ejpam-6072	295	13	lyapunov	lyapunov	NOUN
ejpam-6072	295	14	and	and	CCONJ
ejpam-6072	295	15	schur	schur	PROPN
ejpam-6072	295	16	stability	stability	PROPN
ejpam-6072	295	17	,	,	PUNCT
ejpam-6072	295	18	highlighting	highlight	VERB
ejpam-6072	295	19	how	how	SCONJ
ejpam-6072	295	20	the	the	DET
ejpam-6072	295	21	riccati	riccati	PROPN
ejpam-6072	295	22	framework	framework	NOUN
ejpam-6072	295	23	provides	provide	VERB
ejpam-6072	295	24	a	a	DET
ejpam-6072	295	25	unifying	unifying	ADJ
ejpam-6072	295	26	structure	structure	NOUN
ejpam-6072	295	27	for	for	ADP
ejpam-6072	295	28	ensuring	ensure	VERB
ejpam-6072	295	29	system	system	NOUN
ejpam-6072	295	30	robustness	robustness	NOUN
ejpam-6072	295	31	across	across	ADP
ejpam-6072	295	32	continuous	continuous	ADJ
ejpam-6072	295	33	and	and	CCONJ
ejpam-6072	295	34	discrete	discrete	ADJ
ejpam-6072	295	35	-	-	PUNCT
ejpam-6072	295	36	time	time	NOUN
ejpam-6072	295	37	settings	setting	NOUN
ejpam-6072	295	38	.	.	PUNCT
ejpam-6072	296	1	these	these	DET
ejpam-6072	296	2	results	result	NOUN
ejpam-6072	296	3	indicate	indicate	VERB
ejpam-6072	296	4	that	that	SCONJ
ejpam-6072	296	5	solving	solve	VERB
ejpam-6072	296	6	the	the	DET
ejpam-6072	296	7	riccati	riccati	PROPN
ejpam-6072	296	8	equations	equation	NOUN
ejpam-6072	296	9	for	for	ADP
ejpam-6072	296	10	a	a	DET
ejpam-6072	296	11	family	family	NOUN
ejpam-6072	296	12	of	of	ADP
ejpam-6072	296	13	matrix	matrix	NOUN
ejpam-6072	296	14	pairs	pair	NOUN
ejpam-6072	296	15	yields	yield	VERB
ejpam-6072	296	16	solutions	solution	NOUN
ejpam-6072	296	17	that	that	PRON
ejpam-6072	296	18	inherently	inherently	ADV
ejpam-6072	296	19	satisfy	satisfy	VERB
ejpam-6072	296	20	lyapunov	lyapunov	NOUN
ejpam-6072	296	21	-	-	PUNCT
ejpam-6072	296	22	type	type	NOUN
ejpam-6072	296	23	inequalities	inequality	NOUN
ejpam-6072	296	24	,	,	PUNCT
ejpam-6072	296	25	thus	thus	ADV
ejpam-6072	296	26	extending	extend	VERB
ejpam-6072	296	27	classical	classical	ADJ
ejpam-6072	296	28	notions	notion	NOUN
ejpam-6072	296	29	of	of	ADP
ejpam-6072	296	30	stability	stability	NOUN
ejpam-6072	296	31	to	to	ADP
ejpam-6072	296	32	more	more	ADV
ejpam-6072	296	33	complex	complex	ADJ
ejpam-6072	296	34	system	system	NOUN
ejpam-6072	296	35	structures	structure	NOUN
ejpam-6072	296	36	.	.	PUNCT
ejpam-6072	297	1	in	in	ADP
ejpam-6072	297	2	the	the	DET
ejpam-6072	297	3	next	next	ADJ
ejpam-6072	297	4	section	section	NOUN
ejpam-6072	297	5	,	,	PUNCT
ejpam-6072	297	6	we	we	PRON
ejpam-6072	297	7	build	build	VERB
ejpam-6072	297	8	upon	upon	SCONJ
ejpam-6072	297	9	these	these	DET
ejpam-6072	297	10	results	result	NOUN
ejpam-6072	297	11	by	by	ADP
ejpam-6072	297	12	exploring	explore	VERB
ejpam-6072	297	13	the	the	DET
ejpam-6072	297	14	preservation	preservation	NOUN
ejpam-6072	297	15	of	of	ADP
ejpam-6072	297	16	riccati	riccati	PROPN
ejpam-6072	297	17	stability	stability	NOUN
ejpam-6072	297	18	under	under	ADP
ejpam-6072	297	19	various	various	ADJ
ejpam-6072	297	20	transformations	transformation	NOUN
ejpam-6072	297	21	,	,	PUNCT
ejpam-6072	297	22	further	far	ADV
ejpam-6072	297	23	emphasizing	emphasize	VERB
ejpam-6072	297	24	the	the	DET
ejpam-6072	297	25	robustness	robustness	NOUN
ejpam-6072	297	26	of	of	ADP
ejpam-6072	297	27	the	the	DET
ejpam-6072	297	28	proposed	propose	VERB
ejpam-6072	297	29	approach	approach	NOUN
ejpam-6072	297	30	.	.	PUNCT
ejpam-6072	298	1	a.	a.	PROPN
ejpam-6072	298	2	algefary	algefary	PROPN
ejpam-6072	298	3	,	,	PUNCT
ejpam-6072	298	4	k.	k.	PROPN
ejpam-6072	298	5	a.	a.	PROPN
ejpam-6072	298	6	alqufari	alqufari	PROPN
ejpam-6072	298	7	/	/	SYM
ejpam-6072	298	8	eur	eur	PROPN
ejpam-6072	298	9	.	.	PUNCT
ejpam-6072	299	1	j.	j.	PROPN
ejpam-6072	299	2	pure	pure	PROPN
ejpam-6072	299	3	appl	appl	PROPN
ejpam-6072	299	4	.	.	PROPN
ejpam-6072	299	5	math	math	PROPN
ejpam-6072	299	6	,	,	PUNCT
ejpam-6072	299	7	18	18	NUM
ejpam-6072	299	8	(	(	PUNCT
ejpam-6072	299	9	2	2	NUM
ejpam-6072	299	10	)	)	PUNCT
ejpam-6072	299	11	(	(	PUNCT
ejpam-6072	299	12	2025	2025	NUM
ejpam-6072	299	13	)	)	PUNCT
ejpam-6072	299	14	,	,	PUNCT
ejpam-6072	299	15	6072	6072	NUM
ejpam-6072	299	16	10	10	NUM
ejpam-6072	299	17	of	of	ADP
ejpam-6072	299	18	14	14	NUM
ejpam-6072	299	19	3	3	NUM
ejpam-6072	299	20	.	.	PUNCT
ejpam-6072	299	21	stability	stability	NOUN
ejpam-6072	299	22	preservation	preservation	NOUN
ejpam-6072	299	23	in	in	ADP
ejpam-6072	299	24	scaled	scale	VERB
ejpam-6072	299	25	common	common	ADJ
ejpam-6072	299	26	riccati	riccati	NOUN
ejpam-6072	299	27	families	family	NOUN
ejpam-6072	299	28	in	in	ADP
ejpam-6072	299	29	this	this	DET
ejpam-6072	299	30	section	section	NOUN
ejpam-6072	299	31	,	,	PUNCT
ejpam-6072	299	32	we	we	PRON
ejpam-6072	299	33	explore	explore	VERB
ejpam-6072	299	34	how	how	SCONJ
ejpam-6072	299	35	common	common	ADJ
ejpam-6072	299	36	riccati	riccati	NOUN
ejpam-6072	299	37	stability	stability	NOUN
ejpam-6072	299	38	behaves	behave	VERB
ejpam-6072	299	39	under	under	ADP
ejpam-6072	299	40	transformations	transformation	NOUN
ejpam-6072	299	41	,	,	PUNCT
ejpam-6072	299	42	focusing	focus	VERB
ejpam-6072	299	43	on	on	ADP
ejpam-6072	299	44	scaling	scale	VERB
ejpam-6072	299	45	properties	property	NOUN
ejpam-6072	299	46	and	and	CCONJ
ejpam-6072	299	47	similarity	similarity	NOUN
ejpam-6072	299	48	transformations	transformation	NOUN
ejpam-6072	299	49	.	.	PUNCT
ejpam-6072	300	1	these	these	DET
ejpam-6072	300	2	adaptation	adaptation	NOUN
ejpam-6072	300	3	examine	examine	VERB
ejpam-6072	300	4	how	how	SCONJ
ejpam-6072	300	5	stability	stability	NOUN
ejpam-6072	300	6	characteristics	characteristic	NOUN
ejpam-6072	300	7	are	be	AUX
ejpam-6072	300	8	preserved	preserve	VERB
ejpam-6072	300	9	or	or	CCONJ
ejpam-6072	300	10	modified	modify	VERB
ejpam-6072	300	11	when	when	SCONJ
ejpam-6072	300	12	the	the	DET
ejpam-6072	300	13	family	family	NOUN
ejpam-6072	300	14	of	of	ADP
ejpam-6072	300	15	matrix	matrix	NOUN
ejpam-6072	300	16	pairs	pair	NOUN
ejpam-6072	300	17	undergoes	undergo	VERB
ejpam-6072	300	18	specific	specific	ADJ
ejpam-6072	300	19	alterations	alteration	NOUN
ejpam-6072	300	20	,	,	PUNCT
ejpam-6072	300	21	such	such	ADJ
ejpam-6072	300	22	as	as	ADP
ejpam-6072	300	23	scaling	scale	VERB
ejpam-6072	300	24	by	by	ADP
ejpam-6072	300	25	a	a	DET
ejpam-6072	300	26	positive	positive	ADJ
ejpam-6072	300	27	scalar	scalar	NOUN
ejpam-6072	300	28	or	or	CCONJ
ejpam-6072	300	29	transformations	transformation	NOUN
ejpam-6072	300	30	by	by	ADP
ejpam-6072	300	31	a	a	DET
ejpam-6072	300	32	nonsingular	nonsingular	ADJ
ejpam-6072	300	33	matrix	matrix	NOUN
ejpam-6072	300	34	.	.	PUNCT
ejpam-6072	301	1	this	this	DET
ejpam-6072	301	2	analysis	analysis	NOUN
ejpam-6072	301	3	is	be	AUX
ejpam-6072	301	4	crucial	crucial	ADJ
ejpam-6072	301	5	in	in	ADP
ejpam-6072	301	6	control	control	NOUN
ejpam-6072	301	7	theory	theory	NOUN
ejpam-6072	301	8	applications	application	NOUN
ejpam-6072	301	9	where	where	SCONJ
ejpam-6072	301	10	systems	system	NOUN
ejpam-6072	301	11	may	may	AUX
ejpam-6072	301	12	be	be	AUX
ejpam-6072	301	13	subject	subject	ADJ
ejpam-6072	301	14	to	to	ADP
ejpam-6072	301	15	rescaling	rescaling	NOUN
ejpam-6072	301	16	or	or	CCONJ
ejpam-6072	301	17	coordinate	coordinate	ADJ
ejpam-6072	301	18	transformations	transformation	NOUN
ejpam-6072	301	19	,	,	PUNCT
ejpam-6072	301	20	yet	yet	CCONJ
ejpam-6072	301	21	stability	stability	NOUN
ejpam-6072	301	22	needs	need	VERB
ejpam-6072	301	23	to	to	PART
ejpam-6072	301	24	be	be	AUX
ejpam-6072	301	25	maintained	maintain	VERB
ejpam-6072	301	26	across	across	ADP
ejpam-6072	301	27	these	these	DET
ejpam-6072	301	28	changes	change	NOUN
ejpam-6072	301	29	.	.	PUNCT
ejpam-6072	302	1	theorem	theorem	NOUN
ejpam-6072	302	2	5	5	NUM
ejpam-6072	302	3	.	.	X
ejpam-6072	303	1	for	for	ADP
ejpam-6072	303	2	i	i	PRON
ejpam-6072	303	3	=	=	NOUN
ejpam-6072	303	4	1	1	NUM
ejpam-6072	303	5	,	,	PUNCT
ejpam-6072	303	6	.	.	PUNCT
ejpam-6072	303	7	.	.	PUNCT
ejpam-6072	303	8	.	.	PUNCT
ejpam-6072	304	1	,	,	PUNCT
ejpam-6072	304	2	m	m	VERB
ejpam-6072	304	3	,	,	PUNCT
ejpam-6072	304	4	suppose	suppose	VERB
ejpam-6072	304	5	that	that	SCONJ
ejpam-6072	304	6	ai	ai	VERB
ejpam-6072	304	7	,	,	PUNCT
ejpam-6072	304	8	bi	bi	NOUN
ejpam-6072	304	9	∈	∈	PROPN
ejpam-6072	304	10	rn×n	rn×n	NOUN
ejpam-6072	304	11	.	.	PUNCT
ejpam-6072	305	1	if	if	SCONJ
ejpam-6072	305	2	the	the	DET
ejpam-6072	305	3	family	family	NOUN
ejpam-6072	305	4	u	u	NOUN
ejpam-6072	305	5	=	=	PRON
ejpam-6072	305	6	{	{	PUNCT
ejpam-6072	305	7	(	(	PUNCT
ejpam-6072	305	8	ai	ai	PROPN
ejpam-6072	305	9	,	,	PUNCT
ejpam-6072	305	10	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	305	11	has	have	VERB
ejpam-6072	305	12	common	common	ADJ
ejpam-6072	305	13	riccati	riccati	NOUN
ejpam-6072	305	14	stability	stability	NOUN
ejpam-6072	305	15	,	,	PUNCT
ejpam-6072	305	16	then	then	ADV
ejpam-6072	305	17	the	the	DET
ejpam-6072	305	18	family	family	NOUN
ejpam-6072	305	19	v	v	NOUN
ejpam-6072	305	20	=	=	SYM
ejpam-6072	305	21	{	{	PUNCT
ejpam-6072	305	22	(	(	PUNCT
ejpam-6072	305	23	βai	βai	NOUN
ejpam-6072	305	24	,	,	PUNCT
ejpam-6072	305	25	βbi)}mi=1	βbi)}mi=1	PROPN
ejpam-6072	305	26	has	have	VERB
ejpam-6072	305	27	common	common	ADJ
ejpam-6072	305	28	riccati	riccati	NOUN
ejpam-6072	305	29	stability	stability	NOUN
ejpam-6072	305	30	for	for	ADP
ejpam-6072	305	31	all	all	DET
ejpam-6072	305	32	β	β	X
ejpam-6072	305	33	>	>	X
ejpam-6072	305	34	0	0	X
ejpam-6072	305	35	.	.	PUNCT
ejpam-6072	306	1	proof	proof	NOUN
ejpam-6072	306	2	.	.	PUNCT
ejpam-6072	307	1	assume	assume	VERB
ejpam-6072	307	2	that	that	SCONJ
ejpam-6072	307	3	there	there	PRON
ejpam-6072	307	4	are	be	VERB
ejpam-6072	307	5	positive	positive	ADJ
ejpam-6072	307	6	definite	definite	ADJ
ejpam-6072	307	7	matrices	matrix	NOUN
ejpam-6072	307	8	p	p	NOUN
ejpam-6072	307	9	,	,	PUNCT
ejpam-6072	307	10	q	q	NOUN
ejpam-6072	307	11	,	,	PUNCT
ejpam-6072	307	12	r1	r1	NOUN
ejpam-6072	307	13	,	,	PUNCT
ejpam-6072	307	14	.	.	PUNCT
ejpam-6072	307	15	.	.	PUNCT
ejpam-6072	308	1	.	.	PUNCT
ejpam-6072	309	1	,	,	PUNCT
ejpam-6072	309	2	rm	rm	PROPN
ejpam-6072	309	3	∈	∈	PROPN
ejpam-6072	309	4	rn×n	rn×n	PROPN
ejpam-6072	309	5	such	such	ADJ
ejpam-6072	309	6	that	that	SCONJ
ejpam-6072	309	7	(	(	PUNCT
ejpam-6072	309	8	p	p	X
ejpam-6072	309	9	,	,	PUNCT
ejpam-6072	309	10	q	q	NOUN
ejpam-6072	309	11	)	)	PUNCT
ejpam-6072	309	12	is	be	AUX
ejpam-6072	309	13	a	a	DET
ejpam-6072	309	14	common	common	ADJ
ejpam-6072	309	15	riccati	riccati	NOUN
ejpam-6072	309	16	solution	solution	NOUN
ejpam-6072	309	17	for	for	ADP
ejpam-6072	309	18	u	u	PROPN
ejpam-6072	309	19	.	.	PUNCT
ejpam-6072	310	1	thus	thus	ADV
ejpam-6072	310	2	,	,	PUNCT
ejpam-6072	310	3	the	the	DET
ejpam-6072	310	4	following	follow	VERB
ejpam-6072	310	5	equations	equation	NOUN
ejpam-6072	310	6	hold	hold	VERB
ejpam-6072	310	7	at	at	ADP
ejpam-6072	310	8	i	i	PROPN
ejpam-6072	310	9	p	p	PROPN
ejpam-6072	311	1	+	+	CCONJ
ejpam-6072	311	2	pai	pai	PROPN
ejpam-6072	311	3	+	+	PROPN
ejpam-6072	311	4	q+	q+	ADP
ejpam-6072	311	5	pbiq	pbiq	PROPN
ejpam-6072	312	1	−1bt	−1bt	ADP
ejpam-6072	312	2	i	i	PRON
ejpam-6072	312	3	p	p	X
ejpam-6072	313	1	+	+	PROPN
ejpam-6072	313	2	ri	ri	NOUN
ejpam-6072	313	3	=	=	SYM
ejpam-6072	313	4	0	0	NUM
ejpam-6072	313	5	,	,	PUNCT
ejpam-6072	313	6	for	for	ADP
ejpam-6072	313	7	i	i	PROPN
ejpam-6072	313	8	=	=	NOUN
ejpam-6072	313	9	1	1	NUM
ejpam-6072	313	10	,	,	PUNCT
ejpam-6072	313	11	.	.	PUNCT
ejpam-6072	313	12	.	.	PUNCT
ejpam-6072	314	1	.	.	PUNCT
ejpam-6072	315	1	,	,	PUNCT
ejpam-6072	315	2	m.	m.	NOUN
ejpam-6072	315	3	thus	thus	ADV
ejpam-6072	315	4	,	,	PUNCT
ejpam-6072	315	5	for	for	ADP
ejpam-6072	315	6	every	every	DET
ejpam-6072	315	7	β	β	X
ejpam-6072	315	8	>	>	X
ejpam-6072	315	9	0	0	NUM
ejpam-6072	315	10	,	,	PUNCT
ejpam-6072	315	11	we	we	PRON
ejpam-6072	315	12	have	have	VERB
ejpam-6072	315	13	β(at	β(at	NOUN
ejpam-6072	315	14	i	i	PRON
ejpam-6072	315	15	p	p	X
ejpam-6072	316	1	+	+	NUM
ejpam-6072	316	2	pai	pai	PROPN
ejpam-6072	316	3	+	+	PROPN
ejpam-6072	316	4	q+	q+	ADP
ejpam-6072	316	5	pbiq	pbiq	PROPN
ejpam-6072	317	1	−1bt	−1bt	ADP
ejpam-6072	317	2	i	i	PRON
ejpam-6072	317	3	p	p	X
ejpam-6072	318	1	+	+	NOUN
ejpam-6072	318	2	ri	ri	NOUN
ejpam-6072	318	3	)	)	PUNCT
ejpam-6072	318	4	=	=	SYM
ejpam-6072	318	5	0	0	NUM
ejpam-6072	318	6	,	,	PUNCT
ejpam-6072	318	7	for	for	ADP
ejpam-6072	318	8	i	i	PROPN
ejpam-6072	319	1	=	=	NOUN
ejpam-6072	319	2	1	1	NUM
ejpam-6072	319	3	,	,	PUNCT
ejpam-6072	319	4	.	.	PUNCT
ejpam-6072	319	5	.	.	PUNCT
ejpam-6072	320	1	.	.	PUNCT
ejpam-6072	321	1	,	,	PUNCT
ejpam-6072	321	2	m	m	PROPN
ejpam-6072	321	3	,	,	PUNCT
ejpam-6072	321	4	which	which	PRON
ejpam-6072	321	5	are	be	AUX
ejpam-6072	321	6	equivalent	equivalent	ADJ
ejpam-6072	321	7	to	to	PART
ejpam-6072	321	8	(	(	PUNCT
ejpam-6072	321	9	βai	βai	NOUN
ejpam-6072	321	10	)	)	PUNCT
ejpam-6072	321	11	tp	tp	NOUN
ejpam-6072	322	1	+	+	CCONJ
ejpam-6072	322	2	p	p	X
ejpam-6072	322	3	(	(	PUNCT
ejpam-6072	322	4	βai	βai	NOUN
ejpam-6072	322	5	)	)	PUNCT
ejpam-6072	323	1	+	+	NUM
ejpam-6072	323	2	βq+	βq+	ADJ
ejpam-6072	323	3	p	p	X
ejpam-6072	323	4	(	(	PUNCT
ejpam-6072	323	5	βbi	βbi	NUM
ejpam-6072	323	6	)	)	PUNCT
ejpam-6072	324	1	q−1	q−1	PROPN
ejpam-6072	324	2	β	β	X
ejpam-6072	324	3	(	(	PUNCT
ejpam-6072	324	4	βbi	βbi	NUM
ejpam-6072	324	5	)	)	PUNCT
ejpam-6072	324	6	tp	tp	X
ejpam-6072	324	7	+	+	CCONJ
ejpam-6072	325	1	(	(	PUNCT
ejpam-6072	325	2	βri	βri	NOUN
ejpam-6072	325	3	)	)	PUNCT
ejpam-6072	325	4	=	=	SYM
ejpam-6072	325	5	0	0	NUM
ejpam-6072	325	6	,	,	PUNCT
ejpam-6072	325	7	for	for	ADP
ejpam-6072	325	8	i	i	PROPN
ejpam-6072	325	9	=	=	NOUN
ejpam-6072	325	10	1	1	NUM
ejpam-6072	325	11	,	,	PUNCT
ejpam-6072	325	12	.	.	PUNCT
ejpam-6072	325	13	.	.	PUNCT
ejpam-6072	325	14	.	.	PUNCT
ejpam-6072	326	1	,	,	PUNCT
ejpam-6072	326	2	m.	m.	NOUN
ejpam-6072	326	3	this	this	PRON
ejpam-6072	326	4	implies	imply	VERB
ejpam-6072	326	5	that	that	SCONJ
ejpam-6072	326	6	the	the	DET
ejpam-6072	326	7	pair	pair	NOUN
ejpam-6072	326	8	(	(	PUNCT
ejpam-6072	326	9	p	p	X
ejpam-6072	326	10	,	,	PUNCT
ejpam-6072	326	11	βq	βq	ADJ
ejpam-6072	326	12	)	)	PUNCT
ejpam-6072	326	13	is	be	AUX
ejpam-6072	326	14	a	a	DET
ejpam-6072	326	15	common	common	ADJ
ejpam-6072	326	16	riccati	riccati	NOUN
ejpam-6072	326	17	solution	solution	NOUN
ejpam-6072	326	18	for	for	ADP
ejpam-6072	326	19	the	the	DET
ejpam-6072	326	20	family	family	NOUN
ejpam-6072	326	21	v.	v.	ADP
ejpam-6072	326	22	theorem	theorem	ADJ
ejpam-6072	326	23	6	6	NUM
ejpam-6072	326	24	.	.	X
ejpam-6072	327	1	for	for	ADP
ejpam-6072	327	2	i	i	PRON
ejpam-6072	327	3	=	=	NOUN
ejpam-6072	327	4	1	1	NUM
ejpam-6072	327	5	,	,	PUNCT
ejpam-6072	327	6	.	.	PUNCT
ejpam-6072	327	7	.	.	PUNCT
ejpam-6072	327	8	.	.	PUNCT
ejpam-6072	328	1	,	,	PUNCT
ejpam-6072	328	2	m	m	VERB
ejpam-6072	328	3	,	,	PUNCT
ejpam-6072	328	4	suppose	suppose	VERB
ejpam-6072	328	5	that	that	SCONJ
ejpam-6072	328	6	ai	ai	VERB
ejpam-6072	328	7	,	,	PUNCT
ejpam-6072	328	8	bi	bi	NOUN
ejpam-6072	328	9	∈	∈	PROPN
ejpam-6072	328	10	rn×n	rn×n	NOUN
ejpam-6072	328	11	.	.	PUNCT
ejpam-6072	329	1	if	if	SCONJ
ejpam-6072	329	2	the	the	DET
ejpam-6072	329	3	family	family	NOUN
ejpam-6072	329	4	u	u	NOUN
ejpam-6072	329	5	=	=	PRON
ejpam-6072	329	6	{	{	PUNCT
ejpam-6072	329	7	(	(	PUNCT
ejpam-6072	329	8	ai	ai	PROPN
ejpam-6072	329	9	,	,	PUNCT
ejpam-6072	329	10	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	329	11	has	have	VERB
ejpam-6072	329	12	common	common	ADJ
ejpam-6072	329	13	riccati	riccati	NOUN
ejpam-6072	329	14	stability	stability	NOUN
ejpam-6072	329	15	,	,	PUNCT
ejpam-6072	329	16	then	then	ADV
ejpam-6072	329	17	for	for	ADP
ejpam-6072	329	18	any	any	DET
ejpam-6072	329	19	nonsingular	nonsingular	ADJ
ejpam-6072	329	20	matrix	matrix	NOUN
ejpam-6072	329	21	h	h	NOUN
ejpam-6072	329	22	∈	∈	PROPN
ejpam-6072	329	23	rn×n	rn×n	NOUN
ejpam-6072	329	24	,	,	PUNCT
ejpam-6072	329	25	the	the	DET
ejpam-6072	329	26	pair	pair	NOUN
ejpam-6072	329	27	(	(	PUNCT
ejpam-6072	329	28	h−tph−1	h−tph−1	NOUN
ejpam-6072	329	29	,	,	PUNCT
ejpam-6072	329	30	h−tqh−1	h−tqh−1	NOUN
ejpam-6072	329	31	)	)	PUNCT
ejpam-6072	329	32	is	be	AUX
ejpam-6072	329	33	a	a	DET
ejpam-6072	329	34	common	common	ADJ
ejpam-6072	329	35	riccati	riccati	NOUN
ejpam-6072	329	36	solution	solution	NOUN
ejpam-6072	329	37	for	for	ADP
ejpam-6072	329	38	the	the	DET
ejpam-6072	329	39	family	family	NOUN
ejpam-6072	329	40	v	v	NOUN
ejpam-6072	329	41	=	=	SYM
ejpam-6072	329	42	{	{	PUNCT
ejpam-6072	329	43	(	(	PUNCT
ejpam-6072	329	44	haih	haih	NOUN
ejpam-6072	329	45	−1	−1	NOUN
ejpam-6072	329	46	,	,	PUNCT
ejpam-6072	329	47	hbih	hbih	VERB
ejpam-6072	329	48	−1)}mi=1	−1)}mi=1	X
ejpam-6072	329	49	.	.	PUNCT
ejpam-6072	330	1	proof	proof	NOUN
ejpam-6072	330	2	.	.	PUNCT
ejpam-6072	331	1	suppose	suppose	VERB
ejpam-6072	331	2	that	that	SCONJ
ejpam-6072	331	3	(	(	PUNCT
ejpam-6072	331	4	p	p	X
ejpam-6072	331	5	,	,	PUNCT
ejpam-6072	331	6	q	q	NOUN
ejpam-6072	331	7	)	)	PUNCT
ejpam-6072	331	8	is	be	AUX
ejpam-6072	331	9	a	a	DET
ejpam-6072	331	10	common	common	ADJ
ejpam-6072	331	11	riccati	riccati	NOUN
ejpam-6072	331	12	solution	solution	NOUN
ejpam-6072	331	13	for	for	ADP
ejpam-6072	331	14	the	the	DET
ejpam-6072	331	15	u	u	NOUN
ejpam-6072	331	16	.	.	PUNCT
ejpam-6072	332	1	thus	thus	ADV
ejpam-6072	332	2	,	,	PUNCT
ejpam-6072	332	3	there	there	PRON
ejpam-6072	332	4	are	be	VERB
ejpam-6072	332	5	positive	positive	ADJ
ejpam-6072	332	6	definite	definite	ADJ
ejpam-6072	332	7	matrices	matrix	NOUN
ejpam-6072	332	8	r1	r1	NOUN
ejpam-6072	332	9	,	,	PUNCT
ejpam-6072	332	10	.	.	PUNCT
ejpam-6072	332	11	.	.	PUNCT
ejpam-6072	333	1	.	.	PUNCT
ejpam-6072	334	1	,	,	PUNCT
ejpam-6072	334	2	rm	rm	PROPN
ejpam-6072	334	3	∈	∈	PROPN
ejpam-6072	334	4	rn×n	rn×n	PROPN
ejpam-6072	334	5	satisfying	satisfy	VERB
ejpam-6072	334	6	at	at	ADP
ejpam-6072	334	7	i	i	PROPN
ejpam-6072	334	8	p	p	PROPN
ejpam-6072	335	1	+	+	CCONJ
ejpam-6072	335	2	pai	pai	PROPN
ejpam-6072	335	3	+	+	PROPN
ejpam-6072	335	4	q+	q+	ADP
ejpam-6072	335	5	pbiq	pbiq	PROPN
ejpam-6072	336	1	−1bt	−1bt	ADP
ejpam-6072	336	2	i	i	PRON
ejpam-6072	336	3	p	p	X
ejpam-6072	337	1	+	+	PROPN
ejpam-6072	337	2	ri	ri	NOUN
ejpam-6072	337	3	=	=	SYM
ejpam-6072	337	4	0	0	NUM
ejpam-6072	337	5	,	,	PUNCT
ejpam-6072	337	6	for	for	ADP
ejpam-6072	337	7	i	i	PROPN
ejpam-6072	337	8	=	=	NOUN
ejpam-6072	337	9	1	1	NUM
ejpam-6072	337	10	,	,	PUNCT
ejpam-6072	337	11	.	.	PUNCT
ejpam-6072	337	12	.	.	PUNCT
ejpam-6072	338	1	.	.	PUNCT
ejpam-6072	339	1	,	,	PUNCT
ejpam-6072	339	2	m.	m.	NOUN
ejpam-6072	339	3	consequently	consequently	ADV
ejpam-6072	339	4	,	,	PUNCT
ejpam-6072	339	5	h−t	h−t	NOUN
ejpam-6072	339	6	(	(	PUNCT
ejpam-6072	339	7	at	at	ADP
ejpam-6072	339	8	i	i	PRON
ejpam-6072	339	9	p	p	PROPN
ejpam-6072	340	1	+	+	CCONJ
ejpam-6072	340	2	pai	pai	PROPN
ejpam-6072	340	3	+	+	PROPN
ejpam-6072	340	4	q+	q+	ADP
ejpam-6072	340	5	pbiq	pbiq	PROPN
ejpam-6072	341	1	−1bt	−1bt	ADP
ejpam-6072	341	2	i	i	PRON
ejpam-6072	341	3	p	p	X
ejpam-6072	342	1	+	+	NOUN
ejpam-6072	342	2	ri)h	ri)h	NOUN
ejpam-6072	342	3	−1	−1	NOUN
ejpam-6072	342	4	=	=	SYM
ejpam-6072	342	5	0	0	NUM
ejpam-6072	342	6	,	,	PUNCT
ejpam-6072	342	7	for	for	ADP
ejpam-6072	342	8	all	all	DET
ejpam-6072	342	9	i	i	PRON
ejpam-6072	342	10	,	,	PUNCT
ejpam-6072	342	11	and	and	CCONJ
ejpam-6072	342	12	therefore	therefore	ADV
ejpam-6072	342	13	,	,	PUNCT
ejpam-6072	342	14	we	we	PRON
ejpam-6072	342	15	have	have	VERB
ejpam-6072	342	16	h−tat	h−tat	NOUN
ejpam-6072	342	17	i	i	PRON
ejpam-6072	342	18	ph−1	ph−1	VERB
ejpam-6072	342	19	+	+	NOUN
ejpam-6072	342	20	h−tpaih	h−tpaih	NOUN
ejpam-6072	342	21	−1	−1	NOUN
ejpam-6072	343	1	+	+	NOUN
ejpam-6072	343	2	h−tqh−1	h−tqh−1	X
ejpam-6072	343	3	+	+	ADJ
ejpam-6072	343	4	h−tpbiq	h−tpbiq	NOUN
ejpam-6072	343	5	−1bt	−1bt	VERB
ejpam-6072	343	6	i	i	PRON
ejpam-6072	343	7	ph−1	ph−1	VERB
ejpam-6072	343	8	+	+	NOUN
ejpam-6072	343	9	h−trih	h−trih	X
ejpam-6072	343	10	−1	−1	NOUN
ejpam-6072	343	11	=	=	SYM
ejpam-6072	343	12	0	0	PROPN
ejpam-6072	343	13	.	.	PUNCT
ejpam-6072	343	14	a.	a.	PROPN
ejpam-6072	343	15	algefary	algefary	PROPN
ejpam-6072	343	16	,	,	PUNCT
ejpam-6072	343	17	k.	k.	PROPN
ejpam-6072	343	18	a.	a.	PROPN
ejpam-6072	343	19	alqufari	alqufari	PROPN
ejpam-6072	343	20	/	/	SYM
ejpam-6072	343	21	eur	eur	PROPN
ejpam-6072	343	22	.	.	PUNCT
ejpam-6072	344	1	j.	j.	PROPN
ejpam-6072	344	2	pure	pure	PROPN
ejpam-6072	344	3	appl	appl	PROPN
ejpam-6072	344	4	.	.	PROPN
ejpam-6072	344	5	math	math	PROPN
ejpam-6072	344	6	,	,	PUNCT
ejpam-6072	344	7	18	18	NUM
ejpam-6072	344	8	(	(	PUNCT
ejpam-6072	344	9	2	2	NUM
ejpam-6072	344	10	)	)	PUNCT
ejpam-6072	344	11	(	(	PUNCT
ejpam-6072	344	12	2025	2025	NUM
ejpam-6072	344	13	)	)	PUNCT
ejpam-6072	344	14	,	,	PUNCT
ejpam-6072	344	15	6072	6072	NUM
ejpam-6072	344	16	11	11	NUM
ejpam-6072	344	17	of	of	ADP
ejpam-6072	344	18	14	14	NUM
ejpam-6072	344	19	therefore	therefore	ADV
ejpam-6072	344	20	,	,	PUNCT
ejpam-6072	344	21	we	we	PRON
ejpam-6072	344	22	get	get	VERB
ejpam-6072	344	23	that	that	DET
ejpam-6072	344	24	(	(	PUNCT
ejpam-6072	344	25	haih	haih	NOUN
ejpam-6072	344	26	−1)th−tph−1	−1)th−tph−1	X
ejpam-6072	344	27	+	+	ADJ
ejpam-6072	344	28	h−tph−1(haih	h−tph−1(haih	ADJ
ejpam-6072	344	29	−1	−1	NOUN
ejpam-6072	344	30	)	)	PUNCT
ejpam-6072	345	1	+	+	PUNCT
ejpam-6072	345	2	h−tqh−1	h−tqh−1	NOUN
ejpam-6072	345	3	+	+	SYM
ejpam-6072	345	4	h−tph−1(hbih	h−tph−1(hbih	ADJ
ejpam-6072	345	5	−1)(h−tqh−1)−1(hbih	−1)(h−tqh−1)−1(hbih	NOUN
ejpam-6072	345	6	−1)th−tph−1	−1)th−tph−1	VERB
ejpam-6072	346	1	+	+	NOUN
ejpam-6072	346	2	h−trih	h−trih	X
ejpam-6072	346	3	−1	−1	NOUN
ejpam-6072	346	4	=	=	SYM
ejpam-6072	346	5	0	0	NUM
ejpam-6072	346	6	,	,	PUNCT
ejpam-6072	346	7	for	for	ADP
ejpam-6072	346	8	all	all	DET
ejpam-6072	346	9	i.	i.	NOUN
ejpam-6072	346	10	this	this	PRON
ejpam-6072	346	11	means	mean	VERB
ejpam-6072	346	12	that	that	SCONJ
ejpam-6072	346	13	the	the	DET
ejpam-6072	346	14	pair	pair	NOUN
ejpam-6072	346	15	(	(	PUNCT
ejpam-6072	346	16	h−tph−1	h−tph−1	NOUN
ejpam-6072	346	17	,	,	PUNCT
ejpam-6072	346	18	h−tqh−1	h−tqh−1	NOUN
ejpam-6072	346	19	)	)	PUNCT
ejpam-6072	346	20	is	be	AUX
ejpam-6072	346	21	a	a	DET
ejpam-6072	346	22	common	common	ADJ
ejpam-6072	346	23	riccati	riccati	NOUN
ejpam-6072	346	24	solution	solution	NOUN
ejpam-6072	346	25	for	for	ADP
ejpam-6072	346	26	the	the	DET
ejpam-6072	346	27	family	family	NOUN
ejpam-6072	346	28	v.	v.	ADP
ejpam-6072	346	29	theorem	theorem	ADJ
ejpam-6072	346	30	7	7	NUM
ejpam-6072	346	31	.	.	X
ejpam-6072	347	1	for	for	ADP
ejpam-6072	347	2	i	i	PRON
ejpam-6072	347	3	=	=	NOUN
ejpam-6072	347	4	1	1	NUM
ejpam-6072	347	5	,	,	PUNCT
ejpam-6072	347	6	.	.	PUNCT
ejpam-6072	347	7	.	.	PUNCT
ejpam-6072	347	8	.	.	PUNCT
ejpam-6072	348	1	,	,	PUNCT
ejpam-6072	348	2	m	m	VERB
ejpam-6072	348	3	,	,	PUNCT
ejpam-6072	348	4	suppose	suppose	VERB
ejpam-6072	348	5	that	that	SCONJ
ejpam-6072	348	6	ai	ai	VERB
ejpam-6072	348	7	,	,	PUNCT
ejpam-6072	348	8	bi	bi	NOUN
ejpam-6072	348	9	∈	∈	PROPN
ejpam-6072	348	10	rn×n	rn×n	PROPN
ejpam-6072	348	11	provided	provide	VERB
ejpam-6072	348	12	that	that	SCONJ
ejpam-6072	348	13	bi	bi	NOUN
ejpam-6072	348	14	have	have	VERB
ejpam-6072	348	15	full	full	ADJ
ejpam-6072	348	16	rank	rank	NOUN
ejpam-6072	348	17	for	for	ADP
ejpam-6072	348	18	all	all	DET
ejpam-6072	348	19	i.	i.	NOUN
ejpam-6072	348	20	if	if	SCONJ
ejpam-6072	348	21	the	the	DET
ejpam-6072	348	22	family	family	NOUN
ejpam-6072	348	23	u	u	NOUN
ejpam-6072	348	24	=	=	PRON
ejpam-6072	348	25	{	{	PUNCT
ejpam-6072	348	26	(	(	PUNCT
ejpam-6072	348	27	ai	ai	PROPN
ejpam-6072	348	28	,	,	PUNCT
ejpam-6072	348	29	bi)}mi=1	bi)}mi=1	NOUN
ejpam-6072	348	30	has	have	VERB
ejpam-6072	348	31	common	common	ADJ
ejpam-6072	348	32	riccati	riccati	NOUN
ejpam-6072	348	33	stability	stability	NOUN
ejpam-6072	348	34	,	,	PUNCT
ejpam-6072	348	35	then	then	ADV
ejpam-6072	348	36	the	the	DET
ejpam-6072	348	37	family	family	NOUN
ejpam-6072	348	38	v	v	NOUN
ejpam-6072	348	39	=	=	SYM
ejpam-6072	348	40	{	{	PUNCT
ejpam-6072	348	41	(	(	PUNCT
ejpam-6072	348	42	at	at	ADP
ejpam-6072	348	43	i	i	PRON
ejpam-6072	348	44	,	,	PUNCT
ejpam-6072	348	45	b	b	PROPN
ejpam-6072	348	46	t	t	X
ejpam-6072	348	47	i	i	NOUN
ejpam-6072	348	48	)	)	PUNCT
ejpam-6072	348	49	}	}	PUNCT
ejpam-6072	348	50	mi=1	mi=1	PROPN
ejpam-6072	348	51	has	have	VERB
ejpam-6072	348	52	common	common	ADJ
ejpam-6072	348	53	riccati	riccati	NOUN
ejpam-6072	348	54	stability	stability	NOUN
ejpam-6072	348	55	proof	proof	NOUN
ejpam-6072	348	56	.	.	PUNCT
ejpam-6072	349	1	let	let	VERB
ejpam-6072	349	2	(	(	PUNCT
ejpam-6072	349	3	p	p	X
ejpam-6072	349	4	,	,	PUNCT
ejpam-6072	349	5	q	q	NOUN
ejpam-6072	349	6	)	)	PUNCT
ejpam-6072	349	7	be	be	AUX
ejpam-6072	349	8	the	the	DET
ejpam-6072	349	9	common	common	ADJ
ejpam-6072	349	10	riccati	riccati	NOUN
ejpam-6072	349	11	solution	solution	NOUN
ejpam-6072	349	12	for	for	ADP
ejpam-6072	349	13	u	u	PROPN
ejpam-6072	349	14	,	,	PUNCT
ejpam-6072	349	15	i.e.	i.e.	X
ejpam-6072	349	16	,	,	PUNCT
ejpam-6072	349	17	there	there	PRON
ejpam-6072	349	18	are	be	VERB
ejpam-6072	349	19	positive	positive	ADJ
ejpam-6072	349	20	definte	definte	NOUN
ejpam-6072	349	21	ri	ri	PROPN
ejpam-6072	349	22	∈	∈	PROPN
ejpam-6072	349	23	rn×n	rn×n	PROPN
ejpam-6072	349	24	,	,	PUNCT
ejpam-6072	349	25	i	i	PRON
ejpam-6072	349	26	=	=	NOUN
ejpam-6072	349	27	1	1	NUM
ejpam-6072	349	28	,	,	PUNCT
ejpam-6072	349	29	.	.	PUNCT
ejpam-6072	349	30	.	.	PUNCT
ejpam-6072	349	31	.	.	PUNCT
ejpam-6072	350	1	,	,	PUNCT
ejpam-6072	350	2	m	m	PROPN
ejpam-6072	350	3	,	,	PUNCT
ejpam-6072	350	4	such	such	ADJ
ejpam-6072	350	5	that	that	SCONJ
ejpam-6072	350	6	at	at	ADP
ejpam-6072	350	7	i	i	PRON
ejpam-6072	350	8	p	p	PROPN
ejpam-6072	351	1	+	+	CCONJ
ejpam-6072	351	2	pai	pai	PROPN
ejpam-6072	351	3	+	+	PROPN
ejpam-6072	351	4	q+	q+	ADP
ejpam-6072	351	5	pbiq	pbiq	PROPN
ejpam-6072	352	1	−1bt	−1bt	ADP
ejpam-6072	352	2	i	i	PRON
ejpam-6072	352	3	p	p	X
ejpam-6072	353	1	+	+	PROPN
ejpam-6072	353	2	ri	ri	NOUN
ejpam-6072	353	3	=	=	NOUN
ejpam-6072	353	4	0	0	PROPN
ejpam-6072	353	5	.	.	PUNCT
ejpam-6072	354	1	since	since	ADV
ejpam-6072	354	2	,	,	PUNCT
ejpam-6072	354	3	p	p	PROPN
ejpam-6072	354	4	≻	≻	PROPN
ejpam-6072	354	5	0	0	NUM
ejpam-6072	354	6	,	,	PUNCT
ejpam-6072	354	7	then	then	ADV
ejpam-6072	354	8	p−1	p−1	PROPN
ejpam-6072	354	9	exists	exist	VERB
ejpam-6072	354	10	.	.	PUNCT
ejpam-6072	355	1	thus	thus	ADV
ejpam-6072	355	2	,	,	PUNCT
ejpam-6072	355	3	by	by	ADP
ejpam-6072	355	4	pre	pre	ADJ
ejpam-6072	355	5	and	and	CCONJ
ejpam-6072	355	6	and	and	CCONJ
ejpam-6072	355	7	post	post	ADJ
ejpam-6072	355	8	-	-	ADJ
ejpam-6072	355	9	multiply	multiply	VERB
ejpam-6072	355	10	these	these	DET
ejpam-6072	355	11	last	last	ADJ
ejpam-6072	355	12	equations	equation	NOUN
ejpam-6072	355	13	,	,	PUNCT
ejpam-6072	355	14	we	we	PRON
ejpam-6072	355	15	obtain	obtain	VERB
ejpam-6072	355	16	p−1at	p−1at	ADJ
ejpam-6072	355	17	i	i	PRON
ejpam-6072	355	18	+	+	ADJ
ejpam-6072	355	19	aip	aip	NOUN
ejpam-6072	355	20	−1	−1	NOUN
ejpam-6072	355	21	+	+	CCONJ
ejpam-6072	355	22	p−1qp−1	p−1qp−1	ADJ
ejpam-6072	356	1	+	+	NOUN
ejpam-6072	356	2	biq	biq	NOUN
ejpam-6072	356	3	−1bt	−1bt	VERB
ejpam-6072	357	1	i	i	PRON
ejpam-6072	357	2	+	+	CCONJ
ejpam-6072	357	3	p−1rip	p−1rip	VERB
ejpam-6072	357	4	−1	−1	NOUN
ejpam-6072	357	5	=	=	SYM
ejpam-6072	357	6	0	0	X
ejpam-6072	357	7	.	.	PUNCT
ejpam-6072	358	1	define	define	VERB
ejpam-6072	358	2	p̂	p̂	X
ejpam-6072	358	3	=	=	PUNCT
ejpam-6072	358	4	p−1	p−1	PROPN
ejpam-6072	358	5	≻	≻	PROPN
ejpam-6072	358	6	0	0	NUM
ejpam-6072	358	7	,	,	PUNCT
ejpam-6072	358	8	q̂i	q̂i	X
ejpam-6072	358	9	=	=	SYM
ejpam-6072	358	10	biq	biq	NOUN
ejpam-6072	359	1	−1bt	−1bt	ADV
ejpam-6072	359	2	i	i	PRON
ejpam-6072	359	3	≻	≻	VERB
ejpam-6072	359	4	0	0	PUNCT
ejpam-6072	360	1	and	and	CCONJ
ejpam-6072	360	2	r̂i	r̂i	NOUN
ejpam-6072	360	3	=	=	PUNCT
ejpam-6072	361	1	p−1rip	p−1rip	NOUN
ejpam-6072	361	2	−1	−1	NOUN
ejpam-6072	361	3	≻	≻	NOUN
ejpam-6072	361	4	0	0	NUM
ejpam-6072	361	5	,	,	PUNCT
ejpam-6072	361	6	i	i	PRON
ejpam-6072	361	7	=	=	NOUN
ejpam-6072	361	8	1	1	NUM
ejpam-6072	361	9	,	,	PUNCT
ejpam-6072	361	10	.	.	PUNCT
ejpam-6072	361	11	.	.	PUNCT
ejpam-6072	362	1	.	.	PUNCT
ejpam-6072	363	1	,	,	PUNCT
ejpam-6072	363	2	m.	m.	NOUN
ejpam-6072	363	3	since	since	SCONJ
ejpam-6072	363	4	each	each	DET
ejpam-6072	363	5	bi	bi	NOUN
ejpam-6072	363	6	has	have	VERB
ejpam-6072	363	7	a	a	DET
ejpam-6072	363	8	full	full	ADJ
ejpam-6072	363	9	rank	rank	NOUN
ejpam-6072	363	10	,	,	PUNCT
ejpam-6072	363	11	then	then	ADV
ejpam-6072	363	12	b−1	b−1	PROPN
ejpam-6072	363	13	i	i	PRON
ejpam-6072	363	14	,	,	PUNCT
ejpam-6072	363	15	i	i	PRON
ejpam-6072	363	16	=	=	NOUN
ejpam-6072	363	17	1	1	NUM
ejpam-6072	363	18	,	,	PUNCT
ejpam-6072	363	19	.	.	PUNCT
ejpam-6072	363	20	.	.	PUNCT
ejpam-6072	363	21	.	.	PUNCT
ejpam-6072	364	1	,	,	PUNCT
ejpam-6072	364	2	m	m	PROPN
ejpam-6072	364	3	,	,	PUNCT
ejpam-6072	364	4	exists	exist	VERB
ejpam-6072	364	5	.	.	PUNCT
ejpam-6072	365	1	therefore	therefore	ADV
ejpam-6072	365	2	,	,	PUNCT
ejpam-6072	365	3	q̂i	q̂i	X
ejpam-6072	365	4	−1	−1	NOUN
ejpam-6072	365	5	’s	’s	ADV
ejpam-6072	365	6	are	be	AUX
ejpam-6072	365	7	defined	define	VERB
ejpam-6072	365	8	.	.	PUNCT
ejpam-6072	366	1	thus	thus	ADV
ejpam-6072	366	2	,	,	PUNCT
ejpam-6072	366	3	for	for	ADP
ejpam-6072	366	4	i	i	PROPN
ejpam-6072	366	5	=	=	NOUN
ejpam-6072	366	6	1	1	NUM
ejpam-6072	366	7	,	,	PUNCT
ejpam-6072	366	8	.	.	PUNCT
ejpam-6072	366	9	.	.	PUNCT
ejpam-6072	366	10	.	.	PUNCT
ejpam-6072	367	1	,	,	PUNCT
ejpam-6072	367	2	m	m	PROPN
ejpam-6072	367	3	,	,	PUNCT
ejpam-6072	367	4	the	the	DET
ejpam-6072	367	5	pair	pair	NOUN
ejpam-6072	367	6	(	(	PUNCT
ejpam-6072	367	7	p̂	p̂	X
ejpam-6072	367	8	,	,	PUNCT
ejpam-6072	367	9	q̂i	q̂i	CCONJ
ejpam-6072	367	10	)	)	PUNCT
ejpam-6072	367	11	is	be	AUX
ejpam-6072	367	12	a	a	DET
ejpam-6072	367	13	riccati	riccati	NOUN
ejpam-6072	367	14	solution	solution	NOUN
ejpam-6072	367	15	for	for	ADP
ejpam-6072	367	16	(	(	PUNCT
ejpam-6072	367	17	at	at	ADP
ejpam-6072	367	18	i	i	PRON
ejpam-6072	367	19	,	,	PUNCT
ejpam-6072	367	20	b	b	PROPN
ejpam-6072	367	21	t	t	X
ejpam-6072	367	22	i	i	NOUN
ejpam-6072	367	23	)	)	PUNCT
ejpam-6072	367	24	.	.	PUNCT
ejpam-6072	368	1	to	to	PART
ejpam-6072	368	2	see	see	VERB
ejpam-6072	368	3	this	this	PRON
ejpam-6072	368	4	,	,	PUNCT
ejpam-6072	368	5	for	for	ADP
ejpam-6072	368	6	each	each	DET
ejpam-6072	368	7	i	i	PRON
ejpam-6072	368	8	,	,	PUNCT
ejpam-6072	368	9	observe	observe	VERB
ejpam-6072	368	10	that	that	SCONJ
ejpam-6072	368	11	(	(	PUNCT
ejpam-6072	368	12	at	at	ADP
ejpam-6072	368	13	i	i	PRON
ejpam-6072	368	14	)	)	PUNCT
ejpam-6072	368	15	t	t	NOUN
ejpam-6072	368	16	p̂	p̂	NOUN
ejpam-6072	369	1	+	+	CCONJ
ejpam-6072	370	1	p̂at	p̂at	INTJ
ejpam-6072	370	2	i	i	X
ejpam-6072	370	3	+	+	CCONJ
ejpam-6072	370	4	q̂i	q̂i	X
ejpam-6072	370	5	+	+	CCONJ
ejpam-6072	370	6	p̂bt	p̂bt	ADJ
ejpam-6072	370	7	i	i	PROPN
ejpam-6072	370	8	q̂i	q̂i	X
ejpam-6072	370	9	−1	−1	VERB
ejpam-6072	370	10	(	(	PUNCT
ejpam-6072	370	11	bt	bt	NOUN
ejpam-6072	370	12	i	i	PROPN
ejpam-6072	370	13	)	)	PUNCT
ejpam-6072	370	14	t	t	NOUN
ejpam-6072	370	15	p̂	p̂	NOUN
ejpam-6072	370	16	+	+	CCONJ
ejpam-6072	370	17	r̂i	r̂i	NOUN
ejpam-6072	370	18	=	=	SYM
ejpam-6072	370	19	p−1at	p−1at	VERB
ejpam-6072	370	20	i	i	PRON
ejpam-6072	371	1	+	+	ADJ
ejpam-6072	371	2	aip	aip	NOUN
ejpam-6072	371	3	−1	−1	NOUN
ejpam-6072	371	4	+	+	CCONJ
ejpam-6072	371	5	p−1qp−1	p−1qp−1	ADJ
ejpam-6072	372	1	+	+	NOUN
ejpam-6072	372	2	biq	biq	NOUN
ejpam-6072	372	3	−1bt	−1bt	VERB
ejpam-6072	373	1	i	i	PRON
ejpam-6072	373	2	+	+	CCONJ
ejpam-6072	373	3	p−1rip	p−1rip	VERB
ejpam-6072	373	4	−1	−1	NOUN
ejpam-6072	373	5	.	.	PUNCT
ejpam-6072	374	1	the	the	DET
ejpam-6072	374	2	results	result	NOUN
ejpam-6072	374	3	presented	present	VERB
ejpam-6072	374	4	in	in	ADP
ejpam-6072	374	5	this	this	DET
ejpam-6072	374	6	section	section	NOUN
ejpam-6072	374	7	demonstrate	demonstrate	VERB
ejpam-6072	374	8	that	that	SCONJ
ejpam-6072	374	9	common	common	ADJ
ejpam-6072	374	10	riccati	riccati	NOUN
ejpam-6072	374	11	stability	stability	NOUN
ejpam-6072	374	12	is	be	AUX
ejpam-6072	374	13	preserved	preserve	VERB
ejpam-6072	374	14	under	under	ADP
ejpam-6072	374	15	scaling	scale	VERB
ejpam-6072	374	16	transformations	transformation	NOUN
ejpam-6072	374	17	and	and	CCONJ
ejpam-6072	374	18	similarity	similarity	NOUN
ejpam-6072	374	19	transformations	transformation	NOUN
ejpam-6072	374	20	.	.	PUNCT
ejpam-6072	375	1	these	these	DET
ejpam-6072	375	2	findings	finding	NOUN
ejpam-6072	375	3	underscore	underscore	VERB
ejpam-6072	375	4	the	the	DET
ejpam-6072	375	5	robustness	robustness	NOUN
ejpam-6072	375	6	of	of	ADP
ejpam-6072	375	7	riccati	riccati	NOUN
ejpam-6072	375	8	-	-	PUNCT
ejpam-6072	375	9	based	base	VERB
ejpam-6072	375	10	stability	stability	NOUN
ejpam-6072	375	11	criteria	criterion	NOUN
ejpam-6072	375	12	,	,	PUNCT
ejpam-6072	375	13	which	which	PRON
ejpam-6072	375	14	remain	remain	VERB
ejpam-6072	375	15	unaffected	unaffected	ADJ
ejpam-6072	375	16	by	by	ADP
ejpam-6072	375	17	coordinate	coordinate	NOUN
ejpam-6072	375	18	transformations	transformation	NOUN
ejpam-6072	375	19	or	or	CCONJ
ejpam-6072	375	20	uniform	uniform	ADJ
ejpam-6072	375	21	scaling	scaling	NOUN
ejpam-6072	375	22	of	of	ADP
ejpam-6072	375	23	system	system	NOUN
ejpam-6072	375	24	parameters	parameter	NOUN
ejpam-6072	375	25	.	.	PUNCT
ejpam-6072	376	1	by	by	ADP
ejpam-6072	376	2	establishing	establish	VERB
ejpam-6072	376	3	that	that	SCONJ
ejpam-6072	376	4	the	the	DET
ejpam-6072	376	5	riccati	riccati	PROPN
ejpam-6072	376	6	solution	solution	NOUN
ejpam-6072	376	7	remains	remain	VERB
ejpam-6072	376	8	valid	valid	ADJ
ejpam-6072	376	9	across	across	ADP
ejpam-6072	376	10	such	such	ADJ
ejpam-6072	376	11	transformations	transformation	NOUN
ejpam-6072	376	12	,	,	PUNCT
ejpam-6072	376	13	we	we	PRON
ejpam-6072	376	14	show	show	VERB
ejpam-6072	376	15	that	that	SCONJ
ejpam-6072	376	16	the	the	DET
ejpam-6072	376	17	proposed	propose	VERB
ejpam-6072	376	18	framework	framework	NOUN
ejpam-6072	376	19	is	be	AUX
ejpam-6072	376	20	not	not	PART
ejpam-6072	376	21	only	only	ADV
ejpam-6072	376	22	theoretically	theoretically	ADV
ejpam-6072	376	23	sound	sound	ADJ
ejpam-6072	376	24	but	but	CCONJ
ejpam-6072	376	25	also	also	ADV
ejpam-6072	376	26	practically	practically	ADV
ejpam-6072	376	27	applicable	applicable	ADJ
ejpam-6072	376	28	to	to	ADP
ejpam-6072	376	29	a	a	DET
ejpam-6072	376	30	wide	wide	ADJ
ejpam-6072	376	31	range	range	NOUN
ejpam-6072	376	32	of	of	ADP
ejpam-6072	376	33	control	control	NOUN
ejpam-6072	376	34	systems	system	NOUN
ejpam-6072	376	35	,	,	PUNCT
ejpam-6072	376	36	including	include	VERB
ejpam-6072	376	37	those	those	DET
ejpam-6072	376	38	subject	subject	ADJ
ejpam-6072	376	39	to	to	ADP
ejpam-6072	376	40	rescaling	rescaling	NOUN
ejpam-6072	376	41	or	or	CCONJ
ejpam-6072	376	42	changes	change	NOUN
ejpam-6072	376	43	in	in	ADP
ejpam-6072	376	44	system	system	NOUN
ejpam-6072	376	45	representation	representation	NOUN
ejpam-6072	376	46	.	.	PUNCT
ejpam-6072	377	1	a.	a.	PROPN
ejpam-6072	377	2	algefary	algefary	PROPN
ejpam-6072	377	3	,	,	PUNCT
ejpam-6072	377	4	k.	k.	PROPN
ejpam-6072	377	5	a.	a.	PROPN
ejpam-6072	377	6	alqufari	alqufari	PROPN
ejpam-6072	377	7	/	/	SYM
ejpam-6072	377	8	eur	eur	PROPN
ejpam-6072	377	9	.	.	PUNCT
ejpam-6072	378	1	j.	j.	PROPN
ejpam-6072	378	2	pure	pure	PROPN
ejpam-6072	378	3	appl	appl	PROPN
ejpam-6072	378	4	.	.	PROPN
ejpam-6072	378	5	math	math	PROPN
ejpam-6072	378	6	,	,	PUNCT
ejpam-6072	378	7	18	18	NUM
ejpam-6072	378	8	(	(	PUNCT
ejpam-6072	378	9	2	2	NUM
ejpam-6072	378	10	)	)	PUNCT
ejpam-6072	378	11	(	(	PUNCT
ejpam-6072	378	12	2025	2025	NUM
ejpam-6072	378	13	)	)	PUNCT
ejpam-6072	378	14	,	,	PUNCT
ejpam-6072	378	15	6072	6072	NUM
ejpam-6072	378	16	12	12	NUM
ejpam-6072	378	17	of	of	ADP
ejpam-6072	378	18	14	14	NUM
ejpam-6072	378	19	4	4	NUM
ejpam-6072	378	20	.	.	PUNCT
ejpam-6072	379	1	examples	example	NOUN
ejpam-6072	379	2	and	and	CCONJ
ejpam-6072	379	3	computational	computational	ADJ
ejpam-6072	379	4	verification	verification	NOUN
ejpam-6072	379	5	in	in	ADP
ejpam-6072	379	6	this	this	DET
ejpam-6072	379	7	section	section	NOUN
ejpam-6072	380	1	,	,	PUNCT
ejpam-6072	380	2	we	we	PRON
ejpam-6072	380	3	provide	provide	VERB
ejpam-6072	380	4	numerical	numerical	ADJ
ejpam-6072	380	5	examples	example	NOUN
ejpam-6072	380	6	to	to	PART
ejpam-6072	380	7	demonstrate	demonstrate	VERB
ejpam-6072	380	8	the	the	DET
ejpam-6072	380	9	practical	practical	ADJ
ejpam-6072	380	10	applicability	applicability	NOUN
ejpam-6072	380	11	of	of	ADP
ejpam-6072	380	12	the	the	DET
ejpam-6072	380	13	proposed	propose	VERB
ejpam-6072	380	14	stability	stability	NOUN
ejpam-6072	380	15	criteria	criterion	NOUN
ejpam-6072	380	16	.	.	PUNCT
ejpam-6072	381	1	example	example	NOUN
ejpam-6072	382	1	1	1	NUM
ejpam-6072	382	2	.	.	X
ejpam-6072	382	3	consider	consider	VERB
ejpam-6072	382	4	the	the	DET
ejpam-6072	382	5	family	family	NOUN
ejpam-6072	382	6	u	u	NOUN
ejpam-6072	382	7	=	=	PRON
ejpam-6072	382	8	{	{	PUNCT
ejpam-6072	382	9	(	(	PUNCT
ejpam-6072	382	10	ai	ai	PROPN
ejpam-6072	382	11	,	,	PUNCT
ejpam-6072	382	12	bi)}2i=1	bi)}2i=1	PRON
ejpam-6072	382	13	,	,	PUNCT
ejpam-6072	382	14	where	where	SCONJ
ejpam-6072	382	15	a1	a1	NOUN
ejpam-6072	382	16	=	=	PUNCT
ejpam-6072	382	17	[	[	PUNCT
ejpam-6072	382	18	−2	−2	NOUN
ejpam-6072	382	19	1	1	NUM
ejpam-6072	382	20	0	0	NUM
ejpam-6072	382	21	−3	−3	NOUN
ejpam-6072	382	22	]	]	PUNCT
ejpam-6072	382	23	,	,	PUNCT
ejpam-6072	382	24	a2	a2	PROPN
ejpam-6072	382	25	=	=	PUNCT
ejpam-6072	382	26	[	[	PUNCT
ejpam-6072	382	27	−1	−1	NOUN
ejpam-6072	382	28	1	1	NUM
ejpam-6072	382	29	0	0	NUM
ejpam-6072	382	30	−4	−4	X
ejpam-6072	382	31	]	]	PUNCT
ejpam-6072	382	32	,	,	PUNCT
ejpam-6072	382	33	b1	b1	NOUN
ejpam-6072	382	34	=	=	PUNCT
ejpam-6072	382	35	[	[	PUNCT
ejpam-6072	382	36	0.1	0.1	NUM
ejpam-6072	382	37	0	0	NUM
ejpam-6072	382	38	0	0	NUM
ejpam-6072	382	39	0.003	0.003	NUM
ejpam-6072	382	40	]	]	PUNCT
ejpam-6072	382	41	,	,	PUNCT
ejpam-6072	382	42	and	and	CCONJ
ejpam-6072	382	43	b2	b2	NOUN
ejpam-6072	382	44	=	=	PUNCT
ejpam-6072	382	45	[	[	PUNCT
ejpam-6072	382	46	0.02	0.02	NUM
ejpam-6072	382	47	−0.019	−0.019	NOUN
ejpam-6072	382	48	0	0	NUM
ejpam-6072	382	49	0.23	0.23	NUM
ejpam-6072	382	50	]	]	PUNCT
ejpam-6072	382	51	.	.	PUNCT
ejpam-6072	383	1	it	it	PRON
ejpam-6072	383	2	can	can	AUX
ejpam-6072	383	3	be	be	AUX
ejpam-6072	383	4	easily	easily	ADV
ejpam-6072	383	5	verified	verify	VERB
ejpam-6072	383	6	that	that	SCONJ
ejpam-6072	383	7	p	p	X
ejpam-6072	383	8	=	=	X
ejpam-6072	383	9	[	[	PUNCT
ejpam-6072	383	10	2	2	NUM
ejpam-6072	383	11	1	1	NUM
ejpam-6072	383	12	]	]	PUNCT
ejpam-6072	383	13	and	and	CCONJ
ejpam-6072	383	14	q	q	NOUN
ejpam-6072	383	15	=	=	X
ejpam-6072	383	16	[	[	PUNCT
ejpam-6072	383	17	0.1	0.1	NUM
ejpam-6072	383	18	0.1	0.1	NUM
ejpam-6072	383	19	]	]	PUNCT
ejpam-6072	383	20	form	form	VERB
ejpam-6072	383	21	a	a	DET
ejpam-6072	383	22	common	common	ADJ
ejpam-6072	383	23	riccati	riccati	NOUN
ejpam-6072	383	24	solution	solution	NOUN
ejpam-6072	383	25	for	for	ADP
ejpam-6072	383	26	u	u	PROPN
ejpam-6072	383	27	.	.	PUNCT
ejpam-6072	384	1	a	a	DET
ejpam-6072	384	2	simple	simple	ADJ
ejpam-6072	384	3	calculation	calculation	NOUN
ejpam-6072	384	4	shows	show	VERB
ejpam-6072	384	5	that	that	SCONJ
ejpam-6072	384	6	p	p	NOUN
ejpam-6072	384	7	is	be	AUX
ejpam-6072	384	8	a	a	DET
ejpam-6072	384	9	common	common	ADJ
ejpam-6072	384	10	lyapunov	lyapunov	ADJ
ejpam-6072	384	11	solution	solution	NOUN
ejpam-6072	384	12	for	for	ADP
ejpam-6072	384	13	the	the	DET
ejpam-6072	384	14	family	family	NOUN
ejpam-6072	385	1	a	a	X
ejpam-6072	385	2	=	=	X
ejpam-6072	385	3	{	{	PUNCT
ejpam-6072	385	4	ai}2i=1	ai}2i=1	ADV
ejpam-6072	385	5	and	and	CCONJ
ejpam-6072	385	6	q−1	q−1	PROPN
ejpam-6072	385	7	is	be	AUX
ejpam-6072	385	8	a	a	DET
ejpam-6072	385	9	common	common	ADJ
ejpam-6072	385	10	schur	schur	NOUN
ejpam-6072	385	11	solution	solution	NOUN
ejpam-6072	385	12	for	for	ADP
ejpam-6072	385	13	the	the	DET
ejpam-6072	385	14	family	family	NOUN
ejpam-6072	385	15	{	{	PUNCT
ejpam-6072	385	16	a−1	a−1	PROPN
ejpam-6072	385	17	i	i	PRON
ejpam-6072	385	18	bi}2i=1	bi}2i=1	VERB
ejpam-6072	385	19	,	,	PUNCT
ejpam-6072	385	20	verifying	verify	VERB
ejpam-6072	385	21	theorems	theorem	NOUN
ejpam-6072	385	22	1	1	NUM
ejpam-6072	385	23	and	and	CCONJ
ejpam-6072	385	24	2	2	NUM
ejpam-6072	385	25	.	.	NOUN
ejpam-6072	385	26	example	example	NOUN
ejpam-6072	385	27	2	2	NUM
ejpam-6072	385	28	.	.	X
ejpam-6072	385	29	consider	consider	VERB
ejpam-6072	385	30	the	the	DET
ejpam-6072	385	31	family	family	NOUN
ejpam-6072	385	32	given	give	VERB
ejpam-6072	385	33	in	in	ADP
ejpam-6072	385	34	example	example	NOUN
ejpam-6072	385	35	1	1	NUM
ejpam-6072	385	36	.	.	PUNCT
ejpam-6072	386	1	a	a	DET
ejpam-6072	386	2	simple	simple	ADJ
ejpam-6072	386	3	calculation	calculation	NOUN
ejpam-6072	386	4	shows	show	VERB
ejpam-6072	386	5	that	that	SCONJ
ejpam-6072	386	6	the	the	DET
ejpam-6072	386	7	matrix	matrix	NOUN
ejpam-6072	386	8	p	p	NOUN
ejpam-6072	386	9	and	and	CCONJ
ejpam-6072	386	10	q̄	q̄	ADJ
ejpam-6072	386	11	=	=	PUNCT
ejpam-6072	386	12	[	[	PUNCT
ejpam-6072	386	13	0.1β	0.1β	NOUN
ejpam-6072	386	14	0.1β	0.1β	NOUN
ejpam-6072	386	15	]	]	PUNCT
ejpam-6072	386	16	form	form	VERB
ejpam-6072	386	17	a	a	DET
ejpam-6072	386	18	common	common	ADJ
ejpam-6072	386	19	riccati	riccati	NOUN
ejpam-6072	386	20	solution	solution	NOUN
ejpam-6072	386	21	for	for	ADP
ejpam-6072	386	22	the	the	DET
ejpam-6072	386	23	family	family	NOUN
ejpam-6072	386	24	v	v	NOUN
ejpam-6072	386	25	=	=	SYM
ejpam-6072	386	26	{	{	PUNCT
ejpam-6072	386	27	(	(	PUNCT
ejpam-6072	386	28	βai	βai	NOUN
ejpam-6072	386	29	,	,	PUNCT
ejpam-6072	386	30	βbi)}2i=1	βbi)}2i=1	PUNCT
ejpam-6072	386	31	for	for	ADP
ejpam-6072	386	32	any	any	DET
ejpam-6072	386	33	β	β	X
ejpam-6072	386	34	>	>	X
ejpam-6072	386	35	0	0	NUM
ejpam-6072	386	36	,	,	PUNCT
ejpam-6072	386	37	as	as	SCONJ
ejpam-6072	386	38	asserted	assert	VERB
ejpam-6072	386	39	by	by	ADP
ejpam-6072	386	40	theorem	theorem	NOUN
ejpam-6072	386	41	5	5	NUM
ejpam-6072	386	42	.	.	NOUN
ejpam-6072	386	43	example	example	NOUN
ejpam-6072	386	44	3	3	X
ejpam-6072	386	45	.	.	X
ejpam-6072	386	46	consider	consider	VERB
ejpam-6072	386	47	the	the	DET
ejpam-6072	386	48	nonsingular	nonsingular	ADJ
ejpam-6072	386	49	matrix	matrix	NOUN
ejpam-6072	386	50	h	h	NOUN
ejpam-6072	387	1	=	=	PUNCT
ejpam-6072	388	1	[	[	PUNCT
ejpam-6072	388	2	1	1	NUM
ejpam-6072	388	3	1	1	NUM
ejpam-6072	388	4	0	0	NUM
ejpam-6072	388	5	1	1	NUM
ejpam-6072	388	6	]	]	PUNCT
ejpam-6072	388	7	,	,	PUNCT
ejpam-6072	388	8	and	and	CCONJ
ejpam-6072	388	9	the	the	DET
ejpam-6072	388	10	family	family	NOUN
ejpam-6072	388	11	u	u	NOUN
ejpam-6072	388	12	from	from	ADP
ejpam-6072	388	13	example	example	NOUN
ejpam-6072	388	14	1	1	NUM
ejpam-6072	388	15	.	.	PUNCT
ejpam-6072	389	1	a	a	DET
ejpam-6072	389	2	straightforward	straightforward	ADJ
ejpam-6072	389	3	calculation	calculation	NOUN
ejpam-6072	389	4	shows	show	VERB
ejpam-6072	389	5	that	that	SCONJ
ejpam-6072	389	6	the	the	DET
ejpam-6072	389	7	pair	pair	NOUN
ejpam-6072	389	8	p1	p1	NOUN
ejpam-6072	389	9	=	=	PUNCT
ejpam-6072	389	10	h−tph−1	h−tph−1	X
ejpam-6072	390	1	=	=	PUNCT
ejpam-6072	391	1	[	[	PUNCT
ejpam-6072	391	2	2	2	NUM
ejpam-6072	391	3	−2	−2	NOUN
ejpam-6072	391	4	−2	−2	NOUN
ejpam-6072	391	5	3	3	NUM
ejpam-6072	391	6	]	]	PUNCT
ejpam-6072	391	7	≻	≻	X
ejpam-6072	391	8	0	0	NUM
ejpam-6072	391	9	and	and	CCONJ
ejpam-6072	391	10	q1	q1	PROPN
ejpam-6072	391	11	=	=	PUNCT
ejpam-6072	391	12	h−tqh−1	h−tqh−1	NOUN
ejpam-6072	392	1	=	=	PUNCT
ejpam-6072	392	2	[	[	PUNCT
ejpam-6072	392	3	0.1	0.1	NUM
ejpam-6072	392	4	−0.1	−0.1	NOUN
ejpam-6072	392	5	−0.1	−0.1	PROPN
ejpam-6072	392	6	0.2	0.2	NUM
ejpam-6072	392	7	]	]	PUNCT
ejpam-6072	392	8	≻	≻	X
ejpam-6072	392	9	0	0	NUM
ejpam-6072	392	10	form	form	VERB
ejpam-6072	392	11	a	a	DET
ejpam-6072	392	12	common	common	ADJ
ejpam-6072	392	13	riccati	riccati	NOUN
ejpam-6072	392	14	solution	solution	NOUN
ejpam-6072	392	15	for	for	ADP
ejpam-6072	392	16	the	the	DET
ejpam-6072	392	17	transformed	transform	VERB
ejpam-6072	392	18	family	family	NOUN
ejpam-6072	392	19	v	v	NOUN
ejpam-6072	392	20	=	=	SYM
ejpam-6072	392	21	{	{	PUNCT
ejpam-6072	392	22	(	(	PUNCT
ejpam-6072	392	23	haih	haih	NOUN
ejpam-6072	392	24	−1	−1	NOUN
ejpam-6072	392	25	,	,	PUNCT
ejpam-6072	392	26	hbih	hbih	VERB
ejpam-6072	392	27	−1)}2i=1	−1)}2i=1	ADJ
ejpam-6072	392	28	.	.	PUNCT
ejpam-6072	393	1	this	this	DET
ejpam-6072	393	2	result	result	NOUN
ejpam-6072	393	3	is	be	AUX
ejpam-6072	393	4	consistent	consistent	ADJ
ejpam-6072	393	5	with	with	ADP
ejpam-6072	393	6	theorem	theorem	ADJ
ejpam-6072	393	7	6	6	NUM
ejpam-6072	393	8	,	,	PUNCT
ejpam-6072	393	9	which	which	PRON
ejpam-6072	393	10	asserts	assert	VERB
ejpam-6072	393	11	that	that	SCONJ
ejpam-6072	393	12	common	common	ADJ
ejpam-6072	393	13	riccati	riccati	NOUN
ejpam-6072	393	14	stability	stability	NOUN
ejpam-6072	393	15	is	be	AUX
ejpam-6072	393	16	preserved	preserve	VERB
ejpam-6072	393	17	under	under	ADP
ejpam-6072	393	18	similarity	similarity	NOUN
ejpam-6072	393	19	transformations	transformation	NOUN
ejpam-6072	393	20	.	.	PUNCT
ejpam-6072	394	1	5	5	X
ejpam-6072	394	2	.	.	X
ejpam-6072	394	3	conclusion	conclusion	NOUN
ejpam-6072	394	4	in	in	ADP
ejpam-6072	394	5	this	this	DET
ejpam-6072	394	6	work	work	NOUN
ejpam-6072	394	7	,	,	PUNCT
ejpam-6072	394	8	we	we	PRON
ejpam-6072	394	9	have	have	AUX
ejpam-6072	394	10	explored	explore	VERB
ejpam-6072	394	11	fundamental	fundamental	ADJ
ejpam-6072	394	12	stability	stability	NOUN
ejpam-6072	394	13	properties	property	NOUN
ejpam-6072	394	14	of	of	ADP
ejpam-6072	394	15	matrix	matrix	NOUN
ejpam-6072	394	16	families	family	NOUN
ejpam-6072	394	17	,	,	PUNCT
ejpam-6072	394	18	establishing	establish	VERB
ejpam-6072	394	19	significant	significant	ADJ
ejpam-6072	394	20	links	link	NOUN
ejpam-6072	394	21	between	between	ADP
ejpam-6072	394	22	common	common	ADJ
ejpam-6072	394	23	riccati	riccati	NOUN
ejpam-6072	394	24	stability	stability	NOUN
ejpam-6072	394	25	,	,	PUNCT
ejpam-6072	394	26	lyapunov	lyapunov	NOUN
ejpam-6072	394	27	stability	stability	NOUN
ejpam-6072	394	28	,	,	PUNCT
ejpam-6072	394	29	and	and	CCONJ
ejpam-6072	394	30	schur	schur	ADJ
ejpam-6072	394	31	stability	stability	NOUN
ejpam-6072	394	32	.	.	PUNCT
ejpam-6072	395	1	by	by	ADP
ejpam-6072	395	2	demonstrating	demonstrate	VERB
ejpam-6072	395	3	that	that	SCONJ
ejpam-6072	395	4	common	common	ADJ
ejpam-6072	395	5	riccati	riccati	NOUN
ejpam-6072	395	6	stability	stability	NOUN
ejpam-6072	395	7	implies	imply	VERB
ejpam-6072	395	8	both	both	CCONJ
ejpam-6072	395	9	lyapunov	lyapunov	NOUN
ejpam-6072	395	10	and	and	CCONJ
ejpam-6072	395	11	schur	schur	PROPN
ejpam-6072	395	12	stability	stability	PROPN
ejpam-6072	395	13	,	,	PUNCT
ejpam-6072	395	14	we	we	PRON
ejpam-6072	395	15	have	have	AUX
ejpam-6072	395	16	highlighted	highlight	VERB
ejpam-6072	395	17	the	the	DET
ejpam-6072	395	18	utility	utility	NOUN
ejpam-6072	395	19	of	of	ADP
ejpam-6072	395	20	riccati	riccati	PROPN
ejpam-6072	395	21	stability	stability	NOUN
ejpam-6072	395	22	as	as	ADP
ejpam-6072	395	23	a	a	DET
ejpam-6072	395	24	unifying	unifying	ADJ
ejpam-6072	395	25	concept	concept	NOUN
ejpam-6072	395	26	in	in	ADP
ejpam-6072	395	27	stability	stability	NOUN
ejpam-6072	395	28	analysis	analysis	NOUN
ejpam-6072	395	29	.	.	PUNCT
ejpam-6072	396	1	additionally	additionally	ADV
ejpam-6072	396	2	,	,	PUNCT
ejpam-6072	396	3	we	we	PRON
ejpam-6072	396	4	showed	show	VERB
ejpam-6072	396	5	that	that	SCONJ
ejpam-6072	396	6	common	common	ADJ
ejpam-6072	396	7	riccati	riccati	NOUN
ejpam-6072	396	8	stability	stability	NOUN
ejpam-6072	396	9	is	be	AUX
ejpam-6072	396	10	preserved	preserve	VERB
ejpam-6072	396	11	a.	a.	NOUN
ejpam-6072	396	12	algefary	algefary	PROPN
ejpam-6072	396	13	,	,	PUNCT
ejpam-6072	396	14	k.	k.	PROPN
ejpam-6072	396	15	a.	a.	PROPN
ejpam-6072	396	16	alqufari	alqufari	PROPN
ejpam-6072	396	17	/	/	SYM
ejpam-6072	396	18	eur	eur	PROPN
ejpam-6072	396	19	.	.	PUNCT
ejpam-6072	397	1	j.	j.	PROPN
ejpam-6072	397	2	pure	pure	PROPN
ejpam-6072	397	3	appl	appl	PROPN
ejpam-6072	397	4	.	.	PROPN
ejpam-6072	397	5	math	math	PROPN
ejpam-6072	397	6	,	,	PUNCT
ejpam-6072	397	7	18	18	NUM
ejpam-6072	397	8	(	(	PUNCT
ejpam-6072	397	9	2	2	NUM
ejpam-6072	397	10	)	)	PUNCT
ejpam-6072	397	11	(	(	PUNCT
ejpam-6072	397	12	2025	2025	NUM
ejpam-6072	397	13	)	)	PUNCT
ejpam-6072	397	14	,	,	PUNCT
ejpam-6072	397	15	6072	6072	NUM
ejpam-6072	397	16	13	13	NUM
ejpam-6072	397	17	of	of	ADP
ejpam-6072	397	18	14	14	NUM
ejpam-6072	397	19	under	under	ADP
ejpam-6072	397	20	scaling	scaling	NOUN
ejpam-6072	397	21	and	and	CCONJ
ejpam-6072	397	22	similarity	similarity	NOUN
ejpam-6072	397	23	transformations	transformation	NOUN
ejpam-6072	397	24	,	,	PUNCT
ejpam-6072	397	25	reinforcing	reinforce	VERB
ejpam-6072	397	26	its	its	PRON
ejpam-6072	397	27	robustness	robustness	NOUN
ejpam-6072	397	28	in	in	ADP
ejpam-6072	397	29	various	various	ADJ
ejpam-6072	397	30	applications	application	NOUN
ejpam-6072	397	31	.	.	PUNCT
ejpam-6072	398	1	these	these	DET
ejpam-6072	398	2	results	result	NOUN
ejpam-6072	398	3	provide	provide	VERB
ejpam-6072	398	4	a	a	DET
ejpam-6072	398	5	foundation	foundation	NOUN
ejpam-6072	398	6	for	for	ADP
ejpam-6072	398	7	future	future	ADJ
ejpam-6072	398	8	work	work	NOUN
ejpam-6072	398	9	in	in	ADP
ejpam-6072	398	10	stability	stability	NOUN
ejpam-6072	398	11	analysis	analysis	NOUN
ejpam-6072	398	12	and	and	CCONJ
ejpam-6072	398	13	control	control	NOUN
ejpam-6072	398	14	theory	theory	NOUN
ejpam-6072	398	15	,	,	PUNCT
ejpam-6072	398	16	particularly	particularly	ADV
ejpam-6072	398	17	in	in	ADP
ejpam-6072	398	18	systems	system	NOUN
ejpam-6072	398	19	with	with	ADP
ejpam-6072	398	20	time	time	NOUN
ejpam-6072	398	21	delays	delay	NOUN
ejpam-6072	398	22	or	or	CCONJ
ejpam-6072	398	23	those	those	PRON
ejpam-6072	398	24	requiring	require	VERB
ejpam-6072	398	25	stability	stability	NOUN
ejpam-6072	398	26	across	across	ADP
ejpam-6072	398	27	multiple	multiple	ADJ
ejpam-6072	398	28	configurations	configuration	NOUN
ejpam-6072	398	29	.	.	PUNCT
ejpam-6072	399	1	this	this	DET
ejpam-6072	399	2	study	study	NOUN
ejpam-6072	399	3	’s	’s	PART
ejpam-6072	399	4	findings	finding	NOUN
ejpam-6072	399	5	contribute	contribute	VERB
ejpam-6072	399	6	valuable	valuable	ADJ
ejpam-6072	399	7	insights	insight	NOUN
ejpam-6072	399	8	for	for	ADP
ejpam-6072	399	9	the	the	DET
ejpam-6072	399	10	design	design	NOUN
ejpam-6072	399	11	of	of	ADP
ejpam-6072	399	12	robust	robust	ADJ
ejpam-6072	399	13	control	control	NOUN
ejpam-6072	399	14	systems	system	NOUN
ejpam-6072	399	15	that	that	PRON
ejpam-6072	399	16	require	require	VERB
ejpam-6072	399	17	stability	stability	NOUN
ejpam-6072	399	18	despite	despite	SCONJ
ejpam-6072	399	19	parameter	parameter	NOUN
ejpam-6072	399	20	variations	variation	NOUN
ejpam-6072	399	21	and	and	CCONJ
ejpam-6072	399	22	transformations	transformation	NOUN
ejpam-6072	399	23	.	.	PUNCT
ejpam-6072	400	1	acknowledgements	acknowledgement	NOUN
ejpam-6072	400	2	the	the	DET
ejpam-6072	400	3	authors	author	NOUN
ejpam-6072	400	4	gratefully	gratefully	ADV
ejpam-6072	400	5	acknowledge	acknowledge	VERB
ejpam-6072	400	6	qassim	qassim	PROPN
ejpam-6072	400	7	university	university	PROPN
ejpam-6072	400	8	,	,	PUNCT
ejpam-6072	400	9	represented	represent	VERB
ejpam-6072	400	10	by	by	ADP
ejpam-6072	400	11	the	the	DET
ejpam-6072	400	12	deanship	deanship	NOUN
ejpam-6072	400	13	of	of	ADP
ejpam-6072	400	14	graduate	graduate	NOUN
ejpam-6072	400	15	studies	study	NOUN
ejpam-6072	400	16	and	and	CCONJ
ejpam-6072	400	17	scientific	scientific	ADJ
ejpam-6072	400	18	research	research	NOUN
ejpam-6072	400	19	,	,	PUNCT
ejpam-6072	400	20	on	on	ADP
ejpam-6072	400	21	the	the	DET
ejpam-6072	400	22	financial	financial	ADJ
ejpam-6072	400	23	support	support	NOUN
ejpam-6072	400	24	for	for	ADP
ejpam-6072	400	25	this	this	DET
ejpam-6072	400	26	research	research	NOUN
ejpam-6072	400	27	under	under	ADP
ejpam-6072	400	28	the	the	DET
ejpam-6072	400	29	number	number	NOUN
ejpam-6072	400	30	(	(	PUNCT
ejpam-6072	400	31	qu	qu	PROPN
ejpam-6072	400	32	-	-	PROPN
ejpam-6072	400	33	j	j	NOUN
ejpam-6072	400	34	-	-	PUNCT
ejpam-6072	400	35	ug-2	ug-2	NOUN
ejpam-6072	400	36	-	-	PUNCT
ejpam-6072	400	37	2025	2025	NUM
ejpam-6072	400	38	-	-	SYM
ejpam-6072	400	39	56216	56216	NUM
ejpam-6072	400	40	)	)	PUNCT
ejpam-6072	400	41	during	during	ADP
ejpam-6072	400	42	the	the	DET
ejpam-6072	400	43	academic	academic	ADJ
ejpam-6072	400	44	year	year	NOUN
ejpam-6072	400	45	1446	1446	NUM
ejpam-6072	400	46	ah	ah	INTJ
ejpam-6072	400	47	/	/	SYM
ejpam-6072	400	48	2024	2024	NUM
ejpam-6072	400	49	ad	ad	NOUN
ejpam-6072	400	50	.	.	PUNCT
ejpam-6072	401	1	we	we	PRON
ejpam-6072	401	2	also	also	ADV
ejpam-6072	401	3	sincerely	sincerely	ADV
ejpam-6072	401	4	thank	thank	VERB
ejpam-6072	401	5	the	the	DET
ejpam-6072	401	6	reviewers	reviewer	NOUN
ejpam-6072	401	7	for	for	ADP
ejpam-6072	401	8	their	their	PRON
ejpam-6072	401	9	valuable	valuable	ADJ
ejpam-6072	401	10	feedback	feedback	NOUN
ejpam-6072	401	11	and	and	CCONJ
ejpam-6072	401	12	constructive	constructive	ADJ
ejpam-6072	401	13	comments	comment	NOUN
ejpam-6072	401	14	,	,	PUNCT
ejpam-6072	401	15	which	which	PRON
ejpam-6072	401	16	have	have	AUX
ejpam-6072	401	17	significantly	significantly	ADV
ejpam-6072	401	18	contributed	contribute	VERB
ejpam-6072	401	19	to	to	ADP
ejpam-6072	401	20	enhancing	enhance	VERB
ejpam-6072	401	21	the	the	DET
ejpam-6072	401	22	quality	quality	NOUN
ejpam-6072	401	23	of	of	ADP
ejpam-6072	401	24	this	this	DET
ejpam-6072	401	25	paper	paper	NOUN
ejpam-6072	401	26	.	.	PUNCT
ejpam-6072	402	1	references	reference	NOUN
ejpam-6072	402	2	[	[	X
ejpam-6072	402	3	1	1	NUM
ejpam-6072	402	4	]	]	X
ejpam-6072	402	5	r	r	NOUN
ejpam-6072	402	6	horn	horn	NOUN
ejpam-6072	402	7	and	and	CCONJ
ejpam-6072	402	8	c	c	PROPN
ejpam-6072	402	9	johnson	johnson	PROPN
ejpam-6072	402	10	.	.	PROPN
ejpam-6072	403	1	matrix	matrix	NOUN
ejpam-6072	403	2	analysis	analysis	NOUN
ejpam-6072	403	3	.	.	PUNCT
ejpam-6072	404	1	cambridge	cambridge	PROPN
ejpam-6072	404	2	university	university	PROPN
ejpam-6072	404	3	press	press	NOUN
ejpam-6072	404	4	,	,	PUNCT
ejpam-6072	404	5	1985	1985	NUM
ejpam-6072	404	6	.	.	PUNCT
ejpam-6072	405	1	[	[	X
ejpam-6072	405	2	2	2	X
ejpam-6072	405	3	]	]	X
ejpam-6072	405	4	lloyd	lloyd	PROPN
ejpam-6072	405	5	n	n	PROPN
ejpam-6072	405	6	trefethen	trefethen	NOUN
ejpam-6072	405	7	and	and	CCONJ
ejpam-6072	405	8	david	david	PROPN
ejpam-6072	405	9	bau	bau	PROPN
ejpam-6072	405	10	.	.	PROPN
ejpam-6072	405	11	numerical	numerical	PROPN
ejpam-6072	405	12	linear	linear	PROPN
ejpam-6072	405	13	algebra	algebra	PROPN
ejpam-6072	405	14	.	.	PUNCT
ejpam-6072	406	1	siam	siam	PROPN
ejpam-6072	406	2	,	,	PUNCT
ejpam-6072	406	3	2022	2022	NUM
ejpam-6072	406	4	.	.	PUNCT
ejpam-6072	407	1	[	[	X
ejpam-6072	407	2	3	3	X
ejpam-6072	407	3	]	]	X
ejpam-6072	407	4	roger	roger	NOUN
ejpam-6072	407	5	a	a	DET
ejpam-6072	407	6	horn	horn	NOUN
ejpam-6072	407	7	and	and	CCONJ
ejpam-6072	407	8	charles	charles	PROPN
ejpam-6072	407	9	r	r	PROPN
ejpam-6072	407	10	johnson	johnson	PROPN
ejpam-6072	407	11	.	.	PUNCT
ejpam-6072	408	1	topics	topic	NOUN
ejpam-6072	408	2	in	in	ADP
ejpam-6072	408	3	matrix	matrix	NOUN
ejpam-6072	408	4	analysis	analysis	NOUN
ejpam-6072	408	5	.	.	PUNCT
ejpam-6072	409	1	cambridge	cambridge	PROPN
ejpam-6072	409	2	university	university	PROPN
ejpam-6072	409	3	press	press	NOUN
ejpam-6072	409	4	,	,	PUNCT
ejpam-6072	409	5	1991	1991	NUM
ejpam-6072	409	6	.	.	PUNCT
ejpam-6072	410	1	[	[	X
ejpam-6072	410	2	4	4	X
ejpam-6072	410	3	]	]	PUNCT
ejpam-6072	410	4	eugenius	eugenius	PROPN
ejpam-6072	410	5	kaszkurewicz	kaszkurewicz	PROPN
ejpam-6072	410	6	and	and	CCONJ
ejpam-6072	410	7	amit	amit	PROPN
ejpam-6072	410	8	bhaya	bhaya	PROPN
ejpam-6072	410	9	.	.	PUNCT
ejpam-6072	410	10	matrix	matrix	NOUN
ejpam-6072	410	11	diagonal	diagonal	ADJ
ejpam-6072	410	12	stability	stability	NOUN
ejpam-6072	410	13	in	in	ADP
ejpam-6072	410	14	systems	system	NOUN
ejpam-6072	410	15	and	and	CCONJ
ejpam-6072	410	16	computation	computation	NOUN
ejpam-6072	410	17	.	.	PUNCT
ejpam-6072	411	1	springer	springer	NOUN
ejpam-6072	411	2	science	science	PROPN
ejpam-6072	411	3	&	&	CCONJ
ejpam-6072	411	4	business	business	NOUN
ejpam-6072	411	5	media	medium	NOUN
ejpam-6072	411	6	,	,	PUNCT
ejpam-6072	411	7	2012	2012	NUM
ejpam-6072	411	8	.	.	PUNCT
ejpam-6072	412	1	[	[	X
ejpam-6072	412	2	5	5	X
ejpam-6072	412	3	]	]	PUNCT
ejpam-6072	412	4	robert	robert	PROPN
ejpam-6072	412	5	k	k	PROPN
ejpam-6072	412	6	brayton	brayton	PROPN
ejpam-6072	412	7	and	and	CCONJ
ejpam-6072	412	8	charles	charles	PROPN
ejpam-6072	412	9	c	c	PROPN
ejpam-6072	412	10	conley	conley	PROPN
ejpam-6072	412	11	.	.	PUNCT
ejpam-6072	413	1	some	some	DET
ejpam-6072	413	2	results	result	NOUN
ejpam-6072	413	3	on	on	ADP
ejpam-6072	413	4	the	the	DET
ejpam-6072	413	5	stability	stability	NOUN
ejpam-6072	413	6	and	and	CCONJ
ejpam-6072	413	7	instability	instability	NOUN
ejpam-6072	413	8	of	of	ADP
ejpam-6072	413	9	the	the	DET
ejpam-6072	413	10	backward	backward	ADJ
ejpam-6072	413	11	differentiation	differentiation	NOUN
ejpam-6072	413	12	methods	method	NOUN
ejpam-6072	413	13	with	with	ADP
ejpam-6072	413	14	non	non	ADJ
ejpam-6072	413	15	-	-	ADJ
ejpam-6072	413	16	uniform	uniform	ADJ
ejpam-6072	413	17	time	time	NOUN
ejpam-6072	413	18	steps	step	NOUN
ejpam-6072	413	19	.	.	PUNCT
ejpam-6072	414	1	topics	topic	NOUN
ejpam-6072	414	2	in	in	ADP
ejpam-6072	414	3	numerical	numerical	ADJ
ejpam-6072	414	4	analysis	analysis	NOUN
ejpam-6072	414	5	,	,	PUNCT
ejpam-6072	414	6	pages	page	NOUN
ejpam-6072	414	7	13–33	13–33	NUM
ejpam-6072	414	8	,	,	PUNCT
ejpam-6072	414	9	1972	1972	NUM
ejpam-6072	414	10	.	.	PUNCT
ejpam-6072	415	1	[	[	X
ejpam-6072	415	2	6	6	NUM
ejpam-6072	415	3	]	]	X
ejpam-6072	415	4	robert	robert	PROPN
ejpam-6072	415	5	brayton	brayton	PROPN
ejpam-6072	415	6	and	and	CCONJ
ejpam-6072	415	7	christopher	christopher	PROPN
ejpam-6072	415	8	tong	tong	PROPN
ejpam-6072	415	9	.	.	PUNCT
ejpam-6072	416	1	stability	stability	NOUN
ejpam-6072	416	2	of	of	ADP
ejpam-6072	416	3	dynamical	dynamical	ADJ
ejpam-6072	416	4	systems	system	NOUN
ejpam-6072	416	5	:	:	PUNCT
ejpam-6072	416	6	a	a	DET
ejpam-6072	416	7	constructive	constructive	ADJ
ejpam-6072	416	8	approach	approach	NOUN
ejpam-6072	416	9	.	.	PUNCT
ejpam-6072	417	1	ieee	ieee	NOUN
ejpam-6072	417	2	transactions	transaction	NOUN
ejpam-6072	417	3	on	on	ADP
ejpam-6072	417	4	circuits	circuit	NOUN
ejpam-6072	417	5	and	and	CCONJ
ejpam-6072	417	6	systems	system	NOUN
ejpam-6072	417	7	,	,	PUNCT
ejpam-6072	417	8	26(4):224–234	26(4):224–234	NUM
ejpam-6072	417	9	,	,	PUNCT
ejpam-6072	417	10	1979	1979	NUM
ejpam-6072	417	11	.	.	PUNCT
ejpam-6072	418	1	[	[	X
ejpam-6072	418	2	7	7	X
ejpam-6072	418	3	]	]	X
ejpam-6072	418	4	stephen	stephen	PROPN
ejpam-6072	418	5	boyd	boyd	PROPN
ejpam-6072	418	6	and	and	CCONJ
ejpam-6072	418	7	qinping	qinpe	VERB
ejpam-6072	418	8	yang	yang	PROPN
ejpam-6072	418	9	.	.	PUNCT
ejpam-6072	419	1	structured	structured	ADJ
ejpam-6072	419	2	and	and	CCONJ
ejpam-6072	419	3	simultaneous	simultaneous	ADJ
ejpam-6072	419	4	lyapunov	lyapunov	ADJ
ejpam-6072	419	5	functions	function	NOUN
ejpam-6072	419	6	for	for	ADP
ejpam-6072	419	7	system	system	NOUN
ejpam-6072	419	8	stability	stability	NOUN
ejpam-6072	419	9	problems	problem	NOUN
ejpam-6072	419	10	.	.	PUNCT
ejpam-6072	420	1	international	international	ADJ
ejpam-6072	420	2	journal	journal	PROPN
ejpam-6072	420	3	of	of	ADP
ejpam-6072	420	4	control	control	PROPN
ejpam-6072	420	5	,	,	PUNCT
ejpam-6072	420	6	49(6):2215–2240	49(6):2215–2240	PROPN
ejpam-6072	420	7	,	,	PUNCT
ejpam-6072	420	8	1989	1989	NUM
ejpam-6072	420	9	.	.	PUNCT
ejpam-6072	421	1	[	[	X
ejpam-6072	421	2	8	8	NUM
ejpam-6072	421	3	]	]	X
ejpam-6072	421	4	m	m	VERB
ejpam-6072	421	5	vidyasagar	vidyasagar	ADJ
ejpam-6072	421	6	.	.	PUNCT
ejpam-6072	422	1	on	on	ADP
ejpam-6072	422	2	matrix	matrix	NOUN
ejpam-6072	422	3	measures	measure	NOUN
ejpam-6072	422	4	and	and	CCONJ
ejpam-6072	422	5	convex	convex	VERB
ejpam-6072	422	6	liapunov	liapunov	NOUN
ejpam-6072	422	7	functions	function	NOUN
ejpam-6072	422	8	.	.	PUNCT
ejpam-6072	423	1	journal	journal	NOUN
ejpam-6072	423	2	of	of	ADP
ejpam-6072	423	3	mathematical	mathematical	ADJ
ejpam-6072	423	4	analysis	analysis	NOUN
ejpam-6072	423	5	and	and	CCONJ
ejpam-6072	423	6	applications	application	NOUN
ejpam-6072	423	7	,	,	PUNCT
ejpam-6072	423	8	62(1):90–103	62(1):90–103	NUM
ejpam-6072	423	9	,	,	PUNCT
ejpam-6072	423	10	1978	1978	NUM
ejpam-6072	423	11	.	.	PUNCT
ejpam-6072	424	1	[	[	X
ejpam-6072	424	2	9	9	NUM
ejpam-6072	424	3	]	]	X
ejpam-6072	424	4	david	david	PROPN
ejpam-6072	424	5	angeli	angeli	PROPN
ejpam-6072	424	6	,	,	PUNCT
ejpam-6072	424	7	nikolaos	nikolaos	PROPN
ejpam-6072	424	8	athanasopoulos	athanasopoulo	NOUN
ejpam-6072	424	9	,	,	PUNCT
ejpam-6072	424	10	raphaël	raphaël	PROPN
ejpam-6072	424	11	m	m	VERB
ejpam-6072	424	12	jungers	junger	NOUN
ejpam-6072	424	13	,	,	PUNCT
ejpam-6072	424	14	and	and	CCONJ
ejpam-6072	424	15	matthew	matthew	PROPN
ejpam-6072	424	16	philippe	philippe	PROPN
ejpam-6072	424	17	.	.	PUNCT
ejpam-6072	425	1	path	path	NOUN
ejpam-6072	425	2	-	-	PUNCT
ejpam-6072	425	3	complete	complete	ADJ
ejpam-6072	425	4	graphs	graph	NOUN
ejpam-6072	425	5	and	and	CCONJ
ejpam-6072	425	6	common	common	ADJ
ejpam-6072	425	7	lyapunov	lyapunov	ADJ
ejpam-6072	425	8	functions	function	NOUN
ejpam-6072	425	9	.	.	PUNCT
ejpam-6072	426	1	in	in	ADP
ejpam-6072	426	2	proceedings	proceeding	NOUN
ejpam-6072	426	3	of	of	ADP
ejpam-6072	426	4	the	the	DET
ejpam-6072	426	5	20th	20th	ADJ
ejpam-6072	426	6	international	international	ADJ
ejpam-6072	426	7	conference	conference	NOUN
ejpam-6072	426	8	on	on	ADP
ejpam-6072	426	9	hybrid	hybrid	ADJ
ejpam-6072	426	10	systems	system	NOUN
ejpam-6072	426	11	:	:	PUNCT
ejpam-6072	426	12	computation	computation	NOUN
ejpam-6072	426	13	and	and	CCONJ
ejpam-6072	426	14	control	control	NOUN
ejpam-6072	426	15	,	,	PUNCT
ejpam-6072	426	16	pages	page	NOUN
ejpam-6072	426	17	81–90	81–90	NUM
ejpam-6072	426	18	,	,	PUNCT
ejpam-6072	426	19	2017	2017	NUM
ejpam-6072	426	20	.	.	PUNCT
ejpam-6072	427	1	[	[	X
ejpam-6072	427	2	10	10	NUM
ejpam-6072	427	3	]	]	X
ejpam-6072	427	4	stefania	stefania	PROPN
ejpam-6072	427	5	andersen	andersen	PROPN
ejpam-6072	427	6	,	,	PUNCT
ejpam-6072	427	7	peter	peter	PROPN
ejpam-6072	427	8	giesl	giesl	PROPN
ejpam-6072	427	9	,	,	PUNCT
ejpam-6072	427	10	and	and	CCONJ
ejpam-6072	427	11	sigurdur	sigurdur	ADJ
ejpam-6072	427	12	hafstein	hafstein	NOUN
ejpam-6072	427	13	.	.	PUNCT
ejpam-6072	428	1	common	common	ADJ
ejpam-6072	428	2	lyapunov	lyapunov	ADJ
ejpam-6072	428	3	functions	function	NOUN
ejpam-6072	428	4	for	for	ADP
ejpam-6072	428	5	switched	switch	VERB
ejpam-6072	428	6	linear	linear	ADJ
ejpam-6072	428	7	systems	system	NOUN
ejpam-6072	428	8	:	:	PUNCT
ejpam-6072	428	9	linear	linear	ADJ
ejpam-6072	428	10	programming	programming	NOUN
ejpam-6072	428	11	-	-	PUNCT
ejpam-6072	428	12	based	base	VERB
ejpam-6072	428	13	approach	approach	NOUN
ejpam-6072	428	14	.	.	PUNCT
ejpam-6072	429	1	ieee	ieee	PROPN
ejpam-6072	429	2	control	control	PROPN
ejpam-6072	429	3	systems	systems	PROPN
ejpam-6072	429	4	letters	letter	NOUN
ejpam-6072	429	5	,	,	PUNCT
ejpam-6072	429	6	7:901–906	7:901–906	NUM
ejpam-6072	429	7	,	,	PUNCT
ejpam-6072	429	8	2022	2022	NUM
ejpam-6072	429	9	.	.	PUNCT
ejpam-6072	430	1	[	[	X
ejpam-6072	430	2	11	11	NUM
ejpam-6072	430	3	]	]	X
ejpam-6072	430	4	gw	gw	PROPN
ejpam-6072	430	5	cross	cross	PROPN
ejpam-6072	430	6	.	.	PUNCT
ejpam-6072	431	1	three	three	NUM
ejpam-6072	431	2	types	type	NOUN
ejpam-6072	431	3	of	of	ADP
ejpam-6072	431	4	matrix	matrix	NOUN
ejpam-6072	431	5	stability	stability	NOUN
ejpam-6072	431	6	.	.	PUNCT
ejpam-6072	432	1	linear	linear	ADJ
ejpam-6072	432	2	algebra	algebra	NOUN
ejpam-6072	432	3	and	and	CCONJ
ejpam-6072	432	4	its	its	PRON
ejpam-6072	432	5	applications	application	NOUN
ejpam-6072	432	6	,	,	PUNCT
ejpam-6072	432	7	20(3):253–263	20(3):253–263	PROPN
ejpam-6072	432	8	,	,	PUNCT
ejpam-6072	432	9	1978	1978	NUM
ejpam-6072	432	10	.	.	PUNCT
ejpam-6072	433	1	[	[	X
ejpam-6072	433	2	12	12	NUM
ejpam-6072	433	3	]	]	X
ejpam-6072	433	4	daniel	daniel	PROPN
ejpam-6072	433	5	hershkowitz	hershkowitz	PROPN
ejpam-6072	433	6	.	.	PUNCT
ejpam-6072	434	1	recent	recent	ADJ
ejpam-6072	434	2	directions	direction	NOUN
ejpam-6072	434	3	in	in	ADP
ejpam-6072	434	4	matrix	matrix	NOUN
ejpam-6072	434	5	stability	stability	NOUN
ejpam-6072	434	6	.	.	PUNCT
ejpam-6072	435	1	linear	linear	ADJ
ejpam-6072	435	2	algebra	algebra	NOUN
ejpam-6072	435	3	and	and	CCONJ
ejpam-6072	435	4	its	its	PRON
ejpam-6072	435	5	applications	application	NOUN
ejpam-6072	435	6	,	,	PUNCT
ejpam-6072	435	7	171:161–186	171:161–186	NUM
ejpam-6072	435	8	,	,	PUNCT
ejpam-6072	435	9	1992	1992	NUM
ejpam-6072	435	10	.	.	PUNCT
ejpam-6072	436	1	a.	a.	PROPN
ejpam-6072	436	2	algefary	algefary	PROPN
ejpam-6072	436	3	,	,	PUNCT
ejpam-6072	436	4	k.	k.	PROPN
ejpam-6072	436	5	a.	a.	PROPN
ejpam-6072	436	6	alqufari	alqufari	PROPN
ejpam-6072	436	7	/	/	SYM
ejpam-6072	436	8	eur	eur	PROPN
ejpam-6072	436	9	.	.	PUNCT
ejpam-6072	437	1	j.	j.	PROPN
ejpam-6072	437	2	pure	pure	PROPN
ejpam-6072	437	3	appl	appl	PROPN
ejpam-6072	437	4	.	.	PROPN
ejpam-6072	437	5	math	math	PROPN
ejpam-6072	437	6	,	,	PUNCT
ejpam-6072	437	7	18	18	NUM
ejpam-6072	437	8	(	(	PUNCT
ejpam-6072	437	9	2	2	NUM
ejpam-6072	437	10	)	)	PUNCT
ejpam-6072	437	11	(	(	PUNCT
ejpam-6072	437	12	2025	2025	NUM
ejpam-6072	437	13	)	)	PUNCT
ejpam-6072	437	14	,	,	PUNCT
ejpam-6072	437	15	6072	6072	NUM
ejpam-6072	437	16	14	14	NUM
ejpam-6072	437	17	of	of	ADP
ejpam-6072	437	18	14	14	NUM
ejpam-6072	438	1	[	[	SYM
ejpam-6072	438	2	13	13	NUM
ejpam-6072	438	3	]	]	X
ejpam-6072	438	4	abraham	abraham	PROPN
ejpam-6072	438	5	berman	berman	PROPN
ejpam-6072	438	6	,	,	PUNCT
ejpam-6072	438	7	christopher	christopher	NOUN
ejpam-6072	438	8	king	king	PROPN
ejpam-6072	438	9	,	,	PUNCT
ejpam-6072	438	10	and	and	CCONJ
ejpam-6072	438	11	robert	robert	PROPN
ejpam-6072	438	12	shorten	shorten	PROPN
ejpam-6072	438	13	.	.	PUNCT
ejpam-6072	439	1	a	a	DET
ejpam-6072	439	2	characterisation	characterisation	NOUN
ejpam-6072	439	3	of	of	ADP
ejpam-6072	439	4	common	common	ADJ
ejpam-6072	439	5	diagonal	diagonal	ADJ
ejpam-6072	439	6	stability	stability	NOUN
ejpam-6072	439	7	over	over	ADP
ejpam-6072	439	8	cones	cone	NOUN
ejpam-6072	439	9	.	.	PUNCT
ejpam-6072	440	1	linear	linear	ADJ
ejpam-6072	440	2	and	and	CCONJ
ejpam-6072	440	3	multilinear	multilinear	PROPN
ejpam-6072	440	4	algebra	algebra	PROPN
ejpam-6072	440	5	,	,	PUNCT
ejpam-6072	440	6	60(10):1117	60(10):1117	NUM
ejpam-6072	440	7	–	–	PUNCT
ejpam-6072	440	8	1123	1123	NUM
ejpam-6072	440	9	,	,	PUNCT
ejpam-6072	440	10	2012	2012	NUM
ejpam-6072	440	11	.	.	PUNCT
ejpam-6072	441	1	[	[	X
ejpam-6072	441	2	14	14	NUM
ejpam-6072	441	3	]	]	X
ejpam-6072	441	4	ali	ali	PROPN
ejpam-6072	441	5	algefary	algefary	PROPN
ejpam-6072	441	6	.	.	PUNCT
ejpam-6072	442	1	a	a	DET
ejpam-6072	442	2	characterization	characterization	NOUN
ejpam-6072	442	3	of	of	ADP
ejpam-6072	442	4	common	common	ADJ
ejpam-6072	442	5	lyapunov	lyapunov	ADJ
ejpam-6072	442	6	diagonal	diagonal	ADJ
ejpam-6072	442	7	stability	stability	NOUN
ejpam-6072	442	8	using	use	VERB
ejpam-6072	442	9	khatrirao	khatrirao	PROPN
ejpam-6072	442	10	products	product	NOUN
ejpam-6072	442	11	.	.	PUNCT
ejpam-6072	443	1	aims	aim	VERB
ejpam-6072	443	2	mathematics	mathematic	NOUN
ejpam-6072	443	3	,	,	PUNCT
ejpam-6072	443	4	9(8):20612–20626	9(8):20612–20626	NUM
ejpam-6072	443	5	,	,	PUNCT
ejpam-6072	443	6	2024	2024	NUM
ejpam-6072	443	7	.	.	PUNCT
ejpam-6072	444	1	[	[	X
ejpam-6072	444	2	15	15	NUM
ejpam-6072	444	3	]	]	X
ejpam-6072	444	4	alan	alan	PROPN
ejpam-6072	444	5	v	v	PROPN
ejpam-6072	444	6	oppenheim	oppenheim	PROPN
ejpam-6072	444	7	.	.	PUNCT
ejpam-6072	445	1	discrete	discrete	ADJ
ejpam-6072	445	2	-	-	PUNCT
ejpam-6072	445	3	time	time	NOUN
ejpam-6072	445	4	signal	signal	NOUN
ejpam-6072	445	5	processing	processing	NOUN
ejpam-6072	445	6	.	.	PUNCT
ejpam-6072	446	1	pearson	pearson	PROPN
ejpam-6072	446	2	education	education	PROPN
ejpam-6072	446	3	india	india	PROPN
ejpam-6072	446	4	,	,	PUNCT
ejpam-6072	446	5	1999	1999	NUM
ejpam-6072	446	6	.	.	PUNCT
ejpam-6072	447	1	[	[	X
ejpam-6072	447	2	16	16	NUM
ejpam-6072	447	3	]	]	PUNCT
ejpam-6072	447	4	emilia	emilia	PROPN
ejpam-6072	447	5	fridman	fridman	PROPN
ejpam-6072	447	6	.	.	PUNCT
ejpam-6072	448	1	introduction	introduction	NOUN
ejpam-6072	448	2	to	to	ADP
ejpam-6072	448	3	time	time	NOUN
ejpam-6072	448	4	-	-	PUNCT
ejpam-6072	448	5	delay	delay	NOUN
ejpam-6072	448	6	systems	system	NOUN
ejpam-6072	448	7	.	.	PUNCT
ejpam-6072	449	1	analysis	analysis	NOUN
ejpam-6072	449	2	and	and	CCONJ
ejpam-6072	449	3	control	control	NOUN
ejpam-6072	449	4	.	.	PUNCT
ejpam-6072	450	1	birkhäuser	birkhäuser	NOUN
ejpam-6072	450	2	,	,	PUNCT
ejpam-6072	450	3	75	75	NUM
ejpam-6072	450	4	,	,	PUNCT
ejpam-6072	450	5	2014	2014	NUM
ejpam-6072	450	6	.	.	PUNCT
ejpam-6072	451	1	[	[	X
ejpam-6072	451	2	17	17	NUM
ejpam-6072	451	3	]	]	X
ejpam-6072	451	4	erik	erik	NOUN
ejpam-6072	451	5	i	i	PRON
ejpam-6072	451	6	verliest	verliest	VERB
ejpam-6072	451	7	and	and	CCONJ
ejpam-6072	451	8	anatoli	anatoli	PROPN
ejpam-6072	451	9	f	f	PROPN
ejpam-6072	451	10	ivanov	ivanov	PROPN
ejpam-6072	451	11	.	.	PUNCT
ejpam-6072	452	1	robust	robust	ADJ
ejpam-6072	452	2	stability	stability	NOUN
ejpam-6072	452	3	of	of	ADP
ejpam-6072	452	4	systems	system	NOUN
ejpam-6072	452	5	with	with	ADP
ejpam-6072	452	6	delayed	delayed	ADJ
ejpam-6072	452	7	feedback	feedback	NOUN
ejpam-6072	452	8	.	.	PUNCT
ejpam-6072	453	1	circuits	circuit	NOUN
ejpam-6072	453	2	,	,	PUNCT
ejpam-6072	453	3	systems	system	NOUN
ejpam-6072	453	4	and	and	CCONJ
ejpam-6072	453	5	signal	signal	NOUN
ejpam-6072	453	6	processing	processing	NOUN
ejpam-6072	453	7	,	,	PUNCT
ejpam-6072	453	8	13:213–222	13:213–222	NUM
ejpam-6072	453	9	,	,	PUNCT
ejpam-6072	453	10	1994	1994	NUM
ejpam-6072	453	11	.	.	PUNCT
ejpam-6072	454	1	[	[	X
ejpam-6072	454	2	18	18	NUM
ejpam-6072	454	3	]	]	PUNCT
ejpam-6072	454	4	emilia	emilia	PROPN
ejpam-6072	454	5	fridman	fridman	PROPN
ejpam-6072	454	6	.	.	PUNCT
ejpam-6072	455	1	tutorial	tutorial	NOUN
ejpam-6072	455	2	on	on	ADP
ejpam-6072	455	3	lyapunov	lyapunov	NOUN
ejpam-6072	455	4	-	-	PUNCT
ejpam-6072	455	5	based	base	VERB
ejpam-6072	455	6	methods	method	NOUN
ejpam-6072	455	7	for	for	ADP
ejpam-6072	455	8	time	time	NOUN
ejpam-6072	455	9	-	-	PUNCT
ejpam-6072	455	10	delay	delay	NOUN
ejpam-6072	455	11	systems	system	NOUN
ejpam-6072	455	12	.	.	PUNCT
ejpam-6072	456	1	european	european	PROPN
ejpam-6072	456	2	journal	journal	PROPN
ejpam-6072	456	3	of	of	ADP
ejpam-6072	456	4	control	control	PROPN
ejpam-6072	456	5	,	,	PUNCT
ejpam-6072	456	6	20(6):271–283	20(6):271–283	PROPN
ejpam-6072	456	7	,	,	PUNCT
ejpam-6072	456	8	2014	2014	NUM
ejpam-6072	456	9	.	.	PUNCT
ejpam-6072	457	1	[	[	X
ejpam-6072	457	2	19	19	NUM
ejpam-6072	457	3	]	]	X
ejpam-6072	457	4	vincent	vincent	NOUN
ejpam-6072	457	5	d	d	PROPN
ejpam-6072	457	6	blondel	blondel	NOUN
ejpam-6072	457	7	and	and	CCONJ
ejpam-6072	457	8	alexandre	alexandre	PROPN
ejpam-6072	457	9	megretski	megretski	PROPN
ejpam-6072	457	10	.	.	PUNCT
ejpam-6072	458	1	unsolved	unsolved	ADJ
ejpam-6072	458	2	problems	problem	NOUN
ejpam-6072	458	3	in	in	ADP
ejpam-6072	458	4	mathematical	mathematical	ADJ
ejpam-6072	458	5	systems	system	NOUN
ejpam-6072	458	6	and	and	CCONJ
ejpam-6072	458	7	control	control	PROPN
ejpam-6072	458	8	theory	theory	PROPN
ejpam-6072	458	9	.	.	PUNCT
ejpam-6072	459	1	princeton	princeton	PROPN
ejpam-6072	459	2	university	university	PROPN
ejpam-6072	459	3	press	press	NOUN
ejpam-6072	459	4	,	,	PUNCT
ejpam-6072	459	5	2009	2009	NUM
ejpam-6072	459	6	.	.	PUNCT
ejpam-6072	460	1	[	[	X
ejpam-6072	460	2	20	20	NUM
ejpam-6072	460	3	]	]	PUNCT
ejpam-6072	460	4	erik	erik	PROPN
ejpam-6072	461	1	i	i	PRON
ejpam-6072	461	2	verriest	verriest	VERB
ejpam-6072	461	3	.	.	PUNCT
ejpam-6072	462	1	robust	robust	ADJ
ejpam-6072	462	2	stability	stability	NOUN
ejpam-6072	462	3	and	and	CCONJ
ejpam-6072	462	4	stabilization	stabilization	NOUN
ejpam-6072	462	5	:	:	PUNCT
ejpam-6072	462	6	from	from	ADP
ejpam-6072	462	7	linear	linear	PROPN
ejpam-6072	462	8	to	to	ADP
ejpam-6072	462	9	nonlinear	nonlinear	ADJ
ejpam-6072	462	10	.	.	PUNCT
ejpam-6072	463	1	ifac	ifac	NOUN
ejpam-6072	463	2	proceedings	proceeding	NOUN
ejpam-6072	463	3	volumes	volume	NOUN
ejpam-6072	463	4	,	,	PUNCT
ejpam-6072	463	5	33(23):21–32	33(23):21–32	NUM
ejpam-6072	463	6	,	,	PUNCT
ejpam-6072	463	7	2000	2000	NUM
ejpam-6072	463	8	.	.	PUNCT