id	sid	tid	token	lemma	pos
ejde-719	1	1	electronic	electronic	ADJ
ejde-719	1	2	journal	journal	NOUN
ejde-719	1	3	of	of	ADP
ejde-719	1	4	differential	differential	ADJ
ejde-719	1	5	equations	equation	NOUN
ejde-719	1	6	,	,	PUNCT
ejde-719	1	7	vol	vol	NOUN
ejde-719	1	8	.	.	NOUN
ejde-719	1	9	2024	2024	NUM
ejde-719	1	10	(	(	PUNCT
ejde-719	1	11	2024	2024	NUM
ejde-719	1	12	)	)	PUNCT
ejde-719	1	13	,	,	PUNCT
ejde-719	1	14	no	no	INTJ
ejde-719	1	15	.	.	PROPN
ejde-719	1	16	76	76	NUM
ejde-719	1	17	,	,	PUNCT
ejde-719	1	18	pp	pp	ADJ
ejde-719	1	19	.	.	PUNCT
ejde-719	2	1	1–8	1–8	X
ejde-719	2	2	.	.	PUNCT
ejde-719	2	3	issn	issn	PROPN
ejde-719	2	4	:	:	PUNCT
ejde-719	2	5	1072	1072	NUM
ejde-719	2	6	-	-	SYM
ejde-719	2	7	6691	6691	NUM
ejde-719	2	8	.	.	PUNCT
ejde-719	3	1	url	url	PROPN
ejde-719	3	2	:	:	PUNCT
ejde-719	3	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-719	3	4	,	,	PUNCT
ejde-719	3	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-719	3	6	doi	doi	PROPN
ejde-719	3	7	:	:	PUNCT
ejde-719	3	8	10.58997	10.58997	NUM
ejde-719	3	9	/	/	SYM
ejde-719	3	10	ejde.2024.76	ejde.2024.76	ADJ
ejde-719	3	11	delay	delay	NOUN
ejde-719	3	12	-	-	PUNCT
ejde-719	3	13	dependent	dependent	ADJ
ejde-719	3	14	stability	stability	NOUN
ejde-719	3	15	conditions	condition	NOUN
ejde-719	3	16	for	for	ADP
ejde-719	3	17	delay	delay	NOUN
ejde-719	3	18	differential	differential	ADJ
ejde-719	3	19	equations	equation	NOUN
ejde-719	3	20	with	with	ADP
ejde-719	3	21	unbounded	unbounded	ADJ
ejde-719	3	22	operators	operator	NOUN
ejde-719	3	23	in	in	ADP
ejde-719	3	24	banach	banach	NOUN
ejde-719	3	25	spaces	space	NOUN
ejde-719	3	26	michael	michael	PROPN
ejde-719	3	27	gil	gil	PROPN
ejde-719	3	28	’	'	PUNCT
ejde-719	3	29	abstract	abstract	ADJ
ejde-719	3	30	.	.	PUNCT
ejde-719	4	1	we	we	PRON
ejde-719	4	2	consider	consider	VERB
ejde-719	4	3	the	the	DET
ejde-719	4	4	equation	equation	NOUN
ejde-719	4	5	du(t)/dt	du(t)/dt	NOUN
ejde-719	4	6	=	=	NOUN
ejde-719	4	7	au(t	au(t	PROPN
ejde-719	4	8	)	)	PUNCT
ejde-719	4	9	+	+	CCONJ
ejde-719	4	10	bu(t	bu(t	ADP
ejde-719	4	11	−	−	NOUN
ejde-719	4	12	h	h	NOUN
ejde-719	4	13	)	)	PUNCT
ejde-719	4	14	where	where	SCONJ
ejde-719	4	15	t	t	PROPN
ejde-719	4	16	>	>	X
ejde-719	4	17	0	0	PROPN
ejde-719	4	18	,	,	PUNCT
ejde-719	4	19	h	h	NOUN
ejde-719	4	20	is	be	AUX
ejde-719	4	21	a	a	DET
ejde-719	4	22	positive	positive	ADJ
ejde-719	4	23	constant	constant	ADJ
ejde-719	4	24	,	,	PUNCT
ejde-719	4	25	and	and	CCONJ
ejde-719	4	26	a	a	PRON
ejde-719	4	27	is	be	AUX
ejde-719	4	28	a	a	DET
ejde-719	4	29	linear	linear	ADJ
ejde-719	4	30	unbounded	unbounded	ADJ
ejde-719	4	31	and	and	CCONJ
ejde-719	4	32	b	b	NOUN
ejde-719	4	33	is	be	AUX
ejde-719	4	34	a	a	DET
ejde-719	4	35	linear	linear	ADJ
ejde-719	4	36	bounded	bound	VERB
ejde-719	4	37	operators	operator	NOUN
ejde-719	4	38	.	.	PUNCT
ejde-719	5	1	we	we	PRON
ejde-719	5	2	establish	establish	VERB
ejde-719	5	3	explicit	explicit	ADJ
ejde-719	5	4	delay	delay	NOUN
ejde-719	5	5	-	-	PUNCT
ejde-719	5	6	dependent	dependent	ADJ
ejde-719	5	7	conditions	condition	NOUN
ejde-719	5	8	for	for	ADP
ejde-719	5	9	exponential	exponential	ADJ
ejde-719	5	10	stability	stability	NOUN
ejde-719	5	11	,	,	PUNCT
ejde-719	5	12	and	and	CCONJ
ejde-719	5	13	present	present	ADJ
ejde-719	5	14	applications	application	NOUN
ejde-719	5	15	to	to	ADP
ejde-719	5	16	partial	partial	ADJ
ejde-719	5	17	integro	integro	ADJ
ejde-719	5	18	-	-	PUNCT
ejde-719	5	19	differential	differential	NOUN
ejde-719	5	20	equations	equation	NOUN
ejde-719	5	21	with	with	ADP
ejde-719	5	22	delay	delay	NOUN
ejde-719	5	23	.	.	PUNCT
ejde-719	6	1	1	1	X
ejde-719	6	2	.	.	X
ejde-719	6	3	introduction	introduction	NOUN
ejde-719	6	4	and	and	CCONJ
ejde-719	6	5	statement	statement	NOUN
ejde-719	6	6	of	of	ADP
ejde-719	6	7	the	the	DET
ejde-719	6	8	main	main	ADJ
ejde-719	6	9	result	result	NOUN
ejde-719	6	10	in	in	ADP
ejde-719	6	11	this	this	DET
ejde-719	6	12	article	article	NOUN
ejde-719	6	13	we	we	PRON
ejde-719	6	14	suggest	suggest	VERB
ejde-719	6	15	delay	delay	NOUN
ejde-719	6	16	-	-	PUNCT
ejde-719	6	17	dependent	dependent	ADJ
ejde-719	6	18	stability	stability	NOUN
ejde-719	6	19	conditions	condition	NOUN
ejde-719	6	20	for	for	ADP
ejde-719	6	21	delay	delay	NOUN
ejde-719	6	22	differential	differential	ADJ
ejde-719	6	23	equations	equation	NOUN
ejde-719	6	24	with	with	ADP
ejde-719	6	25	unbound	unbound	NOUN
ejde-719	6	26	operators	operator	NOUN
ejde-719	6	27	in	in	ADP
ejde-719	6	28	a	a	DET
ejde-719	6	29	banach	banach	NOUN
ejde-719	6	30	space	space	NOUN
ejde-719	6	31	.	.	PUNCT
ejde-719	7	1	the	the	DET
ejde-719	7	2	basic	basic	ADJ
ejde-719	7	3	method	method	NOUN
ejde-719	7	4	for	for	ADP
ejde-719	7	5	the	the	DET
ejde-719	7	6	stability	stability	NOUN
ejde-719	7	7	analysis	analysis	NOUN
ejde-719	7	8	of	of	ADP
ejde-719	7	9	functional	functional	ADJ
ejde-719	7	10	differential	differential	ADJ
ejde-719	7	11	equations	equation	NOUN
ejde-719	7	12	is	be	AUX
ejde-719	7	13	the	the	DET
ejde-719	7	14	lyapunov	lyapunov	NOUN
ejde-719	7	15	-	-	PUNCT
ejde-719	7	16	krasovskij	krasovskij	PROPN
ejde-719	7	17	method	method	NOUN
ejde-719	7	18	[	[	X
ejde-719	7	19	4	4	NUM
ejde-719	7	20	,	,	PUNCT
ejde-719	7	21	13	13	NUM
ejde-719	7	22	]	]	PUNCT
ejde-719	7	23	.	.	PUNCT
ejde-719	8	1	by	by	ADP
ejde-719	8	2	that	that	DET
ejde-719	8	3	method	method	NOUN
ejde-719	8	4	,	,	PUNCT
ejde-719	8	5	many	many	ADJ
ejde-719	8	6	results	result	NOUN
ejde-719	8	7	have	have	AUX
ejde-719	8	8	been	be	AUX
ejde-719	8	9	obtained	obtain	VERB
ejde-719	8	10	.	.	PUNCT
ejde-719	9	1	recently	recently	ADV
ejde-719	9	2	,	,	PUNCT
ejde-719	9	3	that	that	DET
ejde-719	9	4	method	method	NOUN
ejde-719	9	5	has	have	AUX
ejde-719	9	6	been	be	AUX
ejde-719	9	7	extended	extend	VERB
ejde-719	9	8	to	to	ADP
ejde-719	9	9	functional	functional	ADJ
ejde-719	9	10	differential	differential	ADJ
ejde-719	9	11	equations	equation	NOUN
ejde-719	9	12	in	in	ADP
ejde-719	9	13	a	a	DET
ejde-719	9	14	hilbert	hilbert	NOUN
ejde-719	9	15	space	space	NOUN
ejde-719	9	16	,	,	PUNCT
ejde-719	9	17	see	see	VERB
ejde-719	9	18	[	[	X
ejde-719	9	19	1	1	NUM
ejde-719	9	20	,	,	PUNCT
ejde-719	9	21	6	6	NUM
ejde-719	9	22	,	,	PUNCT
ejde-719	9	23	14	14	NUM
ejde-719	9	24	,	,	PUNCT
ejde-719	9	25	15	15	NUM
ejde-719	9	26	]	]	PUNCT
ejde-719	9	27	and	and	CCONJ
ejde-719	9	28	references	reference	NOUN
ejde-719	9	29	given	give	VERB
ejde-719	9	30	therein	therein	ADV
ejde-719	9	31	.	.	PUNCT
ejde-719	10	1	in	in	ADP
ejde-719	10	2	[	[	X
ejde-719	10	3	8	8	NUM
ejde-719	10	4	,	,	PUNCT
ejde-719	10	5	10	10	NUM
ejde-719	10	6	]	]	PUNCT
ejde-719	10	7	the	the	DET
ejde-719	10	8	delay	delay	NOUN
ejde-719	10	9	-	-	PUNCT
ejde-719	10	10	dependent	dependent	ADJ
ejde-719	10	11	stability	stability	NOUN
ejde-719	10	12	conditions	condition	NOUN
ejde-719	10	13	for	for	ADP
ejde-719	10	14	equations	equation	NOUN
ejde-719	10	15	in	in	ADP
ejde-719	10	16	a	a	DET
ejde-719	10	17	banach	banach	NOUN
ejde-719	10	18	space	space	NOUN
ejde-719	10	19	with	with	ADP
ejde-719	10	20	bounded	bounded	ADJ
ejde-719	10	21	operators	operator	NOUN
ejde-719	10	22	have	have	AUX
ejde-719	10	23	been	be	AUX
ejde-719	10	24	derived	derive	VERB
ejde-719	10	25	.	.	PUNCT
ejde-719	11	1	to	to	ADP
ejde-719	11	2	the	the	DET
ejde-719	11	3	best	good	ADJ
ejde-719	11	4	of	of	ADP
ejde-719	11	5	our	our	PRON
ejde-719	11	6	knowledge	knowledge	NOUN
ejde-719	11	7	,	,	PUNCT
ejde-719	11	8	the	the	DET
ejde-719	11	9	delaydependent	delaydependent	ADJ
ejde-719	11	10	stability	stability	NOUN
ejde-719	11	11	conditions	condition	NOUN
ejde-719	11	12	for	for	ADP
ejde-719	11	13	equations	equation	NOUN
ejde-719	11	14	in	in	ADP
ejde-719	11	15	a	a	DET
ejde-719	11	16	banach	banach	NOUN
ejde-719	11	17	space	space	NOUN
ejde-719	11	18	with	with	ADP
ejde-719	11	19	unbounded	unbounded	ADJ
ejde-719	11	20	operators	operator	NOUN
ejde-719	11	21	are	be	AUX
ejde-719	11	22	not	not	PART
ejde-719	11	23	investigated	investigate	VERB
ejde-719	11	24	in	in	ADP
ejde-719	11	25	the	the	DET
ejde-719	11	26	available	available	ADJ
ejde-719	11	27	literature	literature	NOUN
ejde-719	11	28	.	.	PUNCT
ejde-719	12	1	it	it	PRON
ejde-719	12	2	should	should	AUX
ejde-719	12	3	be	be	AUX
ejde-719	12	4	noted	note	VERB
ejde-719	12	5	that	that	SCONJ
ejde-719	12	6	finding	find	VERB
ejde-719	12	7	the	the	DET
ejde-719	12	8	lyapunov	lyapunov	NOUN
ejde-719	12	9	-	-	PUNCT
ejde-719	12	10	krasovskij	krasovskij	PROPN
ejde-719	12	11	type	type	NOUN
ejde-719	12	12	functionals	functional	NOUN
ejde-719	12	13	or	or	CCONJ
ejde-719	12	14	solving	solve	VERB
ejde-719	12	15	the	the	DET
ejde-719	12	16	corresponding	correspond	VERB
ejde-719	12	17	operator	operator	NOUN
ejde-719	12	18	inequalities	inequality	NOUN
ejde-719	12	19	are	be	AUX
ejde-719	12	20	often	often	ADV
ejde-719	12	21	connected	connect	VERB
ejde-719	12	22	with	with	ADP
ejde-719	12	23	serious	serious	ADJ
ejde-719	12	24	mathematical	mathematical	ADJ
ejde-719	12	25	difficulties	difficulty	NOUN
ejde-719	12	26	,	,	PUNCT
ejde-719	12	27	to	to	ADP
ejde-719	12	28	the	the	DET
ejde-719	12	29	contrary	contrary	NOUN
ejde-719	12	30	,	,	PUNCT
ejde-719	12	31	the	the	DET
ejde-719	12	32	stability	stability	NOUN
ejde-719	12	33	conditions	condition	NOUN
ejde-719	12	34	presented	present	VERB
ejde-719	12	35	in	in	ADP
ejde-719	12	36	this	this	DET
ejde-719	12	37	paper	paper	NOUN
ejde-719	12	38	are	be	AUX
ejde-719	12	39	explicitly	explicitly	ADV
ejde-719	12	40	formulated	formulate	VERB
ejde-719	12	41	in	in	ADP
ejde-719	12	42	terms	term	NOUN
ejde-719	12	43	of	of	ADP
ejde-719	12	44	the	the	DET
ejde-719	12	45	coefficients	coefficient	NOUN
ejde-719	12	46	and	and	CCONJ
ejde-719	12	47	delays	delay	NOUN
ejde-719	12	48	.	.	PUNCT
ejde-719	13	1	the	the	DET
ejde-719	13	2	literature	literature	NOUN
ejde-719	13	3	on	on	ADP
ejde-719	13	4	the	the	DET
ejde-719	13	5	delaydependent	delaydependent	ADJ
ejde-719	13	6	stability	stability	NOUN
ejde-719	13	7	criteria	criterion	NOUN
ejde-719	13	8	is	be	AUX
ejde-719	13	9	rather	rather	ADV
ejde-719	13	10	rich	rich	ADJ
ejde-719	13	11	,	,	PUNCT
ejde-719	13	12	but	but	CCONJ
ejde-719	13	13	mainly	mainly	ADV
ejde-719	13	14	equations	equation	NOUN
ejde-719	13	15	in	in	ADP
ejde-719	13	16	a	a	DET
ejde-719	13	17	finite	finite	ADJ
ejde-719	13	18	dimensional	dimensional	ADJ
ejde-719	13	19	space	space	NOUN
ejde-719	13	20	are	be	AUX
ejde-719	13	21	considered	consider	VERB
ejde-719	13	22	,	,	PUNCT
ejde-719	13	23	see	see	VERB
ejde-719	13	24	[	[	X
ejde-719	13	25	2	2	NUM
ejde-719	13	26	,	,	PUNCT
ejde-719	13	27	3	3	NUM
ejde-719	13	28	,	,	PUNCT
ejde-719	13	29	13	13	NUM
ejde-719	13	30	]	]	PUNCT
ejde-719	13	31	.	.	PUNCT
ejde-719	14	1	everywhere	everywhere	ADV
ejde-719	14	2	below	below	ADV
ejde-719	14	3	,	,	PUNCT
ejde-719	14	4	x	x	X
ejde-719	14	5	is	be	AUX
ejde-719	14	6	a	a	DET
ejde-719	14	7	complex	complex	ADJ
ejde-719	14	8	banach	banach	NOUN
ejde-719	14	9	space	space	NOUN
ejde-719	14	10	with	with	ADP
ejde-719	14	11	a	a	DET
ejde-719	14	12	norm	norm	NOUN
ejde-719	14	13	∥	∥	X
ejde-719	14	14	·	·	PUNCT
ejde-719	15	1	∥x	∥x	NOUN
ejde-719	15	2	=	=	PUNCT
ejde-719	15	3	∥	∥	X
ejde-719	15	4	·	·	PUNCT
ejde-719	15	5	∥	∥	NOUN
ejde-719	15	6	and	and	CCONJ
ejde-719	15	7	the	the	DET
ejde-719	15	8	unit	unit	NOUN
ejde-719	15	9	operator	operator	NOUN
ejde-719	15	10	ix	ix	PRON
ejde-719	15	11	=	=	NOUN
ejde-719	15	12	i.	i.	NOUN
ejde-719	15	13	by	by	ADP
ejde-719	15	14	b(x	b(x	PROPN
ejde-719	15	15	)	)	PUNCT
ejde-719	15	16	,	,	PUNCT
ejde-719	15	17	we	we	PRON
ejde-719	15	18	denote	denote	VERB
ejde-719	15	19	the	the	DET
ejde-719	15	20	set	set	NOUN
ejde-719	15	21	of	of	ADP
ejde-719	15	22	all	all	DET
ejde-719	15	23	bounded	bound	VERB
ejde-719	15	24	linear	linear	PROPN
ejde-719	15	25	operators	operator	NOUN
ejde-719	15	26	in	in	ADP
ejde-719	15	27	x	x	X
ejde-719	15	28	.	.	PUNCT
ejde-719	16	1	for	for	ADP
ejde-719	16	2	a	a	DET
ejde-719	16	3	linear	linear	ADJ
ejde-719	16	4	operator	operator	NOUN
ejde-719	16	5	t	t	NOUN
ejde-719	16	6	,	,	PUNCT
ejde-719	16	7	σ(t	σ(t	PROPN
ejde-719	16	8	)	)	PUNCT
ejde-719	16	9	is	be	AUX
ejde-719	16	10	the	the	DET
ejde-719	16	11	spectrum	spectrum	NOUN
ejde-719	16	12	and	and	CCONJ
ejde-719	16	13	∥t∥x	∥t∥x	ADV
ejde-719	16	14	=	=	PUNCT
ejde-719	16	15	∥t∥	∥t∥	CCONJ
ejde-719	16	16	is	be	AUX
ejde-719	16	17	the	the	DET
ejde-719	16	18	operator	operator	NOUN
ejde-719	16	19	norm	norm	NOUN
ejde-719	16	20	of	of	ADP
ejde-719	16	21	t	t	PROPN
ejde-719	16	22	if	if	SCONJ
ejde-719	16	23	it	it	PRON
ejde-719	16	24	is	be	AUX
ejde-719	16	25	bounded	bound	VERB
ejde-719	16	26	.	.	PUNCT
ejde-719	17	1	2020	2020	NUM
ejde-719	17	2	mathematics	mathematic	NOUN
ejde-719	17	3	subject	subject	ADJ
ejde-719	17	4	classification	classification	NOUN
ejde-719	17	5	.	.	PUNCT
ejde-719	18	1	34k30	34k30	NUM
ejde-719	18	2	,	,	PUNCT
ejde-719	18	3	34k06	34k06	NUM
ejde-719	18	4	,	,	PUNCT
ejde-719	18	5	34k20	34k20	NUM
ejde-719	18	6	.	.	PUNCT
ejde-719	19	1	key	key	ADJ
ejde-719	19	2	words	word	NOUN
ejde-719	19	3	and	and	CCONJ
ejde-719	19	4	phrases	phrase	NOUN
ejde-719	19	5	.	.	PUNCT
ejde-719	20	1	banach	banach	NOUN
ejde-719	20	2	space	space	NOUN
ejde-719	20	3	;	;	PUNCT
ejde-719	20	4	delay	delay	VERB
ejde-719	20	5	differential	differential	ADJ
ejde-719	20	6	equation	equation	NOUN
ejde-719	20	7	;	;	PUNCT
ejde-719	20	8	stability	stability	NOUN
ejde-719	20	9	;	;	PUNCT
ejde-719	20	10	integro	integro	ADJ
ejde-719	20	11	-	-	PUNCT
ejde-719	20	12	differential	differential	NOUN
ejde-719	20	13	equation	equation	NOUN
ejde-719	20	14	.	.	PUNCT
ejde-719	21	1	©	©	PROPN
ejde-719	21	2	2024	2024	NUM
ejde-719	21	3	.	.	PUNCT
ejde-719	22	1	this	this	DET
ejde-719	22	2	work	work	NOUN
ejde-719	22	3	is	be	AUX
ejde-719	22	4	licensed	license	VERB
ejde-719	22	5	under	under	ADP
ejde-719	22	6	a	a	DET
ejde-719	22	7	cc	cc	NOUN
ejde-719	22	8	by	by	ADP
ejde-719	22	9	4.0	4.0	NUM
ejde-719	22	10	license	license	NOUN
ejde-719	22	11	.	.	PUNCT
ejde-719	23	1	submitted	submit	VERB
ejde-719	23	2	may	may	PROPN
ejde-719	23	3	16	16	NUM
ejde-719	23	4	,	,	PUNCT
ejde-719	23	5	2024	2024	NUM
ejde-719	23	6	.	.	PUNCT
ejde-719	24	1	published	publish	VERB
ejde-719	24	2	november	november	PROPN
ejde-719	24	3	26	26	NUM
ejde-719	24	4	,	,	PUNCT
ejde-719	24	5	2024	2024	NUM
ejde-719	24	6	.	.	PUNCT
ejde-719	24	7	1	1	NUM
ejde-719	24	8	2	2	NUM
ejde-719	24	9	m.	m.	NOUN
ejde-719	24	10	gil	gil	PROPN
ejde-719	24	11	’	'	PUNCT
ejde-719	24	12	ejde-2024/76	ejde-2024/76	ADJ
ejde-719	24	13	furthermore	furthermore	ADV
ejde-719	24	14	,	,	PUNCT
ejde-719	24	15	c(j	c(j	PROPN
ejde-719	24	16	,	,	PUNCT
ejde-719	24	17	x	x	X
ejde-719	24	18	)	)	PUNCT
ejde-719	24	19	is	be	AUX
ejde-719	24	20	the	the	DET
ejde-719	24	21	space	space	NOUN
ejde-719	24	22	of	of	ADP
ejde-719	24	23	x	x	SYM
ejde-719	24	24	-valued	-value	VERB
ejde-719	24	25	functions	function	NOUN
ejde-719	24	26	f	f	NOUN
ejde-719	24	27	defined	define	VERB
ejde-719	24	28	and	and	CCONJ
ejde-719	24	29	continuous	continuous	ADJ
ejde-719	24	30	on	on	ADP
ejde-719	24	31	a	a	DET
ejde-719	24	32	finite	finite	NOUN
ejde-719	24	33	or	or	CCONJ
ejde-719	24	34	infinite	infinite	ADJ
ejde-719	24	35	real	real	ADJ
ejde-719	24	36	segment	segment	NOUN
ejde-719	24	37	j	j	PROPN
ejde-719	24	38	,	,	PUNCT
ejde-719	24	39	and	and	CCONJ
ejde-719	24	40	equipped	equip	VERB
ejde-719	24	41	with	with	ADP
ejde-719	24	42	the	the	DET
ejde-719	24	43	finite	finite	ADJ
ejde-719	24	44	norm	norm	NOUN
ejde-719	24	45	.	.	PUNCT
ejde-719	25	1	∥f∥c(j	∥f∥c(j	ADJ
ejde-719	25	2	)	)	PUNCT
ejde-719	25	3	=	=	SYM
ejde-719	25	4	∥f∥c(j	∥f∥c(j	NOUN
ejde-719	25	5	,	,	PUNCT
ejde-719	25	6	x	x	X
ejde-719	25	7	)	)	PUNCT
ejde-719	25	8	:	:	PUNCT
ejde-719	26	1	=	=	PUNCT
ejde-719	26	2	sup	sup	NOUN
ejde-719	26	3	t∈j	t∈j	NOUN
ejde-719	26	4	∥f(t)∥x	∥f(t)∥x	PROPN
ejde-719	26	5	.	.	PUNCT
ejde-719	27	1	in	in	ADP
ejde-719	27	2	addition	addition	NOUN
ejde-719	27	3	,	,	PUNCT
ejde-719	27	4	w	w	PROPN
ejde-719	27	5	(	(	PUNCT
ejde-719	27	6	j	j	PROPN
ejde-719	27	7	,	,	PUNCT
ejde-719	27	8	x	x	X
ejde-719	27	9	)	)	PUNCT
ejde-719	27	10	is	be	AUX
ejde-719	27	11	the	the	DET
ejde-719	27	12	space	space	NOUN
ejde-719	27	13	of	of	ADP
ejde-719	27	14	x	x	SYM
ejde-719	27	15	-valued	-value	VERB
ejde-719	27	16	functions	function	NOUN
ejde-719	27	17	f	f	NOUN
ejde-719	27	18	defined	define	VERB
ejde-719	27	19	and	and	CCONJ
ejde-719	27	20	strongly	strongly	ADV
ejde-719	27	21	continuously	continuously	ADV
ejde-719	27	22	differentiable	differentiable	ADJ
ejde-719	27	23	on	on	ADP
ejde-719	27	24	j	j	PROPN
ejde-719	27	25	,	,	PUNCT
ejde-719	27	26	and	and	CCONJ
ejde-719	27	27	equipped	equip	VERB
ejde-719	27	28	with	with	ADP
ejde-719	27	29	the	the	DET
ejde-719	27	30	norm	norm	NOUN
ejde-719	27	31	∥f∥w	∥f∥w	PROPN
ejde-719	27	32	(	(	PUNCT
ejde-719	27	33	j	j	NOUN
ejde-719	27	34	)	)	PUNCT
ejde-719	28	1	=	=	SYM
ejde-719	28	2	∥f∥w	∥f∥w	PROPN
ejde-719	28	3	(	(	PUNCT
ejde-719	28	4	j	j	NOUN
ejde-719	28	5	,	,	PUNCT
ejde-719	28	6	x	x	PROPN
ejde-719	28	7	)	)	PUNCT
ejde-719	28	8	:	:	PUNCT
ejde-719	29	1	=	=	PUNCT
ejde-719	29	2	max{sup	max{sup	ADJ
ejde-719	29	3	t∈j	t∈j	VERB
ejde-719	29	4	∥f	∥f	PROPN
ejde-719	29	5	′(t)∥x	′(t)∥x	NUM
ejde-719	29	6	,	,	PUNCT
ejde-719	29	7	sup	sup	NOUN
ejde-719	29	8	t∈j	t∈j	NOUN
ejde-719	29	9	∥f(t)∥x	∥f(t)∥x	PROPN
ejde-719	29	10	}	}	PUNCT
ejde-719	29	11	.	.	PUNCT
ejde-719	30	1	denote	denote	NOUN
ejde-719	30	2	also	also	ADV
ejde-719	30	3	r+	r+	VERB
ejde-719	30	4	=	=	PUNCT
ejde-719	31	1	[	[	X
ejde-719	31	2	0,∞	0,∞	NUM
ejde-719	31	3	)	)	PUNCT
ejde-719	31	4	and	and	CCONJ
ejde-719	31	5	rη	rη	NOUN
ejde-719	31	6	=	=	SYM
ejde-719	32	1	[	[	X
ejde-719	32	2	−η,∞	−η,∞	NOUN
ejde-719	32	3	)	)	PUNCT
ejde-719	32	4	for	for	ADP
ejde-719	32	5	a	a	DET
ejde-719	32	6	finite	finite	PROPN
ejde-719	32	7	η	η	PROPN
ejde-719	32	8	>	>	X
ejde-719	32	9	0	0	NUM
ejde-719	32	10	.	.	PUNCT
ejde-719	33	1	throughout	throughout	ADP
ejde-719	33	2	this	this	DET
ejde-719	33	3	article	article	NOUN
ejde-719	33	4	a	a	PRON
ejde-719	33	5	is	be	AUX
ejde-719	33	6	a	a	DET
ejde-719	33	7	closed	closed	ADJ
ejde-719	33	8	linear	linear	ADJ
ejde-719	33	9	operator	operator	NOUN
ejde-719	33	10	with	with	ADP
ejde-719	33	11	a	a	DET
ejde-719	33	12	dense	dense	ADJ
ejde-719	33	13	domaind(a	domaind(a	NOUN
ejde-719	33	14	)	)	PUNCT
ejde-719	33	15	⊆	⊆	NUM
ejde-719	33	16	x	x	X
ejde-719	33	17	,	,	PUNCT
ejde-719	33	18	generating	generate	VERB
ejde-719	33	19	a	a	DET
ejde-719	33	20	strongly	strongly	ADV
ejde-719	33	21	continuous	continuous	ADJ
ejde-719	33	22	semigroup	semigroup	NOUN
ejde-719	33	23	eat	eat	NOUN
ejde-719	33	24	on	on	ADP
ejde-719	33	25	x	x	X
ejde-719	33	26	,	,	PUNCT
ejde-719	33	27	and	and	CCONJ
ejde-719	33	28	b	b	X
ejde-719	33	29	∈	∈	PROPN
ejde-719	33	30	b(x	b(x	NOUN
ejde-719	33	31	)	)	PUNCT
ejde-719	33	32	maps	map	NOUN
ejde-719	33	33	x	x	PUNCT
ejde-719	33	34	into	into	ADP
ejde-719	33	35	d(a	d(a	PROPN
ejde-719	33	36	)	)	PUNCT
ejde-719	33	37	.	.	PUNCT
ejde-719	34	1	our	our	PRON
ejde-719	34	2	main	main	ADJ
ejde-719	34	3	object	object	NOUN
ejde-719	34	4	is	be	AUX
ejde-719	34	5	to	to	PART
ejde-719	34	6	study	study	VERB
ejde-719	34	7	the	the	DET
ejde-719	34	8	equation	equation	NOUN
ejde-719	34	9	y′(t	y′(t	PUNCT
ejde-719	34	10	)	)	PUNCT
ejde-719	34	11	=	=	SYM
ejde-719	34	12	ay(t	ay(t	X
ejde-719	34	13	)	)	PUNCT
ejde-719	35	1	+	+	NOUN
ejde-719	35	2	by(t−	by(t−	PROPN
ejde-719	35	3	h	h	NOUN
ejde-719	35	4	)	)	PUNCT
ejde-719	35	5	(	(	PUNCT
ejde-719	35	6	t	t	X
ejde-719	35	7	>	>	X
ejde-719	35	8	0	0	NUM
ejde-719	35	9	;	;	PUNCT
ejde-719	35	10	0	0	NUM
ejde-719	35	11	<	<	X
ejde-719	35	12	h	h	PROPN
ejde-719	35	13	=	=	SYM
ejde-719	35	14	const.∞	const.∞	PROPN
ejde-719	35	15	)	)	PUNCT
ejde-719	35	16	(	(	PUNCT
ejde-719	35	17	1.1	1.1	NUM
ejde-719	35	18	)	)	PUNCT
ejde-719	35	19	with	with	ADP
ejde-719	35	20	the	the	DET
ejde-719	35	21	initial	initial	ADJ
ejde-719	35	22	condition	condition	NOUN
ejde-719	35	23	y(t	y(t	NUM
ejde-719	35	24	)	)	PUNCT
ejde-719	36	1	=	=	SYM
ejde-719	36	2	ϕ(t	ϕ(t	NUM
ejde-719	36	3	)	)	PUNCT
ejde-719	36	4	(	(	PUNCT
ejde-719	36	5	−h	−h	VERB
ejde-719	36	6	≤	≤	X
ejde-719	36	7	t	t	NOUN
ejde-719	36	8	≤	≤	NOUN
ejde-719	36	9	0	0	NUM
ejde-719	36	10	)	)	PUNCT
ejde-719	36	11	,	,	PUNCT
ejde-719	36	12	(	(	PUNCT
ejde-719	36	13	1.2	1.2	NUM
ejde-719	36	14	)	)	PUNCT
ejde-719	36	15	where	where	SCONJ
ejde-719	36	16	ϕ	ϕ	NOUN
ejde-719	36	17	∈w	∈w	X
ejde-719	36	18	(	(	PUNCT
ejde-719	37	1	[	[	X
ejde-719	37	2	−h	−h	ADJ
ejde-719	37	3	,	,	PUNCT
ejde-719	37	4	0],x	0],x	NUM
ejde-719	37	5	)	)	PUNCT
ejde-719	38	1	∩d(a	∩d(a	PROPN
ejde-719	38	2	)	)	PUNCT
ejde-719	38	3	is	be	AUX
ejde-719	38	4	given	give	VERB
ejde-719	38	5	.	.	PUNCT
ejde-719	39	1	various	various	ADJ
ejde-719	39	2	integro	integro	ADJ
ejde-719	39	3	-	-	PUNCT
ejde-719	39	4	differential	differential	NOUN
ejde-719	39	5	equations	equation	NOUN
ejde-719	39	6	with	with	ADP
ejde-719	39	7	differential	differential	ADJ
ejde-719	39	8	operators	operator	NOUN
ejde-719	39	9	a	a	DET
ejde-719	39	10	and	and	CCONJ
ejde-719	39	11	integral	integral	ADJ
ejde-719	39	12	operators	operator	NOUN
ejde-719	39	13	b	b	X
ejde-719	39	14	are	be	AUX
ejde-719	39	15	examples	example	NOUN
ejde-719	39	16	of	of	ADP
ejde-719	39	17	(	(	PUNCT
ejde-719	39	18	1.1	1.1	NUM
ejde-719	39	19	)	)	PUNCT
ejde-719	39	20	.	.	PUNCT
ejde-719	40	1	a	a	DET
ejde-719	40	2	solution	solution	NOUN
ejde-719	40	3	of	of	ADP
ejde-719	40	4	problem	problem	NOUN
ejde-719	40	5	(	(	PUNCT
ejde-719	40	6	1.1	1.1	NUM
ejde-719	40	7	)	)	PUNCT
ejde-719	40	8	,	,	PUNCT
ejde-719	40	9	(	(	PUNCT
ejde-719	40	10	1.2	1.2	NUM
ejde-719	40	11	)	)	PUNCT
ejde-719	40	12	is	be	AUX
ejde-719	40	13	defined	define	VERB
ejde-719	40	14	as	as	ADP
ejde-719	40	15	a	a	DET
ejde-719	40	16	continuous	continuous	ADJ
ejde-719	40	17	function	function	NOUN
ejde-719	40	18	y(t	y(t	NUM
ejde-719	40	19	)	)	PUNCT
ejde-719	40	20	defined	define	VERB
ejde-719	40	21	on	on	ADP
ejde-719	40	22	rη	rη	NOUN
ejde-719	40	23	with	with	ADP
ejde-719	40	24	values	value	NOUN
ejde-719	40	25	in	in	ADP
ejde-719	40	26	d(a	d(a	PROPN
ejde-719	40	27	)	)	PUNCT
ejde-719	40	28	,	,	PUNCT
ejde-719	40	29	having	have	VERB
ejde-719	40	30	a	a	DET
ejde-719	40	31	continuous	continuous	ADJ
ejde-719	40	32	derivative	derivative	NOUN
ejde-719	40	33	for	for	ADP
ejde-719	40	34	all	all	DET
ejde-719	40	35	t	t	NOUN
ejde-719	40	36	>	>	X
ejde-719	40	37	0	0	PUNCT
ejde-719	41	1	and	and	CCONJ
ejde-719	41	2	the	the	DET
ejde-719	41	3	right	right	ADJ
ejde-719	41	4	derivative	derivative	NOUN
ejde-719	41	5	at	at	ADP
ejde-719	41	6	zero	zero	NUM
ejde-719	41	7	,	,	PUNCT
ejde-719	41	8	and	and	CCONJ
ejde-719	41	9	satisfying	satisfy	VERB
ejde-719	41	10	(	(	PUNCT
ejde-719	41	11	1.1	1.1	NUM
ejde-719	41	12	)	)	PUNCT
ejde-719	41	13	,	,	PUNCT
ejde-719	41	14	and	and	CCONJ
ejde-719	41	15	(	(	PUNCT
ejde-719	41	16	1.2	1.2	NUM
ejde-719	41	17	)	)	PUNCT
ejde-719	41	18	.	.	PUNCT
ejde-719	42	1	let	let	VERB
ejde-719	42	2	∫	∫	PROPN
ejde-719	42	3	∞	∞	PROPN
ejde-719	42	4	0	0	NUM
ejde-719	42	5	∥eas∥xds	∥eas∥xds	NUM
ejde-719	42	6	<	<	X
ejde-719	42	7	∞.	∞.	PROPN
ejde-719	42	8	(	(	PUNCT
ejde-719	42	9	1.3	1.3	NUM
ejde-719	42	10	)	)	PUNCT
ejde-719	42	11	since	since	SCONJ
ejde-719	42	12	ab	ab	PROPN
ejde-719	42	13	is	be	AUX
ejde-719	42	14	defined	define	VERB
ejde-719	42	15	on	on	ADP
ejde-719	42	16	the	the	DET
ejde-719	42	17	whole	whole	NOUN
ejde-719	42	18	x	x	PUNCT
ejde-719	42	19	,	,	PUNCT
ejde-719	42	20	due	due	ADP
ejde-719	42	21	to	to	ADP
ejde-719	42	22	the	the	DET
ejde-719	42	23	banach	banach	NOUN
ejde-719	42	24	theorem	theorem	NOUN
ejde-719	42	25	[	[	X
ejde-719	42	26	12	12	NUM
ejde-719	42	27	,	,	PUNCT
ejde-719	42	28	section	section	NOUN
ejde-719	42	29	2	2	NUM
ejde-719	42	30	]	]	X
ejde-719	42	31	ab	ab	PROPN
ejde-719	42	32	is	be	AUX
ejde-719	42	33	bounded	bound	VERB
ejde-719	42	34	,	,	PUNCT
ejde-719	42	35	and	and	CCONJ
ejde-719	42	36	consequently	consequently	ADV
ejde-719	42	37	,	,	PUNCT
ejde-719	42	38	ψa	ψa	X
ejde-719	42	39	:	:	PUNCT
ejde-719	42	40	=	=	SYM
ejde-719	42	41	∫	∫	PROPN
ejde-719	42	42	∞	∞	NUM
ejde-719	42	43	0	0	NUM
ejde-719	42	44	∥easab∥xds	∥easab∥xds	X
ejde-719	43	1	<	<	X
ejde-719	43	2	∞.	∞.	PROPN
ejde-719	43	3	in	in	ADP
ejde-719	43	4	addition	addition	NOUN
ejde-719	43	5	,	,	PUNCT
ejde-719	43	6	put	put	VERB
ejde-719	43	7	m	m	NOUN
ejde-719	43	8	=	=	NOUN
ejde-719	43	9	a+b	a+b	PUNCT
ejde-719	43	10	and	and	CCONJ
ejde-719	43	11	assume	assume	VERB
ejde-719	43	12	that∫	that∫	NOUN
ejde-719	43	13	∞	∞	PROPN
ejde-719	43	14	0	0	NUM
ejde-719	43	15	∥ems∥xds	∥ems∥xds	NUM
ejde-719	43	16	<	<	X
ejde-719	43	17	∞.	∞.	PROPN
ejde-719	43	18	(	(	PUNCT
ejde-719	43	19	1.4	1.4	NUM
ejde-719	43	20	)	)	PUNCT
ejde-719	43	21	therefore	therefore	ADV
ejde-719	43	22	ψm	ψm	PUNCT
ejde-719	43	23	:	:	PUNCT
ejde-719	44	1	=	=	NOUN
ejde-719	44	2	∫	∫	PROPN
ejde-719	44	3	∞	∞	NUM
ejde-719	44	4	0	0	NUM
ejde-719	45	1	∥emsb∥xds	∥emsb∥xds	PROPN
ejde-719	45	2	<	<	X
ejde-719	45	3	∞.	∞.	PROPN
ejde-719	45	4	now	now	ADV
ejde-719	45	5	we	we	PRON
ejde-719	45	6	are	be	AUX
ejde-719	45	7	in	in	ADP
ejde-719	45	8	a	a	DET
ejde-719	45	9	position	position	NOUN
ejde-719	45	10	to	to	PART
ejde-719	45	11	formulate	formulate	VERB
ejde-719	45	12	the	the	DET
ejde-719	45	13	main	main	ADJ
ejde-719	45	14	result	result	NOUN
ejde-719	45	15	of	of	ADP
ejde-719	45	16	the	the	DET
ejde-719	45	17	paper	paper	NOUN
ejde-719	45	18	.	.	PUNCT
ejde-719	46	1	theorem	theorem	VERB
ejde-719	46	2	1.1	1.1	NUM
ejde-719	46	3	.	.	PUNCT
ejde-719	47	1	let	let	VERB
ejde-719	47	2	conditions	condition	NOUN
ejde-719	47	3	(	(	PUNCT
ejde-719	47	4	1.3),(1.4	1.3),(1.4	NUM
ejde-719	47	5	)	)	PUNCT
ejde-719	47	6	and	and	CCONJ
ejde-719	47	7	hψm	hψm	NOUN
ejde-719	47	8	(	(	PUNCT
ejde-719	47	9	ψa	ψa	NOUN
ejde-719	47	10	+	+	X
ejde-719	47	11	∥b∥x	∥b∥x	NOUN
ejde-719	47	12	)	)	PUNCT
ejde-719	47	13	<	<	X
ejde-719	47	14	1	1	NUM
ejde-719	47	15	(	(	PUNCT
ejde-719	47	16	1.5	1.5	NUM
ejde-719	47	17	)	)	PUNCT
ejde-719	47	18	hold	hold	NOUN
ejde-719	47	19	.	.	PUNCT
ejde-719	48	1	then	then	ADV
ejde-719	48	2	problem	problem	NOUN
ejde-719	48	3	(	(	PUNCT
ejde-719	48	4	1.1	1.1	NUM
ejde-719	48	5	)	)	PUNCT
ejde-719	48	6	,	,	PUNCT
ejde-719	48	7	(	(	PUNCT
ejde-719	48	8	1.2	1.2	NUM
ejde-719	48	9	)	)	PUNCT
ejde-719	48	10	with	with	ADP
ejde-719	48	11	ϕ	ϕ	PROPN
ejde-719	48	12	∈	∈	PROPN
ejde-719	48	13	w	w	PROPN
ejde-719	48	14	(	(	PUNCT
ejde-719	48	15	−h	−h	ADJ
ejde-719	48	16	,	,	PUNCT
ejde-719	48	17	0	0	X
ejde-719	48	18	)	)	PUNCT
ejde-719	48	19	∩d(a	∩d(a	PROPN
ejde-719	48	20	)	)	PUNCT
ejde-719	48	21	has	have	VERB
ejde-719	48	22	a	a	DET
ejde-719	48	23	unique	unique	ADJ
ejde-719	48	24	solution	solution	NOUN
ejde-719	48	25	y(t	y(t	NUM
ejde-719	48	26	)	)	PUNCT
ejde-719	48	27	,	,	PUNCT
ejde-719	48	28	which	which	PRON
ejde-719	48	29	satisfies	satisfy	VERB
ejde-719	48	30	the	the	DET
ejde-719	48	31	inequality	inequality	NOUN
ejde-719	48	32	∥y∥c(r+	∥y∥c(r+	X
ejde-719	48	33	)	)	PUNCT
ejde-719	48	34	≤	≤	NOUN
ejde-719	48	35	c0∥ϕ∥w	c0∥ϕ∥w	ADV
ejde-719	48	36	(	(	PUNCT
ejde-719	48	37	−h,0	−h,0	NOUN
ejde-719	48	38	)	)	PUNCT
ejde-719	48	39	,	,	PUNCT
ejde-719	48	40	where	where	SCONJ
ejde-719	48	41	the	the	DET
ejde-719	48	42	constant	constant	ADJ
ejde-719	48	43	c0	c0	NOUN
ejde-719	48	44	≥	≥	NUM
ejde-719	48	45	1	1	NUM
ejde-719	48	46	does	do	AUX
ejde-719	48	47	not	not	PART
ejde-719	48	48	depend	depend	VERB
ejde-719	48	49	on	on	ADP
ejde-719	48	50	ϕ.	ϕ.	PROPN
ejde-719	48	51	ejde-2024/76	ejde-2024/76	ADJ
ejde-719	48	52	delay	delay	NOUN
ejde-719	48	53	-	-	PUNCT
ejde-719	48	54	dependent	dependent	ADJ
ejde-719	48	55	stability	stability	NOUN
ejde-719	48	56	conditions	condition	NOUN
ejde-719	48	57	3	3	NUM
ejde-719	48	58	the	the	DET
ejde-719	48	59	proof	proof	NOUN
ejde-719	48	60	of	of	ADP
ejde-719	48	61	this	this	DET
ejde-719	48	62	theorem	theorem	NOUN
ejde-719	48	63	is	be	AUX
ejde-719	48	64	presented	present	VERB
ejde-719	48	65	in	in	ADP
ejde-719	48	66	the	the	DET
ejde-719	48	67	next	next	ADJ
ejde-719	48	68	section	section	NOUN
ejde-719	48	69	.	.	PUNCT
ejde-719	49	1	theorem	theorem	VERB
ejde-719	49	2	1.1	1.1	NUM
ejde-719	49	3	gives	give	VERB
ejde-719	49	4	us	we	PRON
ejde-719	49	5	the	the	DET
ejde-719	49	6	conditions	condition	NOUN
ejde-719	49	7	for	for	ADP
ejde-719	49	8	the	the	DET
ejde-719	49	9	lyapunov	lyapunov	ADJ
ejde-719	49	10	stability	stability	NOUN
ejde-719	49	11	with	with	ADP
ejde-719	49	12	respect	respect	NOUN
ejde-719	49	13	to	to	ADP
ejde-719	49	14	w	w	PROPN
ejde-719	49	15	(	(	PUNCT
ejde-719	49	16	−h	−h	ADJ
ejde-719	49	17	,	,	PUNCT
ejde-719	49	18	0	0	NUM
ejde-719	49	19	)	)	PUNCT
ejde-719	49	20	.	.	PUNCT
ejde-719	50	1	we	we	PRON
ejde-719	50	2	will	will	AUX
ejde-719	50	3	say	say	VERB
ejde-719	50	4	that	that	SCONJ
ejde-719	50	5	(	(	PUNCT
ejde-719	50	6	1.1	1.1	NUM
ejde-719	50	7	)	)	PUNCT
ejde-719	50	8	is	be	AUX
ejde-719	50	9	exponentially	exponentially	ADV
ejde-719	50	10	stable	stable	ADJ
ejde-719	50	11	with	with	ADP
ejde-719	50	12	respect	respect	NOUN
ejde-719	50	13	to	to	ADP
ejde-719	50	14	w	w	PROPN
ejde-719	50	15	(	(	PUNCT
ejde-719	50	16	−h	−h	ADJ
ejde-719	50	17	,	,	PUNCT
ejde-719	50	18	0	0	NUM
ejde-719	50	19	)	)	PUNCT
ejde-719	50	20	,	,	PUNCT
ejde-719	50	21	if	if	SCONJ
ejde-719	50	22	there	there	PRON
ejde-719	50	23	are	be	VERB
ejde-719	50	24	constants	constant	NOUN
ejde-719	50	25	α	α	NOUN
ejde-719	50	26	>	>	X
ejde-719	50	27	0	0	PUNCT
ejde-719	50	28	and	and	CCONJ
ejde-719	50	29	c1	c1	PROPN
ejde-719	50	30	≥	≥	NUM
ejde-719	50	31	1	1	NUM
ejde-719	50	32	independent	independent	NOUN
ejde-719	50	33	of	of	ADP
ejde-719	50	34	ϕ	ϕ	PROPN
ejde-719	50	35	∈w	∈w	PROPN
ejde-719	50	36	(	(	PUNCT
ejde-719	50	37	−h	−h	ADJ
ejde-719	50	38	,	,	PUNCT
ejde-719	50	39	0	0	NUM
ejde-719	50	40	)	)	PUNCT
ejde-719	50	41	,	,	PUNCT
ejde-719	50	42	such	such	ADJ
ejde-719	50	43	that	that	SCONJ
ejde-719	50	44	∥y(t)∥x	∥y(t)∥x	PROPN
ejde-719	50	45	≤	≤	NUM
ejde-719	50	46	c1e	c1e	NOUN
ejde-719	50	47	−αt∥ϕ∥w	−αt∥ϕ∥w	PROPN
ejde-719	50	48	(	(	PUNCT
ejde-719	50	49	−h,0	−h,0	PROPN
ejde-719	50	50	)	)	PUNCT
ejde-719	50	51	(	(	PUNCT
ejde-719	50	52	t	t	PROPN
ejde-719	50	53	≥	≥	NOUN
ejde-719	50	54	0	0	NUM
ejde-719	50	55	)	)	PUNCT
ejde-719	50	56	for	for	ADP
ejde-719	50	57	any	any	DET
ejde-719	50	58	solution	solution	NOUN
ejde-719	50	59	of	of	ADP
ejde-719	50	60	(	(	PUNCT
ejde-719	50	61	1.1	1.1	NUM
ejde-719	50	62	)	)	PUNCT
ejde-719	50	63	,	,	PUNCT
ejde-719	50	64	(	(	PUNCT
ejde-719	50	65	1.2	1.2	NUM
ejde-719	50	66	)	)	PUNCT
ejde-719	50	67	.	.	PUNCT
ejde-719	51	1	assume	assume	VERB
ejde-719	51	2	that	that	SCONJ
ejde-719	51	3	the	the	DET
ejde-719	51	4	semigroups	semigroup	NOUN
ejde-719	51	5	eat	eat	VERB
ejde-719	51	6	and	and	CCONJ
ejde-719	51	7	emt	emt	PROPN
ejde-719	51	8	are	be	AUX
ejde-719	51	9	exponentially	exponentially	ADV
ejde-719	51	10	stable	stable	ADJ
ejde-719	51	11	:	:	PUNCT
ejde-719	51	12	∥eat∥x	∥eat∥x	ADV
ejde-719	51	13	≤	≤	ADJ
ejde-719	51	14	cae	cae	NOUN
ejde-719	51	15	−αat	−αat	NOUN
ejde-719	51	16	and	and	CCONJ
ejde-719	51	17	∥emt∥x	∥emt∥x	ADJ
ejde-719	51	18	≤	≤	NUM
ejde-719	51	19	cme	cme	PROPN
ejde-719	51	20	−αm	−αm	PROPN
ejde-719	51	21	t	t	PROPN
ejde-719	51	22	,	,	PUNCT
ejde-719	51	23	(	(	PUNCT
ejde-719	51	24	1.6	1.6	NUM
ejde-719	51	25	)	)	PUNCT
ejde-719	51	26	where	where	SCONJ
ejde-719	51	27	t	t	PROPN
ejde-719	51	28	≥	≥	NOUN
ejde-719	51	29	0	0	NUM
ejde-719	51	30	,	,	PUNCT
ejde-719	51	31	αa	αa	ADV
ejde-719	51	32	>	>	X
ejde-719	51	33	0	0	NUM
ejde-719	51	34	,	,	PUNCT
ejde-719	51	35	αm	αm	X
ejde-719	51	36	>	>	X
ejde-719	51	37	0	0	PROPN
ejde-719	51	38	,	,	PUNCT
ejde-719	51	39	ca	can	AUX
ejde-719	51	40	≥	≥	NOUN
ejde-719	51	41	1	1	NUM
ejde-719	51	42	,	,	PUNCT
ejde-719	51	43	cm	cm	NOUN
ejde-719	51	44	≥	≥	NOUN
ejde-719	51	45	1	1	NUM
ejde-719	51	46	.	.	PUNCT
ejde-719	52	1	then	then	ADV
ejde-719	52	2	ψa	ψa	X
ejde-719	52	3	≤	≤	NUM
ejde-719	53	1	∥ab∥x	∥ab∥x	PROPN
ejde-719	53	2	∫	∫	PROPN
ejde-719	54	1	∞	∞	PROPN
ejde-719	54	2	0	0	NUM
ejde-719	54	3	cae	cae	NOUN
ejde-719	54	4	−αatdt	−αatdt	NOUN
ejde-719	55	1	=	=	NOUN
ejde-719	55	2	ca∥ab∥x	ca∥ab∥x	PROPN
ejde-719	56	1	/αa	/αa	ADV
ejde-719	56	2	,	,	PUNCT
ejde-719	56	3	ψm	ψm	PROPN
ejde-719	56	4	≤	≤	NUM
ejde-719	56	5	cm∥b∥x	cm∥b∥x	NOUN
ejde-719	56	6	/αm	/αm	INTJ
ejde-719	56	7	.	.	PUNCT
ejde-719	57	1	so	so	ADV
ejde-719	57	2	(	(	PUNCT
ejde-719	57	3	1.5	1.5	NUM
ejde-719	57	4	)	)	PUNCT
ejde-719	57	5	is	be	AUX
ejde-719	57	6	provided	provide	VERB
ejde-719	57	7	by	by	ADP
ejde-719	57	8	the	the	DET
ejde-719	57	9	inequality	inequality	NOUN
ejde-719	57	10	hcm∥b∥x	hcm∥b∥x	PROPN
ejde-719	57	11	αm	αm	NOUN
ejde-719	57	12	(	(	PUNCT
ejde-719	57	13	ca∥ab∥x	ca∥ab∥x	PROPN
ejde-719	57	14	αa	αa	PROPN
ejde-719	57	15	+	+	NUM
ejde-719	57	16	∥b∥x	∥b∥x	NOUN
ejde-719	57	17	)	)	PUNCT
ejde-719	57	18	<	<	X
ejde-719	58	1	1	1	X
ejde-719	58	2	.	.	PUNCT
ejde-719	58	3	(	(	PUNCT
ejde-719	58	4	1.7	1.7	NUM
ejde-719	58	5	)	)	PUNCT
ejde-719	58	6	now	now	ADV
ejde-719	58	7	theorem	theorem	VERB
ejde-719	58	8	1.1	1.1	NUM
ejde-719	58	9	implies	imply	VERB
ejde-719	58	10	∥y∥c(r+	∥y∥c(r+	NOUN
ejde-719	58	11	)	)	PUNCT
ejde-719	58	12	≤	≤	PUNCT
ejde-719	58	13	c2∥ϕ∥w	c2∥ϕ∥w	PROPN
ejde-719	58	14	(	(	PUNCT
ejde-719	58	15	−h,0	−h,0	NOUN
ejde-719	58	16	)	)	PUNCT
ejde-719	58	17	,	,	PUNCT
ejde-719	58	18	(	(	PUNCT
ejde-719	58	19	1.8	1.8	NUM
ejde-719	58	20	)	)	PUNCT
ejde-719	58	21	where	where	SCONJ
ejde-719	58	22	c2	c2	PROPN
ejde-719	58	23	does	do	AUX
ejde-719	58	24	not	not	PART
ejde-719	58	25	depend	depend	VERB
ejde-719	58	26	on	on	ADP
ejde-719	58	27	ϕ.	ϕ.	PROPN
ejde-719	58	28	in	in	ADP
ejde-719	58	29	the	the	DET
ejde-719	58	30	next	next	ADJ
ejde-719	58	31	section	section	NOUN
ejde-719	58	32	we	we	PRON
ejde-719	58	33	also	also	ADV
ejde-719	58	34	show	show	VERB
ejde-719	58	35	that	that	SCONJ
ejde-719	58	36	theorem	theorem	VERB
ejde-719	58	37	1.1	1.1	NUM
ejde-719	58	38	implies	imply	VERB
ejde-719	58	39	the	the	DET
ejde-719	58	40	following	follow	VERB
ejde-719	58	41	result	result	NOUN
ejde-719	58	42	.	.	PUNCT
ejde-719	59	1	corollary	corollary	ADJ
ejde-719	59	2	1.2	1.2	NUM
ejde-719	59	3	.	.	PUNCT
ejde-719	60	1	let	let	VERB
ejde-719	60	2	conditions	condition	NOUN
ejde-719	60	3	(	(	PUNCT
ejde-719	60	4	1.6	1.6	NUM
ejde-719	60	5	)	)	PUNCT
ejde-719	60	6	and	and	CCONJ
ejde-719	60	7	(	(	PUNCT
ejde-719	60	8	1.7	1.7	NUM
ejde-719	60	9	)	)	PUNCT
ejde-719	60	10	hold	hold	NOUN
ejde-719	60	11	.	.	PUNCT
ejde-719	61	1	then	then	ADV
ejde-719	61	2	(	(	PUNCT
ejde-719	61	3	1.1	1.1	NUM
ejde-719	61	4	)	)	PUNCT
ejde-719	61	5	is	be	AUX
ejde-719	61	6	exponentially	exponentially	ADV
ejde-719	61	7	stable	stable	ADJ
ejde-719	61	8	with	with	ADP
ejde-719	61	9	respect	respect	NOUN
ejde-719	61	10	to	to	ADP
ejde-719	61	11	w	w	PROPN
ejde-719	61	12	(	(	PUNCT
ejde-719	61	13	−h	−h	ADJ
ejde-719	61	14	,	,	PUNCT
ejde-719	61	15	0	0	NUM
ejde-719	61	16	)	)	PUNCT
ejde-719	61	17	.	.	PUNCT
ejde-719	62	1	this	this	DET
ejde-719	62	2	corollary	corollary	NOUN
ejde-719	62	3	is	be	AUX
ejde-719	62	4	sharp	sharp	ADJ
ejde-719	62	5	:	:	PUNCT
ejde-719	62	6	if	if	SCONJ
ejde-719	62	7	b	b	X
ejde-719	62	8	=	=	SYM
ejde-719	62	9	0	0	NUM
ejde-719	62	10	,	,	PUNCT
ejde-719	62	11	then	then	ADV
ejde-719	62	12	its	its	PRON
ejde-719	62	13	conditions	condition	NOUN
ejde-719	62	14	are	be	AUX
ejde-719	62	15	necessary	necessary	ADJ
ejde-719	62	16	for	for	ADP
ejde-719	62	17	the	the	DET
ejde-719	62	18	exponential	exponential	ADJ
ejde-719	62	19	stability	stability	NOUN
ejde-719	62	20	.	.	PUNCT
ejde-719	63	1	moreover	moreover	ADV
ejde-719	63	2	,	,	PUNCT
ejde-719	63	3	its	its	PRON
ejde-719	63	4	conditions	condition	NOUN
ejde-719	63	5	are	be	AUX
ejde-719	63	6	necessary	necessary	ADJ
ejde-719	63	7	if	if	SCONJ
ejde-719	63	8	h	h	NOUN
ejde-719	63	9	=	=	NOUN
ejde-719	63	10	0	0	NUM
ejde-719	63	11	and	and	CCONJ
ejde-719	63	12	a	a	DET
ejde-719	63	13	=	=	NOUN
ejde-719	63	14	0	0	NUM
ejde-719	63	15	.	.	NOUN
ejde-719	64	1	2	2	X
ejde-719	64	2	.	.	X
ejde-719	64	3	proofs	proof	NOUN
ejde-719	64	4	of	of	ADP
ejde-719	64	5	theorem	theorem	ADJ
ejde-719	64	6	1.1	1.1	NUM
ejde-719	64	7	and	and	CCONJ
ejde-719	64	8	corollary	corollary	ADJ
ejde-719	64	9	1.2	1.2	NUM
ejde-719	64	10	proof	proof	NOUN
ejde-719	64	11	of	of	ADP
ejde-719	64	12	theorem	theorem	ADJ
ejde-719	64	13	1.1	1.1	NUM
ejde-719	64	14	.	.	PUNCT
ejde-719	65	1	according	accord	VERB
ejde-719	65	2	to	to	ADP
ejde-719	65	3	[	[	X
ejde-719	65	4	9	9	NUM
ejde-719	65	5	,	,	PUNCT
ejde-719	65	6	theorem	theorem	VERB
ejde-719	65	7	1	1	NUM
ejde-719	65	8	]	]	PUNCT
ejde-719	65	9	,	,	PUNCT
ejde-719	65	10	problem	problem	NOUN
ejde-719	65	11	(	(	PUNCT
ejde-719	65	12	1.1	1.1	NUM
ejde-719	65	13	)	)	PUNCT
ejde-719	65	14	,	,	PUNCT
ejde-719	65	15	(	(	PUNCT
ejde-719	65	16	1.2	1.2	NUM
ejde-719	65	17	)	)	PUNCT
ejde-719	65	18	has	have	VERB
ejde-719	65	19	a	a	DET
ejde-719	65	20	unique	unique	ADJ
ejde-719	65	21	differentiable	differentiable	ADJ
ejde-719	65	22	solution	solution	NOUN
ejde-719	65	23	y(t	y(t	NUM
ejde-719	65	24	)	)	PUNCT
ejde-719	65	25	.	.	PUNCT
ejde-719	66	1	since	since	SCONJ
ejde-719	66	2	y(t	y(t	NUM
ejde-719	66	3	)	)	PUNCT
ejde-719	66	4	∈	∈	PROPN
ejde-719	66	5	d(a	d(a	PROPN
ejde-719	66	6	)	)	PUNCT
ejde-719	66	7	,	,	PUNCT
ejde-719	66	8	by	by	ADP
ejde-719	66	9	the	the	DET
ejde-719	66	10	variation	variation	NOUN
ejde-719	66	11	of	of	ADP
ejde-719	66	12	constants	constant	NOUN
ejde-719	66	13	formula	formula	NOUN
ejde-719	66	14	[	[	X
ejde-719	66	15	5	5	NUM
ejde-719	66	16	,	,	PUNCT
ejde-719	66	17	sect	sect	NOUN
ejde-719	66	18	.	.	PUNCT
ejde-719	67	1	iii.1	iii.1	VERB
ejde-719	67	2	]	]	X
ejde-719	67	3	,	,	PUNCT
ejde-719	67	4	(	(	PUNCT
ejde-719	67	5	1.1	1.1	NUM
ejde-719	67	6	)	)	PUNCT
ejde-719	67	7	is	be	AUX
ejde-719	67	8	equivalent	equivalent	ADJ
ejde-719	67	9	to	to	ADP
ejde-719	67	10	the	the	DET
ejde-719	67	11	equation	equation	NOUN
ejde-719	67	12	y(t	y(t	PUNCT
ejde-719	67	13	)	)	PUNCT
ejde-719	68	1	=	=	SYM
ejde-719	68	2	eatϕ(0	eatϕ(0	NOUN
ejde-719	68	3	)	)	PUNCT
ejde-719	69	1	+	+	CCONJ
ejde-719	69	2	∫	∫	PROPN
ejde-719	69	3	t	t	NOUN
ejde-719	69	4	0	0	NUM
ejde-719	69	5	ea(t−s)by(s−	ea(t−s)by(s−	PROPN
ejde-719	69	6	h)ds	h)ds	PROPN
ejde-719	69	7	.	.	PUNCT
ejde-719	69	8	consequently	consequently	ADV
ejde-719	69	9	,	,	PUNCT
ejde-719	69	10	in	in	ADP
ejde-719	69	11	view	view	NOUN
ejde-719	69	12	of	of	ADP
ejde-719	69	13	(	(	PUNCT
ejde-719	69	14	1.1	1.1	NUM
ejde-719	69	15	)	)	PUNCT
ejde-719	69	16	,	,	PUNCT
ejde-719	69	17	dy(t)/dt	dy(t)/dt	PROPN
ejde-719	69	18	=	=	SYM
ejde-719	69	19	ay(t	ay(t	PROPN
ejde-719	69	20	)	)	PUNCT
ejde-719	70	1	+	+	NOUN
ejde-719	70	2	by(t−	by(t−	PROPN
ejde-719	70	3	h	h	NOUN
ejde-719	70	4	)	)	PUNCT
ejde-719	70	5	=	=	SYM
ejde-719	70	6	a(eatϕ(0	a(eatϕ(0	PRON
ejde-719	70	7	)	)	PUNCT
ejde-719	71	1	+	+	CCONJ
ejde-719	71	2	∫	∫	PROPN
ejde-719	71	3	t	t	NOUN
ejde-719	71	4	0	0	NUM
ejde-719	71	5	ea(t−s)by(s−	ea(t−s)by(s−	PROPN
ejde-719	71	6	h)ds	h)ds	PROPN
ejde-719	71	7	)	)	PUNCT
ejde-719	71	8	+	+	NOUN
ejde-719	71	9	by(t−	by(t−	PROPN
ejde-719	71	10	h	h	NOUN
ejde-719	71	11	)	)	PUNCT
ejde-719	71	12	.	.	PUNCT
ejde-719	72	1	since	since	SCONJ
ejde-719	72	2	ab	ab	PROPN
ejde-719	72	3	is	be	AUX
ejde-719	72	4	bounded	bound	VERB
ejde-719	73	1	the	the	DET
ejde-719	73	2	integral	integral	ADJ
ejde-719	73	3	∫	∫	PROPN
ejde-719	73	4	t	t	PROPN
ejde-719	73	5	0	0	NUM
ejde-719	73	6	ea(t−s)aby(s	ea(t−s)aby(s	PROPN
ejde-719	73	7	−	−	PROPN
ejde-719	74	1	h)ds	h)ds	PROPN
ejde-719	74	2	(	(	PUNCT
ejde-719	74	3	0	0	NUM
ejde-719	74	4	<	<	X
ejde-719	74	5	t	t	X
ejde-719	74	6	<	<	X
ejde-719	74	7	∞	∞	PROPN
ejde-719	74	8	)	)	PUNCT
ejde-719	74	9	converges	converge	NOUN
ejde-719	74	10	and	and	CCONJ
ejde-719	74	11	a	a	DET
ejde-719	74	12	∫	∫	PROPN
ejde-719	74	13	t	t	NOUN
ejde-719	74	14	0	0	NUM
ejde-719	74	15	ea(t−s)by(s−	ea(t−s)by(s−	PROPN
ejde-719	75	1	h)ds	h)ds	PROPN
ejde-719	75	2	=	=	SYM
ejde-719	75	3	∫	∫	PROPN
ejde-719	75	4	t	t	PROPN
ejde-719	75	5	0	0	NUM
ejde-719	76	1	ea(t−s)aby(s−	ea(t−s)aby(s−	PROPN
ejde-719	76	2	h)ds	h)ds	PROPN
ejde-719	76	3	.	.	PUNCT
ejde-719	77	1	thus	thus	ADV
ejde-719	77	2	,	,	PUNCT
ejde-719	77	3	(	(	PUNCT
ejde-719	77	4	1.1	1.1	NUM
ejde-719	77	5	)	)	PUNCT
ejde-719	77	6	can	can	AUX
ejde-719	77	7	be	be	AUX
ejde-719	77	8	written	write	VERB
ejde-719	77	9	as	as	ADP
ejde-719	77	10	dy	dy	NOUN
ejde-719	77	11	dt	dt	NOUN
ejde-719	77	12	=	=	SYM
ejde-719	77	13	aeatϕ(0	aeatϕ(0	NUM
ejde-719	77	14	)	)	PUNCT
ejde-719	78	1	+	+	CCONJ
ejde-719	79	1	∫	∫	PROPN
ejde-719	79	2	t	t	X
ejde-719	79	3	0	0	NUM
ejde-719	80	1	ea(t−s)aby(s−	ea(t−s)aby(s−	PROPN
ejde-719	80	2	h)ds+by(t−	h)ds+by(t−	PROPN
ejde-719	80	3	h	h	PROPN
ejde-719	80	4	)	)	PUNCT
ejde-719	80	5	.	.	PUNCT
ejde-719	81	1	hence	hence	ADV
ejde-719	81	2	,	,	PUNCT
ejde-719	81	3	with	with	ADP
ejde-719	81	4	the	the	DET
ejde-719	81	5	notation	notation	NOUN
ejde-719	81	6	|y|t	|y|t	PROPN
ejde-719	81	7	:	:	PUNCT
ejde-719	81	8	=	=	PUNCT
ejde-719	81	9	sup	sup	NOUN
ejde-719	81	10	0≤s≤t	0≤s≤t	NUM
ejde-719	81	11	∥y(s)∥x	∥y(s)∥x	NOUN
ejde-719	81	12	(	(	PUNCT
ejde-719	81	13	0	0	NUM
ejde-719	81	14	<	<	X
ejde-719	81	15	t	t	X
ejde-719	81	16	<	<	X
ejde-719	81	17	∞	∞	PROPN
ejde-719	81	18	)	)	PUNCT
ejde-719	81	19	and	and	CCONJ
ejde-719	81	20	a0	a0	NOUN
ejde-719	81	21	:	:	PUNCT
ejde-719	81	22	=	=	SYM
ejde-719	82	1	sup	sup	NUM
ejde-719	82	2	t≥0	t≥0	NOUN
ejde-719	82	3	∥eat∥x	∥eat∥x	ADV
ejde-719	82	4	,	,	PUNCT
ejde-719	82	5	4	4	NUM
ejde-719	82	6	m.	m.	NOUN
ejde-719	82	7	gil	gil	PROPN
ejde-719	82	8	’	'	PUNCT
ejde-719	82	9	ejde-2024/76	ejde-2024/76	NOUN
ejde-719	82	10	we	we	PRON
ejde-719	82	11	can	can	AUX
ejde-719	82	12	write	write	VERB
ejde-719	82	13	|y′|t	|y′|t	PROPN
ejde-719	82	14	≤	≤	NUM
ejde-719	82	15	a0∥aϕ(0)∥x	a0∥aϕ(0)∥x	PUNCT
ejde-719	83	1	+	+	NUM
ejde-719	83	2	∫	∫	PROPN
ejde-719	83	3	t	t	NOUN
ejde-719	83	4	0	0	NUM
ejde-719	83	5	∥ea(t−s)aby(s−	∥ea(t−s)aby(s−	PROPN
ejde-719	83	6	h)∥xds+	h)∥xds+	NOUN
ejde-719	83	7	∥b∥x	∥b∥x	NOUN
ejde-719	83	8	sup	sup	NOUN
ejde-719	83	9	0≤s≤t	0≤s≤t	NUM
ejde-719	83	10	∥y(s−	∥y(s−	PROPN
ejde-719	83	11	h)∥x	h)∥x	NOUN
ejde-719	83	12	,	,	PUNCT
ejde-719	83	13	and	and	CCONJ
ejde-719	83	14	therefore	therefore	ADV
ejde-719	83	15	|y′|t	|y′|t	ADJ
ejde-719	83	16	≤	≤	NUM
ejde-719	83	17	a0∥aϕ(0)∥x	a0∥aϕ(0)∥x	PUNCT
ejde-719	84	1	+	+	CCONJ
ejde-719	84	2	(	(	PUNCT
ejde-719	84	3	ψa	ψa	X
ejde-719	84	4	+	+	X
ejde-719	84	5	∥b∥x	∥b∥x	NOUN
ejde-719	84	6	)	)	PUNCT
ejde-719	84	7	sup	sup	NOUN
ejde-719	84	8	0≤s≤t	0≤s≤t	NUM
ejde-719	84	9	∥y(s−	∥y(s−	PROPN
ejde-719	84	10	h)∥x	h)∥x	NOUN
ejde-719	84	11	,	,	PUNCT
ejde-719	84	12	i.	i.	PROPN
ejde-719	84	13	e.	e.	PROPN
ejde-719	84	14	|y′|t	|y′|t	PROPN
ejde-719	84	15	≤	≤	NUM
ejde-719	84	16	a0∥aϕ(0)∥x	a0∥aϕ(0)∥x	PUNCT
ejde-719	85	1	+	+	CCONJ
ejde-719	85	2	(	(	PUNCT
ejde-719	85	3	ψa	ψa	X
ejde-719	85	4	+	+	X
ejde-719	85	5	∥b∥x	∥b∥x	NOUN
ejde-719	85	6	)	)	PUNCT
ejde-719	85	7	(	(	PUNCT
ejde-719	85	8	∥ϕ∥c(−h,0	∥ϕ∥c(−h,0	PROPN
ejde-719	85	9	)	)	PUNCT
ejde-719	85	10	+	+	CCONJ
ejde-719	85	11	|y|t	|y|t	PROPN
ejde-719	85	12	)	)	PUNCT
ejde-719	85	13	.	.	PUNCT
ejde-719	86	1	(	(	PUNCT
ejde-719	86	2	2.1	2.1	NUM
ejde-719	86	3	)	)	PUNCT
ejde-719	86	4	from	from	ADP
ejde-719	86	5	(	(	PUNCT
ejde-719	86	6	1.1	1.1	NUM
ejde-719	86	7	)	)	PUNCT
ejde-719	86	8	and	and	CCONJ
ejde-719	86	9	(	(	PUNCT
ejde-719	86	10	1.2	1.2	NUM
ejde-719	86	11	)	)	PUNCT
ejde-719	86	12	it	it	PRON
ejde-719	86	13	follows	follow	VERB
ejde-719	86	14	that	that	PRON
ejde-719	86	15	ϕ′(0	ϕ′(0	PROPN
ejde-719	86	16	)	)	PUNCT
ejde-719	87	1	=	=	SYM
ejde-719	87	2	aϕ(0	aϕ(0	PROPN
ejde-719	87	3	)	)	PUNCT
ejde-719	87	4	+	+	NOUN
ejde-719	87	5	bϕ(−h	bϕ(−h	NOUN
ejde-719	87	6	)	)	PUNCT
ejde-719	87	7	.	.	PUNCT
ejde-719	88	1	hence	hence	ADV
ejde-719	88	2	,	,	PUNCT
ejde-719	88	3	∥aϕ(0)∥x	∥aϕ(0)∥x	PUNCT
ejde-719	88	4	≤	≤	NOUN
ejde-719	88	5	(	(	PUNCT
ejde-719	88	6	1	1	NUM
ejde-719	88	7	+	+	CCONJ
ejde-719	88	8	∥b∥x	∥b∥x	NOUN
ejde-719	88	9	)	)	PUNCT
ejde-719	88	10	∥ϕ∥w	∥ϕ∥w	NOUN
ejde-719	88	11	(	(	PUNCT
ejde-719	88	12	−h,0	−h,0	NOUN
ejde-719	88	13	)	)	PUNCT
ejde-719	88	14	.	.	PUNCT
ejde-719	89	1	now	now	ADV
ejde-719	89	2	(	(	PUNCT
ejde-719	89	3	2.1	2.1	NUM
ejde-719	89	4	)	)	PUNCT
ejde-719	89	5	yields	yield	VERB
ejde-719	89	6	|y′|t	|y′|t	PROPN
ejde-719	89	7	≤	≤	PUNCT
ejde-719	89	8	a0(1	a0(1	NOUN
ejde-719	89	9	+	+	CCONJ
ejde-719	89	10	∥b∥x	∥b∥x	NOUN
ejde-719	89	11	)	)	PUNCT
ejde-719	89	12	∥ϕ∥w	∥ϕ∥w	NOUN
ejde-719	89	13	(	(	PUNCT
ejde-719	89	14	−h,0	−h,0	NOUN
ejde-719	89	15	)	)	PUNCT
ejde-719	89	16	+	+	CCONJ
ejde-719	89	17	(	(	PUNCT
ejde-719	89	18	ψa	ψa	X
ejde-719	89	19	+	+	CCONJ
ejde-719	89	20	∥b∥x	∥b∥x	NOUN
ejde-719	89	21	)	)	PUNCT
ejde-719	89	22	∥ϕ∥c(−h,0	∥ϕ∥c(−h,0	PROPN
ejde-719	89	23	)	)	PUNCT
ejde-719	90	1	+	+	CCONJ
ejde-719	90	2	(	(	PUNCT
ejde-719	90	3	ψa	ψa	X
ejde-719	90	4	+	+	X
ejde-719	90	5	∥b∥x	∥b∥x	NOUN
ejde-719	90	6	)	)	PUNCT
ejde-719	90	7	|y|t	|y|t	PROPN
ejde-719	90	8	and	and	CCONJ
ejde-719	90	9	thus	thus	ADV
ejde-719	90	10	|y′|t	|y′|t	PROPN
ejde-719	90	11	≤	≤	NUM
ejde-719	90	12	ĉ∥ϕ∥w	ĉ∥ϕ∥w	PROPN
ejde-719	90	13	(	(	PUNCT
ejde-719	90	14	−h,0	−h,0	NOUN
ejde-719	90	15	)	)	PUNCT
ejde-719	90	16	+	+	CCONJ
ejde-719	90	17	(	(	PUNCT
ejde-719	90	18	ψa	ψa	X
ejde-719	90	19	+	+	X
ejde-719	90	20	∥b∥x	∥b∥x	NOUN
ejde-719	90	21	)	)	PUNCT
ejde-719	90	22	|y|t	|y|t	PROPN
ejde-719	90	23	,	,	PUNCT
ejde-719	90	24	(	(	PUNCT
ejde-719	90	25	2.2	2.2	NUM
ejde-719	90	26	)	)	PUNCT
ejde-719	90	27	where	where	SCONJ
ejde-719	90	28	ĉ	ĉ	ADV
ejde-719	90	29	=	=	SYM
ejde-719	90	30	a0(1	a0(1	NOUN
ejde-719	90	31	+	+	CCONJ
ejde-719	90	32	∥b∥x	∥b∥x	NOUN
ejde-719	90	33	)	)	PUNCT
ejde-719	91	1	+	+	CCONJ
ejde-719	91	2	ψa	ψa	X
ejde-719	91	3	+	+	X
ejde-719	91	4	∥b∥x	∥b∥x	NOUN
ejde-719	91	5	.	.	PUNCT
ejde-719	92	1	furthermore	furthermore	ADV
ejde-719	92	2	,	,	PUNCT
ejde-719	92	3	we	we	PRON
ejde-719	92	4	rewrite	rewrite	VERB
ejde-719	92	5	(	(	PUNCT
ejde-719	92	6	1.1	1.1	NUM
ejde-719	92	7	)	)	PUNCT
ejde-719	92	8	as	as	ADP
ejde-719	92	9	y′(t	y′(t	NOUN
ejde-719	92	10	)	)	PUNCT
ejde-719	92	11	=	=	NOUN
ejde-719	92	12	my(t	my(t	X
ejde-719	92	13	)	)	PUNCT
ejde-719	93	1	+	+	PROPN
ejde-719	93	2	b(y(t−	b(y(t−	ADP
ejde-719	93	3	h)−	h)−	PROPN
ejde-719	93	4	y(t	y(t	PROPN
ejde-719	93	5	)	)	PUNCT
ejde-719	93	6	)	)	PUNCT
ejde-719	93	7	(	(	PUNCT
ejde-719	93	8	t	t	X
ejde-719	93	9	>	>	X
ejde-719	93	10	0	0	NUM
ejde-719	93	11	)	)	PUNCT
ejde-719	93	12	.	.	PUNCT
ejde-719	94	1	(	(	PUNCT
ejde-719	94	2	2.3	2.3	NUM
ejde-719	94	3	)	)	PUNCT
ejde-719	94	4	recall	recall	NOUN
ejde-719	94	5	that	that	PRON
ejde-719	94	6	m	m	VERB
ejde-719	94	7	=	=	SYM
ejde-719	94	8	a+b	a+b	NUM
ejde-719	94	9	.	.	PUNCT
ejde-719	95	1	from	from	ADP
ejde-719	95	2	the	the	DET
ejde-719	95	3	above	above	ADJ
ejde-719	95	4	mentioned	mention	VERB
ejde-719	95	5	variation	variation	NOUN
ejde-719	95	6	of	of	ADP
ejde-719	95	7	constants	constant	NOUN
ejde-719	95	8	formula	formula	NOUN
ejde-719	95	9	,	,	PUNCT
ejde-719	95	10	y(t	y(t	NUM
ejde-719	95	11	)	)	PUNCT
ejde-719	95	12	=	=	PUNCT
ejde-719	95	13	emtϕ(0	emtϕ(0	NOUN
ejde-719	95	14	)	)	PUNCT
ejde-719	96	1	+	+	CCONJ
ejde-719	97	1	∫	∫	PROPN
ejde-719	97	2	t	t	PROPN
ejde-719	97	3	0	0	NUM
ejde-719	97	4	em(t−s)b(y(s−	em(t−s)b(y(s−	PROPN
ejde-719	97	5	h)−	h)−	PROPN
ejde-719	97	6	y(s))ds	y(s))ds	PROPN
ejde-719	97	7	.	.	PUNCT
ejde-719	98	1	hence	hence	ADV
ejde-719	98	2	,	,	PUNCT
ejde-719	98	3	|y|t	|y|t	PROPN
ejde-719	98	4	≤	≤	PROPN
ejde-719	98	5	m0∥ϕ(0)∥x	m0∥ϕ(0)∥x	VERB
ejde-719	99	1	+	+	CCONJ
ejde-719	99	2	∫	∫	PROPN
ejde-719	99	3	t	t	PROPN
ejde-719	99	4	0	0	NUM
ejde-719	99	5	∥em(t−s)b∥xds	∥em(t−s)b∥xds	NOUN
ejde-719	99	6	sup	sup	PROPN
ejde-719	99	7	s≤t	s≤t	PROPN
ejde-719	99	8	∥y(s−	∥y(s−	PROPN
ejde-719	99	9	h)−	h)−	PROPN
ejde-719	99	10	y(s)∥x	y(s)∥x	PROPN
ejde-719	99	11	,	,	PUNCT
ejde-719	99	12	(	(	PUNCT
ejde-719	99	13	2.4	2.4	NUM
ejde-719	99	14	)	)	PUNCT
ejde-719	100	1	where	where	SCONJ
ejde-719	100	2	m0	m0	NOUN
ejde-719	100	3	:	:	PUNCT
ejde-719	100	4	=	=	SYM
ejde-719	100	5	supt≥0	supt≥0	PROPN
ejde-719	100	6	∥emt∥x	∥emt∥x	ADV
ejde-719	100	7	,	,	PUNCT
ejde-719	100	8	and	and	CCONJ
ejde-719	100	9	therefore	therefore	ADV
ejde-719	100	10	|y|t	|y|t	PROPN
ejde-719	100	11	≤	≤	PROPN
ejde-719	100	12	m0∥ϕ(0)∥x	m0∥ϕ(0)∥x	VERB
ejde-719	100	13	+	+	CCONJ
ejde-719	100	14	ψm	ψm	PROPN
ejde-719	100	15	sup	sup	NOUN
ejde-719	100	16	0≤s≤t	0≤s≤t	NUM
ejde-719	100	17	∥y(s−	∥y(s−	PROPN
ejde-719	100	18	h)−	h)−	PROPN
ejde-719	100	19	y(s)∥x	y(s)∥x	PROPN
ejde-719	100	20	.	.	PUNCT
ejde-719	101	1	(	(	PUNCT
ejde-719	101	2	2.5	2.5	NUM
ejde-719	101	3	)	)	PUNCT
ejde-719	101	4	note	note	VERB
ejde-719	101	5	that	that	SCONJ
ejde-719	101	6	∥y(s−	∥y(s−	PROPN
ejde-719	101	7	h)−	h)−	PROPN
ejde-719	101	8	y(s)∥x	y(s)∥x	PROPN
ejde-719	101	9	=	=	PUNCT
ejde-719	102	1	∥	∥	NUM
ejde-719	102	2	∫	∫	X
ejde-719	102	3	s	s	PART
ejde-719	102	4	s−h	s−h	PROPN
ejde-719	102	5	y′(s1)ds1∥x	y′(s1)ds1∥x	PROPN
ejde-719	102	6	≤	≤	PROPN
ejde-719	102	7	h∥y′∥c(−h	h∥y′∥c(−h	PROPN
ejde-719	102	8	,	,	PUNCT
ejde-719	102	9	t	t	PROPN
ejde-719	102	10	)	)	PUNCT
ejde-719	102	11	≤	≤	NUM
ejde-719	102	12	h∥ϕ′∥c(−h,0	h∥ϕ′∥c(−h,0	NOUN
ejde-719	102	13	)	)	PUNCT
ejde-719	103	1	+	+	CCONJ
ejde-719	103	2	h|y′|t	h|y′|t	NUM
ejde-719	103	3	(	(	PUNCT
ejde-719	103	4	s	s	NOUN
ejde-719	103	5	≤	≤	NUM
ejde-719	103	6	t	t	PROPN
ejde-719	103	7	)	)	PUNCT
ejde-719	103	8	.	.	PUNCT
ejde-719	104	1	using	use	VERB
ejde-719	104	2	(	(	PUNCT
ejde-719	104	3	2.5	2.5	NUM
ejde-719	104	4	)	)	PUNCT
ejde-719	104	5	,	,	PUNCT
ejde-719	104	6	we	we	PRON
ejde-719	104	7	arrive	arrive	VERB
ejde-719	104	8	at	at	ADP
ejde-719	104	9	the	the	DET
ejde-719	104	10	inequality	inequality	NOUN
ejde-719	104	11	|y|t	|y|t	PROPN
ejde-719	104	12	≤	≤	PROPN
ejde-719	104	13	m0∥ϕ(0)∥x	m0∥ϕ(0)∥x	NOUN
ejde-719	104	14	+	+	CCONJ
ejde-719	104	15	ψmh(∥ϕ′∥c(−h,0	ψmh(∥ϕ′∥c(−h,0	NOUN
ejde-719	104	16	)	)	PUNCT
ejde-719	105	1	+	+	CCONJ
ejde-719	105	2	|y′|t	|y′|t	NOUN
ejde-719	105	3	)	)	PUNCT
ejde-719	105	4	.	.	PUNCT
ejde-719	106	1	now	now	ADV
ejde-719	106	2	(	(	PUNCT
ejde-719	106	3	2.2	2.2	NUM
ejde-719	106	4	)	)	PUNCT
ejde-719	106	5	implies	imply	VERB
ejde-719	106	6	|y|t	|y|t	PROPN
ejde-719	106	7	≤	≤	ADJ
ejde-719	106	8	∥ϕ∥w	∥ϕ∥w	NOUN
ejde-719	106	9	(	(	PUNCT
ejde-719	106	10	−h,0)(m0	−h,0)(m0	PROPN
ejde-719	106	11	+	+	CCONJ
ejde-719	106	12	ψmh+	ψmh+	NOUN
ejde-719	106	13	hψm	hψm	NOUN
ejde-719	106	14	ĉ	ĉ	NOUN
ejde-719	106	15	)	)	PUNCT
ejde-719	107	1	+	+	CCONJ
ejde-719	107	2	hψm	hψm	NOUN
ejde-719	107	3	(	(	PUNCT
ejde-719	107	4	ψa	ψa	NOUN
ejde-719	107	5	+	+	X
ejde-719	107	6	∥b∥x	∥b∥x	NOUN
ejde-719	107	7	)	)	PUNCT
ejde-719	107	8	|y|t	|y|t	PROPN
ejde-719	107	9	,	,	PUNCT
ejde-719	107	10	or	or	CCONJ
ejde-719	107	11	|y|t	|y|t	PROPN
ejde-719	107	12	≤	≤	ADV
ejde-719	107	13	ĉ2∥ϕ∥w	ĉ2∥ϕ∥w	PROPN
ejde-719	107	14	(	(	PUNCT
ejde-719	107	15	−h,0	−h,0	PROPN
ejde-719	107	16	)	)	PUNCT
ejde-719	107	17	+	+	NUM
ejde-719	107	18	hψm	hψm	NOUN
ejde-719	107	19	(	(	PUNCT
ejde-719	107	20	ψa	ψa	NOUN
ejde-719	107	21	+	+	X
ejde-719	107	22	∥b∥x	∥b∥x	NOUN
ejde-719	107	23	)	)	PUNCT
ejde-719	107	24	|y|t	|y|t	PROPN
ejde-719	107	25	,	,	PUNCT
ejde-719	107	26	ejde-2024/76	ejde-2024/76	ADJ
ejde-719	107	27	delay	delay	NOUN
ejde-719	107	28	-	-	PUNCT
ejde-719	107	29	dependent	dependent	ADJ
ejde-719	107	30	stability	stability	NOUN
ejde-719	107	31	conditions	condition	NOUN
ejde-719	107	32	5	5	NUM
ejde-719	107	33	where	where	SCONJ
ejde-719	107	34	ĉ2	ĉ2	PROPN
ejde-719	107	35	=	=	SYM
ejde-719	107	36	m0	m0	PROPN
ejde-719	107	37	+	+	CCONJ
ejde-719	107	38	ψmh+	ψmh+	NOUN
ejde-719	107	39	hψm	hψm	NOUN
ejde-719	107	40	ĉ.	ĉ.	NOUN
ejde-719	107	41	according	accord	VERB
ejde-719	107	42	(	(	PUNCT
ejde-719	107	43	1.5	1.5	NUM
ejde-719	107	44	)	)	PUNCT
ejde-719	107	45	we	we	PRON
ejde-719	107	46	obtain	obtain	VERB
ejde-719	107	47	|y|t	|y|t	PROPN
ejde-719	107	48	≤	≤	ADV
ejde-719	107	49	ĉ2∥ϕ∥w	ĉ2∥ϕ∥w	PROPN
ejde-719	107	50	(	(	PUNCT
ejde-719	107	51	−h,0)(1−	−h,0)(1−	ADJ
ejde-719	107	52	hψm	hψm	NOUN
ejde-719	107	53	(	(	PUNCT
ejde-719	107	54	ψa	ψa	NOUN
ejde-719	107	55	+	+	X
ejde-719	107	56	∥b∥x	∥b∥x	NOUN
ejde-719	107	57	)	)	PUNCT
ejde-719	107	58	)	)	PUNCT
ejde-719	107	59	−1	−1	NOUN
ejde-719	107	60	.	.	PUNCT
ejde-719	108	1	hence	hence	ADV
ejde-719	108	2	,	,	PUNCT
ejde-719	108	3	letting	let	VERB
ejde-719	108	4	t→	t→	PROPN
ejde-719	108	5	∞	∞	PROPN
ejde-719	108	6	,	,	PUNCT
ejde-719	108	7	we	we	PRON
ejde-719	108	8	obtain	obtain	VERB
ejde-719	108	9	∥y∥c(r+	∥y∥c(r+	NOUN
ejde-719	108	10	)	)	PUNCT
ejde-719	108	11	≤	≤	NOUN
ejde-719	108	12	(	(	PUNCT
ejde-719	108	13	1−	1−	NUM
ejde-719	108	14	hψm	hψm	NOUN
ejde-719	108	15	(	(	PUNCT
ejde-719	108	16	ψa	ψa	NOUN
ejde-719	108	17	+	+	X
ejde-719	108	18	∥b∥x	∥b∥x	NOUN
ejde-719	108	19	)	)	PUNCT
ejde-719	108	20	)	)	PUNCT
ejde-719	109	1	−1ĉ2∥ϕ∥w	−1ĉ2∥ϕ∥w	PROPN
ejde-719	109	2	(	(	PUNCT
ejde-719	109	3	−h,0	−h,0	PROPN
ejde-719	109	4	)	)	PUNCT
ejde-719	109	5	.	.	PUNCT
ejde-719	110	1	this	this	PRON
ejde-719	110	2	proves	prove	VERB
ejde-719	110	3	the	the	DET
ejde-719	110	4	required	required	ADJ
ejde-719	110	5	result	result	NOUN
ejde-719	110	6	.	.	PUNCT
ejde-719	111	1	□	□	PUNCT
ejde-719	111	2	proof	proof	NOUN
ejde-719	111	3	of	of	ADP
ejde-719	111	4	corollary	corollary	ADJ
ejde-719	111	5	1.2	1.2	NUM
ejde-719	111	6	.	.	PUNCT
ejde-719	112	1	substitute	substitute	PROPN
ejde-719	112	2	y(t	y(t	PROPN
ejde-719	112	3	)	)	PUNCT
ejde-719	113	1	=	=	SYM
ejde-719	113	2	e−ϵtyϵ(t	e−ϵtyϵ(t	PROPN
ejde-719	113	3	)	)	PUNCT
ejde-719	113	4	(	(	PUNCT
ejde-719	113	5	2.6	2.6	NUM
ejde-719	113	6	)	)	PUNCT
ejde-719	113	7	with	with	ADP
ejde-719	113	8	ϵ	ϵ	PROPN
ejde-719	113	9	>	>	X
ejde-719	113	10	0	0	PUNCT
ejde-719	113	11	into	into	ADP
ejde-719	113	12	(	(	PUNCT
ejde-719	113	13	1.1	1.1	NUM
ejde-719	113	14	)	)	PUNCT
ejde-719	113	15	.	.	PUNCT
ejde-719	114	1	we	we	PRON
ejde-719	114	2	obtain	obtain	VERB
ejde-719	114	3	the	the	DET
ejde-719	114	4	equation	equation	NOUN
ejde-719	114	5	y′ϵ(t	y′ϵ(t	NOUN
ejde-719	114	6	)	)	PUNCT
ejde-719	114	7	=	=	SYM
ejde-719	114	8	(	(	PUNCT
ejde-719	114	9	a+	a+	X
ejde-719	114	10	ϵi)yϵ(t	ϵi)yϵ(t	NOUN
ejde-719	114	11	)	)	PUNCT
ejde-719	115	1	+	+	NOUN
ejde-719	115	2	beϵhyϵ(t−	beϵhyϵ(t−	NOUN
ejde-719	115	3	h	h	NOUN
ejde-719	115	4	)	)	PUNCT
ejde-719	115	5	(	(	PUNCT
ejde-719	115	6	t	t	X
ejde-719	115	7	>	>	X
ejde-719	115	8	0	0	NUM
ejde-719	115	9	)	)	PUNCT
ejde-719	115	10	.	.	PUNCT
ejde-719	116	1	(	(	PUNCT
ejde-719	116	2	2.7	2.7	X
ejde-719	116	3	)	)	PUNCT
ejde-719	116	4	put	put	VERB
ejde-719	116	5	m(ϵ	m(ϵ	NOUN
ejde-719	116	6	)	)	PUNCT
ejde-719	116	7	=	=	PRON
ejde-719	116	8	a+	a+	PUNCT
ejde-719	116	9	ϵi	ϵi	X
ejde-719	117	1	+	+	ADV
ejde-719	117	2	beϵh	beϵh	ADJ
ejde-719	117	3	.	.	PUNCT
ejde-719	118	1	we	we	PRON
ejde-719	118	2	have	have	VERB
ejde-719	118	3	em(ϵ)t	em(ϵ)t	PROPN
ejde-719	118	4	−	−	PROPN
ejde-719	118	5	emt	emt	PROPN
ejde-719	118	6	=	=	SYM
ejde-719	118	7	∫	∫	PROPN
ejde-719	118	8	t	t	NOUN
ejde-719	118	9	0	0	X
ejde-719	119	1	em(t−s)(m(ϵ)−m)em(ϵ)sds	em(t−s)(m(ϵ)−m)em(ϵ)sds	NOUN
ejde-719	119	2	=	=	PUNCT
ejde-719	120	1	−	−	PROPN
ejde-719	120	2	∫	∫	PROPN
ejde-719	120	3	t	t	PROPN
ejde-719	120	4	0	0	NUM
ejde-719	120	5	em(t−s)(ϵi	em(t−s)(ϵi	NOUN
ejde-719	120	6	+	+	PROPN
ejde-719	120	7	b(eϵh	b(eϵh	VERB
ejde-719	120	8	−	−	PROPN
ejde-719	120	9	1))em(ϵ)sds	1))em(ϵ)sds	NUM
ejde-719	120	10	.	.	PUNCT
ejde-719	121	1	hence	hence	ADV
ejde-719	121	2	,	,	PUNCT
ejde-719	121	3	∥em(ϵ)t∥	∥em(ϵ)t∥	PROPN
ejde-719	121	4	≤	≤	PROPN
ejde-719	121	5	∥emt∥+	∥emt∥+	ADJ
ejde-719	121	6	∫	∫	PROPN
ejde-719	121	7	t	t	PROPN
ejde-719	121	8	0	0	NUM
ejde-719	121	9	∥em(t−s)∥δ(ϵ)∥em(ϵ)s∥ds	∥em(t−s)∥δ(ϵ)∥em(ϵ)s∥ds	NOUN
ejde-719	121	10	≤	≤	NOUN
ejde-719	121	11	e−αm	e−αm	PROPN
ejde-719	121	12	t	t	PROPN
ejde-719	121	13	+	+	CCONJ
ejde-719	121	14	δ(ϵ	δ(ϵ	PROPN
ejde-719	121	15	)	)	PUNCT
ejde-719	122	1	∫	∫	PROPN
ejde-719	123	1	t	t	PROPN
ejde-719	123	2	0	0	NUM
ejde-719	124	1	e−αm	e−αm	PROPN
ejde-719	124	2	(	(	PUNCT
ejde-719	124	3	t−s)∥em(ϵ)s∥ds	t−s)∥em(ϵ)s∥ds	PROPN
ejde-719	124	4	,	,	PUNCT
ejde-719	124	5	where	where	SCONJ
ejde-719	124	6	δ(ϵ	δ(ϵ	NOUN
ejde-719	124	7	)	)	PUNCT
ejde-719	124	8	=	=	PUNCT
ejde-719	124	9	∥ϵi	∥ϵi	PART
ejde-719	125	1	+	+	ADJ
ejde-719	125	2	b(eϵh	b(eϵh	VERB
ejde-719	125	3	−	−	PROPN
ejde-719	125	4	1)∥	1)∥	NUM
ejde-719	125	5	→	→	SYM
ejde-719	125	6	0	0	PUNCT
ejde-719	125	7	as	as	ADP
ejde-719	125	8	ϵ→	ϵ→	PROPN
ejde-719	125	9	0	0	NUM
ejde-719	125	10	.	.	PUNCT
ejde-719	126	1	thus	thus	ADV
ejde-719	126	2	we	we	PRON
ejde-719	126	3	obtain	obtain	VERB
ejde-719	126	4	∥e(m(ϵ)+αmi)t∥	∥e(m(ϵ)+αmi)t∥	PUNCT
ejde-719	126	5	≤	≤	ADV
ejde-719	126	6	1	1	NUM
ejde-719	126	7	+	+	CCONJ
ejde-719	126	8	δ(ϵ	δ(ϵ	PROPN
ejde-719	126	9	)	)	PUNCT
ejde-719	126	10	∫	∫	PROPN
ejde-719	126	11	t	t	PROPN
ejde-719	126	12	0	0	NUM
ejde-719	126	13	∥e(m(ϵ)+αmi)s∥ds	∥e(m(ϵ)+αmi)s∥ds	NOUN
ejde-719	126	14	.	.	PUNCT
ejde-719	127	1	now	now	ADV
ejde-719	127	2	the	the	DET
ejde-719	127	3	gronwall	gronwall	ADJ
ejde-719	127	4	lemma	lemma	PROPN
ejde-719	127	5	yields	yield	NOUN
ejde-719	127	6	∥em(ϵ)t∥	∥em(ϵ)t∥	PROPN
ejde-719	127	7	≤	≤	ADV
ejde-719	127	8	e−αm	e−αm	PROPN
ejde-719	127	9	(	(	PUNCT
ejde-719	127	10	ϵ)t	ϵ)t	NOUN
ejde-719	127	11	,	,	PUNCT
ejde-719	127	12	where	where	SCONJ
ejde-719	127	13	αm	αm	INTJ
ejde-719	127	14	(	(	PUNCT
ejde-719	127	15	ϵ	ϵ	NOUN
ejde-719	127	16	)	)	PUNCT
ejde-719	127	17	=	=	NOUN
ejde-719	128	1	αm	αm	NUM
ejde-719	128	2	−	−	PROPN
ejde-719	128	3	δ(ϵ	δ(ϵ	PROPN
ejde-719	128	4	)	)	PUNCT
ejde-719	128	5	.	.	PUNCT
ejde-719	129	1	so	so	ADV
ejde-719	129	2	αm	αm	INTJ
ejde-719	129	3	(	(	PUNCT
ejde-719	129	4	0	0	NUM
ejde-719	129	5	)	)	PUNCT
ejde-719	129	6	=	=	VERB
ejde-719	129	7	αm	αm	INTJ
ejde-719	129	8	.	.	PUNCT
ejde-719	130	1	if	if	SCONJ
ejde-719	130	2	(	(	PUNCT
ejde-719	130	3	1.6	1.6	NUM
ejde-719	130	4	)	)	PUNCT
ejde-719	130	5	,	,	PUNCT
ejde-719	130	6	(	(	PUNCT
ejde-719	130	7	1.7	1.7	NUM
ejde-719	130	8	)	)	PUNCT
ejde-719	130	9	hold	hold	VERB
ejde-719	130	10	,	,	PUNCT
ejde-719	130	11	then	then	ADV
ejde-719	130	12	for	for	ADP
ejde-719	130	13	small	small	ADJ
ejde-719	130	14	enough	enough	ADV
ejde-719	130	15	ϵ	ϵ	X
ejde-719	130	16	>	>	X
ejde-719	130	17	0	0	PROPN
ejde-719	130	18	,	,	PUNCT
ejde-719	130	19	hcme	hcme	PROPN
ejde-719	130	20	ϵh∥b∥	ϵh∥b∥	PROPN
ejde-719	131	1	αm	αm	NOUN
ejde-719	131	2	(	(	PUNCT
ejde-719	131	3	ϵ	ϵ	NOUN
ejde-719	131	4	)	)	PUNCT
ejde-719	131	5	(	(	PUNCT
ejde-719	131	6	caeϵh∥ab	caeϵh∥ab	PROPN
ejde-719	131	7	+	+	CCONJ
ejde-719	131	8	ϵb∥	ϵb∥	PROPN
ejde-719	132	1	αa	αa	ADP
ejde-719	132	2	−	−	PROPN
ejde-719	133	1	ϵ	ϵ	X
ejde-719	133	2	+	+	CCONJ
ejde-719	133	3	eϵh∥b∥	eϵh∥b∥	NUM
ejde-719	133	4	)	)	PUNCT
ejde-719	133	5	<	<	X
ejde-719	134	1	1	1	X
ejde-719	134	2	.	.	PUNCT
ejde-719	134	3	from	from	ADP
ejde-719	134	4	inequality	inequality	NOUN
ejde-719	134	5	(	(	PUNCT
ejde-719	134	6	1.8	1.8	NUM
ejde-719	134	7	)	)	PUNCT
ejde-719	134	8	,	,	PUNCT
ejde-719	134	9	which	which	PRON
ejde-719	134	10	follows	follow	VERB
ejde-719	134	11	from	from	ADP
ejde-719	134	12	theorem	theorem	ADJ
ejde-719	134	13	1.1	1.1	NUM
ejde-719	134	14	,	,	PUNCT
ejde-719	134	15	a	a	DET
ejde-719	134	16	solution	solution	NOUN
ejde-719	134	17	of	of	ADP
ejde-719	134	18	(	(	PUNCT
ejde-719	134	19	2.7	2.7	NUM
ejde-719	134	20	)	)	PUNCT
ejde-719	134	21	with	with	ADP
ejde-719	134	22	the	the	DET
ejde-719	134	23	initial	initial	ADJ
ejde-719	134	24	function	function	NOUN
ejde-719	134	25	ϕ	ϕ	PROPN
ejde-719	134	26	∈	∈	PROPN
ejde-719	134	27	w	w	PROPN
ejde-719	134	28	(	(	PUNCT
ejde-719	134	29	−h	−h	ADJ
ejde-719	134	30	,	,	PUNCT
ejde-719	134	31	0	0	NUM
ejde-719	134	32	)	)	PUNCT
ejde-719	134	33	satisfies	satisfy	VERB
ejde-719	134	34	the	the	DET
ejde-719	134	35	inequality	inequality	NOUN
ejde-719	134	36	∥yϵ∥c(r+	∥yϵ∥c(r+	PROPN
ejde-719	134	37	)	)	PUNCT
ejde-719	134	38	≤	≤	NUM
ejde-719	134	39	cϵ∥ϕ∥w	cϵ∥ϕ∥w	ADJ
ejde-719	134	40	(	(	PUNCT
ejde-719	134	41	−h,0	−h,0	NOUN
ejde-719	134	42	)	)	PUNCT
ejde-719	134	43	,	,	PUNCT
ejde-719	134	44	where	where	SCONJ
ejde-719	134	45	cϵ	cϵ	NOUN
ejde-719	134	46	does	do	AUX
ejde-719	134	47	not	not	PART
ejde-719	134	48	depend	depend	VERB
ejde-719	134	49	on	on	ADP
ejde-719	134	50	ϕ.	ϕ.	PROPN
ejde-719	134	51	hence	hence	ADV
ejde-719	134	52	,	,	PUNCT
ejde-719	134	53	(	(	PUNCT
ejde-719	134	54	2.6	2.6	NUM
ejde-719	134	55	)	)	PUNCT
ejde-719	134	56	yields	yield	NOUN
ejde-719	134	57	∥y(t)∥c(r+	∥y(t)∥c(r+	NOUN
ejde-719	134	58	)	)	PUNCT
ejde-719	134	59	≤	≤	PROPN
ejde-719	134	60	cϵe	cϵe	NOUN
ejde-719	134	61	−ϵt∥ϕ∥w	−ϵt∥ϕ∥w	PROPN
ejde-719	134	62	(	(	PUNCT
ejde-719	134	63	−h,0	−h,0	PROPN
ejde-719	134	64	)	)	PUNCT
ejde-719	134	65	(	(	PUNCT
ejde-719	134	66	t	t	PROPN
ejde-719	134	67	≥	≥	NOUN
ejde-719	134	68	0	0	NUM
ejde-719	134	69	)	)	PUNCT
ejde-719	134	70	.	.	PUNCT
ejde-719	135	1	this	this	PRON
ejde-719	135	2	proves	prove	VERB
ejde-719	135	3	the	the	DET
ejde-719	135	4	exponential	exponential	ADJ
ejde-719	135	5	stability	stability	NOUN
ejde-719	135	6	.	.	PUNCT
ejde-719	136	1	□	□	PUNCT
ejde-719	136	2	6	6	NUM
ejde-719	136	3	m.	m.	NOUN
ejde-719	136	4	gil	gil	PROPN
ejde-719	136	5	’	'	PUNCT
ejde-719	136	6	ejde-2024/76	ejde-2024/76	ADJ
ejde-719	136	7	3	3	NUM
ejde-719	136	8	.	.	NOUN
ejde-719	136	9	example	example	NOUN
ejde-719	136	10	in	in	ADP
ejde-719	136	11	this	this	DET
ejde-719	136	12	section	section	NOUN
ejde-719	136	13	x	x	NOUN
ejde-719	136	14	=	=	SYM
ejde-719	136	15	l2(0	l2(0	NOUN
ejde-719	136	16	,	,	PUNCT
ejde-719	136	17	1	1	NUM
ejde-719	136	18	)	)	PUNCT
ejde-719	136	19	,	,	PUNCT
ejde-719	136	20	where	where	SCONJ
ejde-719	136	21	l2(0	l2(0	NOUN
ejde-719	136	22	,	,	PUNCT
ejde-719	136	23	1	1	NUM
ejde-719	136	24	)	)	PUNCT
ejde-719	136	25	=	=	NOUN
ejde-719	136	26	l2	l2	NOUN
ejde-719	136	27	is	be	AUX
ejde-719	136	28	the	the	DET
ejde-719	136	29	traditional	traditional	ADJ
ejde-719	136	30	hilbert	hilbert	NOUN
ejde-719	136	31	space	space	NOUN
ejde-719	136	32	of	of	ADP
ejde-719	136	33	complex	complex	ADJ
ejde-719	136	34	-	-	PUNCT
ejde-719	136	35	valued	value	VERB
ejde-719	136	36	functions	function	NOUN
ejde-719	136	37	defined	define	VERB
ejde-719	136	38	on	on	ADP
ejde-719	136	39	[	[	X
ejde-719	136	40	0	0	NUM
ejde-719	136	41	,	,	PUNCT
ejde-719	136	42	1	1	NUM
ejde-719	136	43	]	]	PUNCT
ejde-719	136	44	with	with	ADP
ejde-719	136	45	the	the	DET
ejde-719	136	46	scalar	scalar	ADJ
ejde-719	136	47	product	product	NOUN
ejde-719	136	48	(	(	PUNCT
ejde-719	136	49	f	f	X
ejde-719	136	50	,	,	PUNCT
ejde-719	136	51	f1	f1	NOUN
ejde-719	136	52	)	)	PUNCT
ejde-719	136	53	=	=	SYM
ejde-719	137	1	∫	∫	PROPN
ejde-719	137	2	1	1	NUM
ejde-719	137	3	0	0	NUM
ejde-719	137	4	f(x)f1(x)dx	f(x)f1(x)dx	NOUN
ejde-719	137	5	(	(	PUNCT
ejde-719	137	6	f	f	X
ejde-719	137	7	,	,	PUNCT
ejde-719	137	8	f1	f1	PROPN
ejde-719	137	9	∈	∈	PROPN
ejde-719	137	10	l2	l2	NOUN
ejde-719	137	11	)	)	PUNCT
ejde-719	137	12	.	.	PUNCT
ejde-719	138	1	we	we	PRON
ejde-719	138	2	consider	consider	VERB
ejde-719	138	3	the	the	DET
ejde-719	138	4	equation	equation	NOUN
ejde-719	138	5	∂u(t	∂u(t	PROPN
ejde-719	138	6	,	,	PUNCT
ejde-719	138	7	x	x	NOUN
ejde-719	138	8	)	)	PUNCT
ejde-719	138	9	∂t	∂t	PROPN
ejde-719	138	10	=	=	SYM
ejde-719	138	11	∂2u(t	∂2u(t	PROPN
ejde-719	138	12	,	,	PUNCT
ejde-719	138	13	x	x	X
ejde-719	138	14	)	)	PUNCT
ejde-719	138	15	∂x2	∂x2	NOUN
ejde-719	138	16	+	+	SYM
ejde-719	138	17	b(x)u(t	b(x)u(t	PROPN
ejde-719	138	18	,	,	PUNCT
ejde-719	138	19	x	x	NOUN
ejde-719	138	20	)	)	PUNCT
ejde-719	139	1	+	+	CCONJ
ejde-719	139	2	∫	∫	PROPN
ejde-719	139	3	1	1	NUM
ejde-719	139	4	0	0	NUM
ejde-719	139	5	k(x	k(x	PROPN
ejde-719	139	6	,	,	PUNCT
ejde-719	139	7	s)u(t−	s)u(t−	NOUN
ejde-719	140	1	h	h	NOUN
ejde-719	140	2	,	,	PUNCT
ejde-719	140	3	s)ds	s)ds	PROPN
ejde-719	140	4	(	(	PUNCT
ejde-719	140	5	3.1	3.1	NUM
ejde-719	140	6	)	)	PUNCT
ejde-719	140	7	for	for	ADP
ejde-719	140	8	0	0	NUM
ejde-719	140	9	≤	≤	NUM
ejde-719	140	10	x	x	SYM
ejde-719	140	11	≤	≤	NUM
ejde-719	140	12	1	1	NUM
ejde-719	140	13	and	and	CCONJ
ejde-719	140	14	t	t	PROPN
ejde-719	140	15	≥	≥	NUM
ejde-719	140	16	0	0	NUM
ejde-719	140	17	,	,	PUNCT
ejde-719	140	18	where	where	SCONJ
ejde-719	140	19	b(x	b(x	NOUN
ejde-719	140	20	)	)	PUNCT
ejde-719	140	21	is	be	AUX
ejde-719	140	22	a	a	DET
ejde-719	140	23	complex	complex	ADJ
ejde-719	140	24	valued	value	VERB
ejde-719	140	25	function	function	NOUN
ejde-719	140	26	defined	define	VERB
ejde-719	140	27	and	and	CCONJ
ejde-719	140	28	bounded	bound	VERB
ejde-719	140	29	on	on	ADP
ejde-719	140	30	[	[	X
ejde-719	140	31	0	0	NUM
ejde-719	140	32	,	,	PUNCT
ejde-719	140	33	1	1	NUM
ejde-719	140	34	]	]	PUNCT
ejde-719	140	35	;	;	PUNCT
ejde-719	140	36	k(x	k(x	PROPN
ejde-719	140	37	,	,	PUNCT
ejde-719	140	38	s	s	PART
ejde-719	140	39	)	)	PUNCT
ejde-719	140	40	is	be	AUX
ejde-719	140	41	defined	define	VERB
ejde-719	140	42	on	on	ADP
ejde-719	140	43	[	[	X
ejde-719	140	44	0	0	NUM
ejde-719	140	45	,	,	PUNCT
ejde-719	140	46	1]×[0	1]×[0	NUM
ejde-719	140	47	,	,	PUNCT
ejde-719	140	48	1	1	NUM
ejde-719	140	49	]	]	PUNCT
ejde-719	140	50	,	,	PUNCT
ejde-719	140	51	twice	twice	ADV
ejde-719	140	52	continuously	continuously	ADV
ejde-719	140	53	differentiable	differentiable	ADJ
ejde-719	140	54	in	in	ADP
ejde-719	140	55	x	x	PUNCT
ejde-719	140	56	∈	∈	PROPN
ejde-719	141	1	[	[	X
ejde-719	141	2	0	0	NUM
ejde-719	141	3	,	,	PUNCT
ejde-719	141	4	1	1	NUM
ejde-719	141	5	]	]	PUNCT
ejde-719	141	6	,	,	PUNCT
ejde-719	141	7	and	and	CCONJ
ejde-719	141	8	bounded	bound	VERB
ejde-719	141	9	and	and	CCONJ
ejde-719	141	10	measurable	measurable	ADJ
ejde-719	141	11	in	in	ADP
ejde-719	141	12	s	s	PROPN
ejde-719	141	13	,	,	PUNCT
ejde-719	141	14	and	and	CCONJ
ejde-719	141	15	k(0	k(0	PROPN
ejde-719	141	16	,	,	PUNCT
ejde-719	141	17	s	s	PART
ejde-719	141	18	)	)	PUNCT
ejde-719	141	19	=	=	SYM
ejde-719	141	20	k(1	k(1	PROPN
ejde-719	141	21	,	,	PUNCT
ejde-719	141	22	s	s	PART
ejde-719	141	23	)	)	PUNCT
ejde-719	141	24	=	=	SYM
ejde-719	141	25	0	0	PUNCT
ejde-719	141	26	(	(	PUNCT
ejde-719	141	27	s	s	NOUN
ejde-719	141	28	∈	∈	X
ejde-719	142	1	[	[	X
ejde-719	142	2	0	0	NUM
ejde-719	142	3	,	,	PUNCT
ejde-719	142	4	1	1	NUM
ejde-719	142	5	]	]	NUM
ejde-719	142	6	)	)	PUNCT
ejde-719	142	7	.	.	PUNCT
ejde-719	143	1	we	we	PRON
ejde-719	143	2	consider	consider	VERB
ejde-719	143	3	the	the	DET
ejde-719	143	4	boundary	boundary	ADJ
ejde-719	143	5	conditions	condition	NOUN
ejde-719	143	6	u(0	u(0	PROPN
ejde-719	143	7	,	,	PUNCT
ejde-719	143	8	t	t	PROPN
ejde-719	143	9	)	)	PUNCT
ejde-719	143	10	=	=	SYM
ejde-719	144	1	u(1	u(1	PROPN
ejde-719	144	2	,	,	PUNCT
ejde-719	144	3	t	t	PROPN
ejde-719	144	4	)	)	PUNCT
ejde-719	144	5	=	=	SYM
ejde-719	144	6	0	0	PUNCT
ejde-719	144	7	(	(	PUNCT
ejde-719	144	8	t	t	PROPN
ejde-719	144	9	≥	≥	PROPN
ejde-719	144	10	0	0	NUM
ejde-719	144	11	)	)	PUNCT
ejde-719	144	12	.	.	PUNCT
ejde-719	145	1	(	(	PUNCT
ejde-719	145	2	3.2	3.2	NUM
ejde-719	145	3	)	)	PUNCT
ejde-719	145	4	we	we	PRON
ejde-719	145	5	will	will	AUX
ejde-719	145	6	consider	consider	VERB
ejde-719	145	7	problem	problem	NOUN
ejde-719	145	8	(	(	PUNCT
ejde-719	145	9	3.1	3.1	NUM
ejde-719	145	10	)	)	PUNCT
ejde-719	145	11	,	,	PUNCT
ejde-719	145	12	(	(	PUNCT
ejde-719	145	13	3.2	3.2	NUM
ejde-719	145	14	)	)	PUNCT
ejde-719	145	15	in	in	ADP
ejde-719	145	16	l2(0	l2(0	NOUN
ejde-719	145	17	,	,	PUNCT
ejde-719	145	18	1	1	NUM
ejde-719	145	19	)	)	PUNCT
ejde-719	145	20	with	with	ADP
ejde-719	145	21	d(a	d(a	PROPN
ejde-719	145	22	)	)	PUNCT
ejde-719	145	23	=	=	PRON
ejde-719	145	24	{	{	PUNCT
ejde-719	145	25	f	f	PROPN
ejde-719	145	26	∈	∈	PROPN
ejde-719	145	27	l2(0	l2(0	NOUN
ejde-719	145	28	,	,	PUNCT
ejde-719	145	29	1	1	NUM
ejde-719	145	30	)	)	PUNCT
ejde-719	145	31	:	:	PUNCT
ejde-719	145	32	f	f	X
ejde-719	145	33	′′	′′	PROPN
ejde-719	145	34	∈	∈	PROPN
ejde-719	145	35	l2(0	l2(0	NOUN
ejde-719	145	36	,	,	PUNCT
ejde-719	145	37	1	1	NUM
ejde-719	145	38	)	)	PUNCT
ejde-719	145	39	,	,	PUNCT
ejde-719	145	40	f(0	f(0	NOUN
ejde-719	145	41	)	)	PUNCT
ejde-719	145	42	=	=	PUNCT
ejde-719	146	1	f(1	f(1	PROPN
ejde-719	146	2	)	)	PUNCT
ejde-719	146	3	=	=	SYM
ejde-719	146	4	0	0	NUM
ejde-719	146	5	}	}	PUNCT
ejde-719	146	6	,	,	PUNCT
ejde-719	146	7	a	a	DET
ejde-719	146	8	and	and	CCONJ
ejde-719	146	9	b	b	NOUN
ejde-719	146	10	are	be	AUX
ejde-719	146	11	defined	define	VERB
ejde-719	146	12	by	by	ADP
ejde-719	146	13	(	(	PUNCT
ejde-719	146	14	af)(x	af)(x	PROPN
ejde-719	146	15	)	)	PUNCT
ejde-719	147	1	=	=	SYM
ejde-719	147	2	d2f(x	d2f(x	PROPN
ejde-719	147	3	)	)	PUNCT
ejde-719	147	4	dx2	dx2	PROPN
ejde-719	147	5	+	+	CCONJ
ejde-719	147	6	b(x)f(x	b(x)f(x	NOUN
ejde-719	147	7	)	)	PUNCT
ejde-719	147	8	(	(	PUNCT
ejde-719	147	9	f	f	PROPN
ejde-719	147	10	∈	∈	PROPN
ejde-719	147	11	d(a	d(a	PROPN
ejde-719	147	12	)	)	PUNCT
ejde-719	147	13	)	)	PUNCT
ejde-719	147	14	,	,	PUNCT
ejde-719	147	15	(	(	PUNCT
ejde-719	147	16	bf)(x	bf)(x	PROPN
ejde-719	147	17	)	)	PUNCT
ejde-719	148	1	=	=	PUNCT
ejde-719	149	1	∫	∫	PROPN
ejde-719	150	1	1	1	NUM
ejde-719	150	2	0	0	X
ejde-719	150	3	k(x	k(x	PROPN
ejde-719	150	4	,	,	PUNCT
ejde-719	150	5	s)f(s)ds	s)f(s)ds	NOUN
ejde-719	150	6	(	(	PUNCT
ejde-719	150	7	f	f	PROPN
ejde-719	150	8	∈	∈	PROPN
ejde-719	150	9	l2	l2	NOUN
ejde-719	150	10	)	)	PUNCT
ejde-719	150	11	.	.	PUNCT
ejde-719	151	1	thus	thus	ADV
ejde-719	151	2	b	b	X
ejde-719	151	3	maps	maps	PROPN
ejde-719	151	4	l2(0	l2(0	NOUN
ejde-719	151	5	,	,	PUNCT
ejde-719	151	6	1	1	NUM
ejde-719	151	7	)	)	PUNCT
ejde-719	151	8	into	into	ADP
ejde-719	151	9	d(a	d(a	PROPN
ejde-719	151	10	)	)	PUNCT
ejde-719	151	11	.	.	PUNCT
ejde-719	152	1	also	also	ADV
ejde-719	152	2	(	(	PUNCT
ejde-719	152	3	abf)(x	abf)(x	PROPN
ejde-719	152	4	)	)	PUNCT
ejde-719	152	5	=	=	SYM
ejde-719	153	1	∫	∫	PROPN
ejde-719	153	2	1	1	NUM
ejde-719	153	3	0	0	NUM
ejde-719	154	1	[	[	X
ejde-719	154	2	k	k	X
ejde-719	154	3	′′(x	′′(x	PROPN
ejde-719	154	4	,	,	PUNCT
ejde-719	154	5	s	s	PART
ejde-719	154	6	)	)	PUNCT
ejde-719	154	7	+	+	NUM
ejde-719	154	8	b(x)k(x	b(x)k(x	NOUN
ejde-719	154	9	,	,	PUNCT
ejde-719	154	10	s)]f(s)ds	s)]f(s)ds	X
ejde-719	154	11	(	(	PUNCT
ejde-719	154	12	f	f	PROPN
ejde-719	154	13	∈	∈	PROPN
ejde-719	154	14	l2(0	l2(0	NOUN
ejde-719	154	15	,	,	PUNCT
ejde-719	154	16	1	1	NUM
ejde-719	154	17	)	)	PUNCT
ejde-719	154	18	)	)	PUNCT
ejde-719	154	19	.	.	PUNCT
ejde-719	155	1	simple	simple	ADJ
ejde-719	155	2	calculations	calculation	NOUN
ejde-719	155	3	show	show	VERB
ejde-719	155	4	that	that	SCONJ
ejde-719	155	5	the	the	DET
ejde-719	155	6	largest	large	ADJ
ejde-719	155	7	eigenvalue	eigenvalue	NOUN
ejde-719	155	8	of	of	ADP
ejde-719	155	9	the	the	DET
ejde-719	155	10	self	self	NOUN
ejde-719	155	11	-	-	PUNCT
ejde-719	155	12	adjoint	adjoint	NOUN
ejde-719	155	13	operator	operator	NOUN
ejde-719	155	14	d2	d2	PROPN
ejde-719	155	15	dx2	dx2	PROPN
ejde-719	155	16	on	on	ADP
ejde-719	155	17	d(a	d(a	PROPN
ejde-719	155	18	)	)	PUNCT
ejde-719	155	19	is	be	AUX
ejde-719	155	20	−π2	−π2	NOUN
ejde-719	155	21	and	and	CCONJ
ejde-719	155	22	sup	sup	NOUN
ejde-719	155	23	f∈d(a	f∈d(a	NUM
ejde-719	155	24	)	)	PUNCT
ejde-719	155	25	re(af	re(af	PROPN
ejde-719	155	26	,	,	PUNCT
ejde-719	155	27	f)/(f	f)/(f	PROPN
ejde-719	155	28	,	,	PUNCT
ejde-719	155	29	f	f	NOUN
ejde-719	155	30	)	)	PUNCT
ejde-719	155	31	≤	≤	NOUN
ejde-719	156	1	ν̂a	ν̂a	NUM
ejde-719	156	2	:	:	PUNCT
ejde-719	156	3	=	=	PUNCT
ejde-719	156	4	−π2	−π2	NOUN
ejde-719	156	5	+	+	CCONJ
ejde-719	156	6	sup	sup	NOUN
ejde-719	156	7	x	x	VERB
ejde-719	156	8	re	re	NOUN
ejde-719	156	9	b(x	b(x	NOUN
ejde-719	156	10	)	)	PUNCT
ejde-719	156	11	.	.	PUNCT
ejde-719	157	1	note	note	VERB
ejde-719	157	2	that	that	SCONJ
ejde-719	157	3	the	the	DET
ejde-719	157	4	function	function	NOUN
ejde-719	157	5	w(t	w(t	PROPN
ejde-719	157	6	)	)	PUNCT
ejde-719	157	7	=	=	SYM
ejde-719	157	8	eatw(0	eatw(0	PROPN
ejde-719	157	9	)	)	PUNCT
ejde-719	157	10	with	with	ADP
ejde-719	157	11	w(0	w(0	PROPN
ejde-719	157	12	)	)	PUNCT
ejde-719	157	13	∈	∈	PROPN
ejde-719	157	14	d(a	d(a	PROPN
ejde-719	157	15	)	)	PUNCT
ejde-719	157	16	satisfies	satisfie	NOUN
ejde-719	157	17	d	d	X
ejde-719	157	18	dt	dt	X
ejde-719	157	19	(	(	PUNCT
ejde-719	157	20	w(t	w(t	PROPN
ejde-719	157	21	)	)	PUNCT
ejde-719	157	22	,	,	PUNCT
ejde-719	157	23	w(t	w(t	PROPN
ejde-719	157	24	)	)	PUNCT
ejde-719	157	25	)	)	PUNCT
ejde-719	158	1	=	=	PRON
ejde-719	158	2	(	(	PUNCT
ejde-719	158	3	w′(t	w′(t	NOUN
ejde-719	158	4	)	)	PUNCT
ejde-719	158	5	,	,	PUNCT
ejde-719	158	6	w(t	w(t	PROPN
ejde-719	158	7	)	)	PUNCT
ejde-719	158	8	)	)	PUNCT
ejde-719	159	1	+	+	CCONJ
ejde-719	159	2	(	(	PUNCT
ejde-719	159	3	w(t	w(t	PROPN
ejde-719	159	4	)	)	PUNCT
ejde-719	159	5	,	,	PUNCT
ejde-719	159	6	w′(t	w′(t	NOUN
ejde-719	159	7	)	)	PUNCT
ejde-719	159	8	)	)	PUNCT
ejde-719	160	1	=	=	SYM
ejde-719	160	2	(	(	PUNCT
ejde-719	160	3	aw(t	aw(t	NOUN
ejde-719	160	4	)	)	PUNCT
ejde-719	160	5	,	,	PUNCT
ejde-719	160	6	w(t	w(t	PROPN
ejde-719	160	7	)	)	PUNCT
ejde-719	160	8	)	)	PUNCT
ejde-719	161	1	+	+	CCONJ
ejde-719	161	2	(	(	PUNCT
ejde-719	161	3	w(t	w(t	PROPN
ejde-719	161	4	)	)	PUNCT
ejde-719	161	5	,	,	PUNCT
ejde-719	161	6	aw(t	aw(t	NOUN
ejde-719	161	7	)	)	PUNCT
ejde-719	161	8	)	)	PUNCT
ejde-719	162	1	≤	≤	NUM
ejde-719	162	2	2ν̂a(w(t	2ν̂a(w(t	NUM
ejde-719	162	3	)	)	PUNCT
ejde-719	162	4	,	,	PUNCT
ejde-719	162	5	w(t	w(t	PROPN
ejde-719	162	6	)	)	PUNCT
ejde-719	162	7	)	)	PUNCT
ejde-719	162	8	.	.	PUNCT
ejde-719	163	1	hence	hence	ADV
ejde-719	163	2	d	d	ADV
ejde-719	163	3	dt	dt	PUNCT
ejde-719	163	4	∥w(t)∥	∥w(t)∥	PROPN
ejde-719	163	5	≤	≤	NOUN
ejde-719	163	6	ν̂a∥w(t)∥	ν̂a∥w(t)∥	NOUN
ejde-719	163	7	and	and	CCONJ
ejde-719	163	8	therefore	therefore	ADV
ejde-719	163	9	∥eat∥	∥eat∥	VERB
ejde-719	163	10	≤	≤	ADJ
ejde-719	163	11	eν̂at	eν̂at	NOUN
ejde-719	163	12	(	(	PUNCT
ejde-719	163	13	t	t	PROPN
ejde-719	163	14	≥	≥	PROPN
ejde-719	163	15	0	0	NUM
ejde-719	163	16	)	)	PUNCT
ejde-719	163	17	.	.	PUNCT
ejde-719	164	1	(	(	PUNCT
ejde-719	164	2	3.3	3.3	NUM
ejde-719	164	3	)	)	PUNCT
ejde-719	164	4	with	with	ADP
ejde-719	164	5	ν̂a	ν̂a	NOUN
ejde-719	164	6	=	=	PUNCT
ejde-719	164	7	−π2	−π2	NOUN
ejde-719	164	8	+	+	CCONJ
ejde-719	164	9	sup	sup	NOUN
ejde-719	164	10	x	x	VERB
ejde-719	164	11	re	re	NOUN
ejde-719	164	12	b(x	b(x	NOUN
ejde-719	164	13	)	)	PUNCT
ejde-719	164	14	<	<	X
ejde-719	164	15	0	0	NUM
ejde-719	164	16	ejde-2024/76	ejde-2024/76	ADJ
ejde-719	164	17	delay	delay	NOUN
ejde-719	164	18	-	-	PUNCT
ejde-719	164	19	dependent	dependent	ADJ
ejde-719	164	20	stability	stability	NOUN
ejde-719	164	21	conditions	condition	NOUN
ejde-719	164	22	7	7	NUM
ejde-719	164	23	we	we	PRON
ejde-719	164	24	have	have	VERB
ejde-719	164	25	ψa	ψa	PART
ejde-719	164	26	=	=	SYM
ejde-719	164	27	∫	∫	PROPN
ejde-719	164	28	∞	∞	PROPN
ejde-719	164	29	0	0	NUM
ejde-719	165	1	∥eatab∥dt	∥eatab∥dt	NOUN
ejde-719	165	2	≤	≤	NUM
ejde-719	165	3	∥ab∥/|ν̂a|	∥ab∥/|ν̂a|	NOUN
ejde-719	165	4	.	.	PUNCT
ejde-719	166	1	(	(	PUNCT
ejde-719	166	2	3.4	3.4	NUM
ejde-719	166	3	)	)	PUNCT
ejde-719	166	4	furthermore	furthermore	ADV
ejde-719	166	5	,	,	PUNCT
ejde-719	166	6	with	with	ADP
ejde-719	166	7	m	m	PROPN
ejde-719	166	8	=	=	SYM
ejde-719	166	9	a+b	a+b	NUM
ejde-719	166	10	,	,	PUNCT
ejde-719	166	11	we	we	PRON
ejde-719	166	12	obtain	obtain	VERB
ejde-719	166	13	sup	sup	NOUN
ejde-719	166	14	f∈d(a	f∈d(a	NUM
ejde-719	166	15	)	)	PUNCT
ejde-719	166	16	re(mf	re(mf	PROPN
ejde-719	166	17	,	,	PUNCT
ejde-719	166	18	f)/(f	f)/(f	PROPN
ejde-719	166	19	,	,	PUNCT
ejde-719	166	20	f	f	NOUN
ejde-719	166	21	)	)	PUNCT
ejde-719	166	22	≤	≤	NOUN
ejde-719	166	23	ν̂m	ν̂m	NUM
ejde-719	166	24	:	:	PUNCT
ejde-719	166	25	=	=	SYM
ejde-719	166	26	ν̂a	ν̂a	PART
ejde-719	166	27	+	+	CCONJ
ejde-719	166	28	ν̂b	ν̂b	VERB
ejde-719	166	29	where	where	SCONJ
ejde-719	166	30	ν̂b	ν̂b	VERB
ejde-719	166	31	:	:	PUNCT
ejde-719	166	32	=	=	SYM
ejde-719	166	33	1	1	NUM
ejde-719	166	34	2	2	NUM
ejde-719	166	35	sup	sup	NOUN
ejde-719	166	36	f∈l2(0,1	f∈l2(0,1	NOUN
ejde-719	166	37	)	)	PUNCT
ejde-719	166	38	(	(	PUNCT
ejde-719	166	39	(	(	PUNCT
ejde-719	166	40	b	b	X
ejde-719	166	41	+	+	NOUN
ejde-719	166	42	b∗)f	b∗)f	PROPN
ejde-719	166	43	,	,	PUNCT
ejde-719	166	44	f)/(f	f)/(f	PROPN
ejde-719	166	45	,	,	PUNCT
ejde-719	166	46	f	f	NOUN
ejde-719	166	47	)	)	PUNCT
ejde-719	166	48	<	<	X
ejde-719	166	49	∞	∞	PROPN
ejde-719	166	50	,	,	PUNCT
ejde-719	166	51	where	where	SCONJ
ejde-719	166	52	b∗	b∗	ADJ
ejde-719	166	53	is	be	AUX
ejde-719	166	54	the	the	DET
ejde-719	166	55	adjoint	adjoint	NOUN
ejde-719	166	56	of	of	ADP
ejde-719	166	57	b	b	PROPN
ejde-719	166	58	,	,	PUNCT
ejde-719	166	59	i.e.	i.e.	X
ejde-719	166	60	ν̂b	ν̂b	PROPN
ejde-719	166	61	is	be	AUX
ejde-719	166	62	the	the	DET
ejde-719	166	63	largest	large	ADJ
ejde-719	166	64	eigenvalue	eigenvalue	NOUN
ejde-719	166	65	of	of	ADP
ejde-719	166	66	the	the	DET
ejde-719	166	67	self	self	NOUN
ejde-719	166	68	-	-	PUNCT
ejde-719	166	69	adjoint	adjoint	NOUN
ejde-719	166	70	operator	operator	NOUN
ejde-719	166	71	(	(	PUNCT
ejde-719	166	72	b	b	NOUN
ejde-719	166	73	+	+	NOUN
ejde-719	166	74	b∗)/2	b∗)/2	X
ejde-719	166	75	.	.	PUNCT
ejde-719	167	1	with	with	ADP
ejde-719	167	2	ν̂m	ν̂m	NUM
ejde-719	167	3	<	<	X
ejde-719	167	4	0	0	X
ejde-719	167	5	similarly	similarly	ADV
ejde-719	167	6	to	to	ADP
ejde-719	167	7	(	(	PUNCT
ejde-719	167	8	3.3	3.3	NUM
ejde-719	167	9	)	)	PUNCT
ejde-719	167	10	and	and	CCONJ
ejde-719	167	11	(	(	PUNCT
ejde-719	167	12	3.4	3.4	NUM
ejde-719	167	13	)	)	PUNCT
ejde-719	167	14	we	we	PRON
ejde-719	167	15	have	have	VERB
ejde-719	167	16	∥emt∥l2	∥emt∥l2	NOUN
ejde-719	167	17	≤	≤	NUM
ejde-719	167	18	eν̂m	eν̂m	PROPN
ejde-719	167	19	t	t	PROPN
ejde-719	167	20	(	(	PUNCT
ejde-719	167	21	t	t	PROPN
ejde-719	167	22	≥	≥	PROPN
ejde-719	167	23	0	0	NUM
ejde-719	167	24	)	)	PUNCT
ejde-719	167	25	,	,	PUNCT
ejde-719	167	26	ψm	ψm	PUNCT
ejde-719	168	1	=	=	NOUN
ejde-719	168	2	∫	∫	PROPN
ejde-719	168	3	∞	∞	PROPN
ejde-719	168	4	0	0	NUM
ejde-719	168	5	∥emtb∥dt	∥emtb∥dt	ADP
ejde-719	168	6	≤	≤	NOUN
ejde-719	168	7	∥b∥l2/|ν̂m	∥b∥l2/|ν̂m	NOUN
ejde-719	168	8	|	|	NOUN
ejde-719	168	9	.	.	PUNCT
ejde-719	169	1	(	(	PUNCT
ejde-719	169	2	3.5	3.5	NUM
ejde-719	169	3	)	)	PUNCT
ejde-719	169	4	according	accord	VERB
ejde-719	169	5	to	to	ADP
ejde-719	169	6	(	(	PUNCT
ejde-719	169	7	3.3	3.3	NUM
ejde-719	169	8	)	)	PUNCT
ejde-719	169	9	and	and	CCONJ
ejde-719	169	10	(	(	PUNCT
ejde-719	169	11	3.5	3.5	NUM
ejde-719	169	12	)	)	PUNCT
ejde-719	169	13	ca	ca	NOUN
ejde-719	169	14	=	=	SYM
ejde-719	169	15	cm	cm	NOUN
ejde-719	169	16	=	=	SYM
ejde-719	170	1	1	1	X
ejde-719	170	2	.	.	X
ejde-719	170	3	using	use	VERB
ejde-719	170	4	corollary	corollary	ADJ
ejde-719	170	5	1.2	1.2	NUM
ejde-719	170	6	,	,	PUNCT
ejde-719	170	7	we	we	PRON
ejde-719	170	8	arrive	arrive	VERB
ejde-719	170	9	at	at	ADP
ejde-719	170	10	the	the	DET
ejde-719	170	11	following	following	ADJ
ejde-719	170	12	result	result	NOUN
ejde-719	170	13	.	.	PUNCT
ejde-719	171	1	theorem	theorem	VERB
ejde-719	171	2	3.1	3.1	NUM
ejde-719	171	3	.	.	PUNCT
ejde-719	172	1	let	let	VERB
ejde-719	172	2	ν̂a	ν̂a	PRON
ejde-719	172	3	<	<	X
ejde-719	172	4	0	0	PROPN
ejde-719	172	5	,	,	PUNCT
ejde-719	172	6	ν̂m	ν̂m	X
ejde-719	172	7	<	<	X
ejde-719	172	8	0	0	PUNCT
ejde-719	172	9	and	and	CCONJ
ejde-719	172	10	h∥b∥l2	h∥b∥l2	PROPN
ejde-719	173	1	ν̂m	ν̂m	NUM
ejde-719	173	2	(	(	PUNCT
ejde-719	173	3	∥ab∥l2	∥ab∥l2	PROPN
ejde-719	173	4	ν̂a	ν̂a	NOUN
ejde-719	173	5	+	+	CCONJ
ejde-719	173	6	∥b∥l2	∥b∥l2	NOUN
ejde-719	173	7	)	)	PUNCT
ejde-719	173	8	<	<	X
ejde-719	173	9	1	1	X
ejde-719	173	10	.	.	PUNCT
ejde-719	174	1	then	then	ADV
ejde-719	174	2	(	(	PUNCT
ejde-719	174	3	3.1	3.1	NUM
ejde-719	174	4	)	)	PUNCT
ejde-719	174	5	,	,	PUNCT
ejde-719	174	6	(	(	PUNCT
ejde-719	174	7	3.2	3.2	NUM
ejde-719	174	8	)	)	PUNCT
ejde-719	174	9	is	be	AUX
ejde-719	174	10	exponentially	exponentially	ADV
ejde-719	174	11	stable	stable	ADJ
ejde-719	174	12	with	with	ADP
ejde-719	174	13	respect	respect	NOUN
ejde-719	174	14	to	to	ADP
ejde-719	174	15	w	w	PROPN
ejde-719	174	16	(	(	PUNCT
ejde-719	174	17	−h	−h	ADJ
ejde-719	174	18	,	,	PUNCT
ejde-719	174	19	0	0	NUM
ejde-719	174	20	)	)	PUNCT
ejde-719	174	21	.	.	PUNCT
ejde-719	175	1	acknowledgments	acknowledgment	NOUN
ejde-719	175	2	.	.	PUNCT
ejde-719	176	1	the	the	DET
ejde-719	176	2	author	author	NOUN
ejde-719	176	3	is	be	AUX
ejde-719	176	4	very	very	ADV
ejde-719	176	5	grateful	grateful	ADJ
ejde-719	176	6	to	to	ADP
ejde-719	176	7	the	the	DET
ejde-719	176	8	anonymous	anonymous	ADJ
ejde-719	176	9	referee	referee	NOUN
ejde-719	176	10	for	for	ADP
ejde-719	176	11	his	his	PRON
ejde-719	176	12	/	/	SYM
ejde-719	176	13	her	her	PRON
ejde-719	176	14	helpful	helpful	ADJ
ejde-719	176	15	remarks	remark	NOUN
ejde-719	176	16	.	.	PUNCT
ejde-719	177	1	references	reference	NOUN
ejde-719	177	2	[	[	X
ejde-719	177	3	1	1	NUM
ejde-719	177	4	]	]	X
ejde-719	177	5	o.	o.	PROPN
ejde-719	177	6	arino	arino	PROPN
ejde-719	177	7	,	,	PUNCT
ejde-719	177	8	m.l	m.l	PROPN
ejde-719	177	9	.	.	PROPN
ejde-719	177	10	hbid	hbid	PROPN
ejde-719	177	11	,	,	PUNCT
ejde-719	177	12	e.h	e.h	PROPN
ejde-719	177	13	.	.	PROPN
ejde-719	177	14	dads	dad	NOUN
ejde-719	177	15	(	(	PUNCT
ejde-719	177	16	eds	ed	NOUN
ejde-719	177	17	.	.	PUNCT
ejde-719	177	18	)	)	PUNCT
ejde-719	177	19	;	;	PUNCT
ejde-719	177	20	delay	delay	VERB
ejde-719	177	21	differential	differential	ADJ
ejde-719	177	22	equations	equation	NOUN
ejde-719	177	23	and	and	CCONJ
ejde-719	177	24	applications	application	NOUN
ejde-719	177	25	,	,	PUNCT
ejde-719	177	26	springer	springer	NOUN
ejde-719	177	27	,	,	PUNCT
ejde-719	177	28	dordrecht	dordrecht	PROPN
ejde-719	177	29	,	,	PUNCT
ejde-719	177	30	the	the	DET
ejde-719	177	31	netherlands	netherlands	PROPN
ejde-719	177	32	,	,	PUNCT
ejde-719	177	33	2006	2006	NUM
ejde-719	177	34	.	.	PUNCT
ejde-719	178	1	[	[	X
ejde-719	178	2	2	2	NUM
ejde-719	178	3	]	]	X
ejde-719	178	4	l.	l.	PROPN
ejde-719	178	5	berezansky	berezansky	PROPN
ejde-719	178	6	,	,	PUNCT
ejde-719	178	7	e.braverman	e.braverman	NOUN
ejde-719	178	8	;	;	PUNCT
ejde-719	178	9	on	on	ADP
ejde-719	178	10	exponential	exponential	ADJ
ejde-719	178	11	stability	stability	NOUN
ejde-719	178	12	of	of	ADP
ejde-719	178	13	linear	linear	PROPN
ejde-719	178	14	delay	delay	NOUN
ejde-719	178	15	equations	equation	NOUN
ejde-719	178	16	with	with	ADP
ejde-719	178	17	oscillatory	oscillatory	ADJ
ejde-719	178	18	coefficients	coefficient	NOUN
ejde-719	178	19	and	and	CCONJ
ejde-719	178	20	kernels	kernel	NOUN
ejde-719	178	21	.	.	PUNCT
ejde-719	179	1	differential	differential	ADJ
ejde-719	179	2	and	and	CCONJ
ejde-719	179	3	integral	integral	ADJ
ejde-719	179	4	equations	equation	NOUN
ejde-719	179	5	,	,	PUNCT
ejde-719	179	6	35	35	NUM
ejde-719	179	7	,	,	PUNCT
ejde-719	179	8	no	no	NOUN
ejde-719	179	9	.	.	NOUN
ejde-719	180	1	9	9	NUM
ejde-719	180	2	-	-	SYM
ejde-719	180	3	10	10	NUM
ejde-719	180	4	(	(	PUNCT
ejde-719	180	5	2022	2022	NUM
ejde-719	180	6	)	)	PUNCT
ejde-719	180	7	,	,	PUNCT
ejde-719	180	8	559–580	559–580	NUM
ejde-719	180	9	.	.	PUNCT
ejde-719	181	1	[	[	X
ejde-719	181	2	3	3	X
ejde-719	181	3	]	]	X
ejde-719	181	4	l.	l.	PROPN
ejde-719	181	5	berezansky	berezansky	PROPN
ejde-719	181	6	,	,	PUNCT
ejde-719	181	7	j.	j.	PROPN
ejde-719	181	8	diblik	diblik	PROPN
ejde-719	181	9	,	,	PUNCT
ejde-719	181	10	z.	z.	PROPN
ejde-719	181	11	svoboda	svoboda	PROPN
ejde-719	181	12	,	,	PUNCT
ejde-719	181	13	z.	z.	PROPN
ejde-719	181	14	šmarda	šmarda	PROPN
ejde-719	181	15	;	;	PUNCT
ejde-719	181	16	simple	simple	ADJ
ejde-719	181	17	tests	test	NOUN
ejde-719	181	18	for	for	ADP
ejde-719	181	19	uniform	uniform	ADJ
ejde-719	181	20	exponential	exponential	ADJ
ejde-719	181	21	stability	stability	NOUN
ejde-719	181	22	of	of	ADP
ejde-719	181	23	a	a	DET
ejde-719	181	24	linear	linear	ADJ
ejde-719	181	25	delayed	delay	VERB
ejde-719	181	26	vector	vector	NOUN
ejde-719	181	27	differential	differential	NOUN
ejde-719	181	28	equation	equation	NOUN
ejde-719	181	29	.	.	PUNCT
ejde-719	182	1	ieee	ieee	PROPN
ejde-719	182	2	trans	trans	PROPN
ejde-719	182	3	.	.	PROPN
ejde-719	182	4	automat	automat	PROPN
ejde-719	182	5	.	.	PUNCT
ejde-719	183	1	control	control	PROPN
ejde-719	183	2	67	67	NUM
ejde-719	183	3	,	,	PUNCT
ejde-719	183	4	no	no	INTJ
ejde-719	183	5	.	.	NOUN
ejde-719	183	6	3	3	NUM
ejde-719	183	7	(	(	PUNCT
ejde-719	183	8	2022	2022	NUM
ejde-719	183	9	)	)	PUNCT
ejde-719	183	10	,	,	PUNCT
ejde-719	183	11	1537–1542	1537–1542	NUM
ejde-719	183	12	.	.	PUNCT
ejde-719	184	1	[	[	X
ejde-719	184	2	4	4	NUM
ejde-719	184	3	]	]	X
ejde-719	184	4	c.	c.	NOUN
ejde-719	184	5	corduneanu	corduneanu	PROPN
ejde-719	184	6	,	,	PUNCT
ejde-719	184	7	yizeng	yizeng	PROPN
ejde-719	184	8	li	li	PROPN
ejde-719	184	9	,	,	PUNCT
ejde-719	184	10	m.	m.	NOUN
ejde-719	184	11	mahdavi	mahdavi	PROPN
ejde-719	184	12	;	;	PUNCT
ejde-719	184	13	functional	functional	ADJ
ejde-719	184	14	differential	differential	ADJ
ejde-719	184	15	equations	equation	NOUN
ejde-719	184	16	.	.	PUNCT
ejde-719	185	1	advances	advance	NOUN
ejde-719	185	2	and	and	CCONJ
ejde-719	185	3	applications	application	NOUN
ejde-719	185	4	,	,	PUNCT
ejde-719	185	5	pure	pure	ADJ
ejde-719	185	6	and	and	CCONJ
ejde-719	185	7	applied	applied	ADJ
ejde-719	185	8	mathematics	mathematic	NOUN
ejde-719	185	9	(	(	PUNCT
ejde-719	185	10	hoboken	hoboken	PROPN
ejde-719	185	11	)	)	PUNCT
ejde-719	185	12	.	.	PUNCT
ejde-719	186	1	john	john	PROPN
ejde-719	186	2	wiley	wiley	PROPN
ejde-719	186	3	&	&	CCONJ
ejde-719	186	4	sons	sons	PROPN
ejde-719	186	5	,	,	PUNCT
ejde-719	186	6	inc	inc	PROPN
ejde-719	186	7	.	.	PROPN
ejde-719	186	8	,	,	PUNCT
ejde-719	186	9	hoboken	hoboken	PROPN
ejde-719	186	10	,	,	PUNCT
ejde-719	186	11	nj	nj	PROPN
ejde-719	186	12	,	,	PUNCT
ejde-719	186	13	2016	2016	NUM
ejde-719	186	14	.	.	PUNCT
ejde-719	187	1	[	[	X
ejde-719	187	2	5	5	NUM
ejde-719	187	3	]	]	PUNCT
ejde-719	187	4	k.-j	k.-j	PROPN
ejde-719	187	5	.	.	PUNCT
ejde-719	187	6	engel	engel	PROPN
ejde-719	187	7	,	,	PUNCT
ejde-719	187	8	r.	r.	PROPN
ejde-719	187	9	nagel	nagel	PROPN
ejde-719	187	10	;	;	PUNCT
ejde-719	187	11	a	a	DET
ejde-719	187	12	short	short	ADJ
ejde-719	187	13	course	course	NOUN
ejde-719	187	14	on	on	ADP
ejde-719	187	15	operator	operator	NOUN
ejde-719	187	16	semigroups	semigroup	NOUN
ejde-719	187	17	.	.	PUNCT
ejde-719	188	1	universitext	universitext	PROPN
ejde-719	188	2	.	.	PUNCT
ejde-719	188	3	springer	springer	PROPN
ejde-719	188	4	,	,	PUNCT
ejde-719	188	5	new	new	PROPN
ejde-719	188	6	york	york	PROPN
ejde-719	188	7	,	,	PUNCT
ejde-719	188	8	2006	2006	NUM
ejde-719	188	9	.	.	PUNCT
ejde-719	189	1	[	[	X
ejde-719	189	2	6	6	NUM
ejde-719	189	3	]	]	PUNCT
ejde-719	189	4	e.	e.	PROPN
ejde-719	189	5	fridman	fridman	PROPN
ejde-719	189	6	;	;	PUNCT
ejde-719	189	7	tutorial	tutorial	NOUN
ejde-719	189	8	on	on	ADP
ejde-719	189	9	lyapunov	lyapunov	NOUN
ejde-719	189	10	-	-	PUNCT
ejde-719	189	11	based	base	VERB
ejde-719	189	12	methods	method	NOUN
ejde-719	189	13	for	for	ADP
ejde-719	189	14	time	time	NOUN
ejde-719	189	15	-	-	PUNCT
ejde-719	189	16	delay	delay	NOUN
ejde-719	189	17	systems	system	NOUN
ejde-719	189	18	.	.	PUNCT
ejde-719	190	1	eur	eur	PROPN
ejde-719	190	2	.	.	PUNCT
ejde-719	191	1	j.	j.	PROPN
ejde-719	191	2	control	control	PROPN
ejde-719	191	3	,	,	PUNCT
ejde-719	191	4	20	20	NUM
ejde-719	191	5	,	,	PUNCT
ejde-719	191	6	no	no	INTJ
ejde-719	191	7	.	.	NOUN
ejde-719	191	8	6	6	NUM
ejde-719	191	9	(	(	PUNCT
ejde-719	191	10	2014	2014	NUM
ejde-719	191	11	)	)	PUNCT
ejde-719	191	12	,	,	PUNCT
ejde-719	191	13	271–283	271–283	NUM
ejde-719	191	14	.	.	PUNCT
ejde-719	192	1	[	[	X
ejde-719	192	2	7	7	X
ejde-719	192	3	]	]	X
ejde-719	192	4	e.	e.	PROPN
ejde-719	192	5	fridman	fridman	PROPN
ejde-719	192	6	,	,	PUNCT
ejde-719	192	7	y.	y.	PROPN
ejde-719	192	8	orlov	orlov	PROPN
ejde-719	192	9	;	;	PUNCT
ejde-719	192	10	exponential	exponential	ADJ
ejde-719	192	11	stability	stability	NOUN
ejde-719	192	12	of	of	ADP
ejde-719	192	13	linear	linear	ADJ
ejde-719	192	14	distributed	distribute	VERB
ejde-719	192	15	parameter	parameter	NOUN
ejde-719	192	16	systems	system	NOUN
ejde-719	192	17	with	with	ADP
ejde-719	192	18	time	time	NOUN
ejde-719	192	19	-	-	PUNCT
ejde-719	192	20	varying	vary	VERB
ejde-719	192	21	delays	delay	NOUN
ejde-719	192	22	,	,	PUNCT
ejde-719	192	23	automatica	automatica	PROPN
ejde-719	192	24	,	,	PUNCT
ejde-719	192	25	45	45	NUM
ejde-719	192	26	,	,	PUNCT
ejde-719	192	27	(	(	PUNCT
ejde-719	192	28	2009	2009	NUM
ejde-719	192	29	)	)	PUNCT
ejde-719	192	30	,	,	PUNCT
ejde-719	192	31	194	194	NUM
ejde-719	192	32	-	-	SYM
ejde-719	192	33	201	201	NUM
ejde-719	192	34	.	.	PUNCT
ejde-719	193	1	[	[	X
ejde-719	193	2	8	8	NUM
ejde-719	193	3	]	]	PUNCT
ejde-719	193	4	m.	m.	NOUN
ejde-719	193	5	i.	i.	PROPN
ejde-719	193	6	gil	gil	PROPN
ejde-719	193	7	’	'	PUNCT
ejde-719	193	8	;	;	PUNCT
ejde-719	193	9	delay	delay	NOUN
ejde-719	193	10	-	-	PUNCT
ejde-719	193	11	dependent	dependent	ADJ
ejde-719	193	12	stability	stability	NOUN
ejde-719	193	13	conditions	condition	NOUN
ejde-719	193	14	for	for	ADP
ejde-719	193	15	non	non	ADJ
ejde-719	193	16	-	-	ADJ
ejde-719	193	17	autonomous	autonomous	ADJ
ejde-719	193	18	functional	functional	ADJ
ejde-719	193	19	differential	differential	NOUN
ejde-719	193	20	equations	equation	NOUN
ejde-719	193	21	with	with	ADP
ejde-719	193	22	several	several	ADJ
ejde-719	193	23	delays	delay	NOUN
ejde-719	193	24	in	in	ADP
ejde-719	193	25	a	a	DET
ejde-719	193	26	banach	banach	NOUN
ejde-719	193	27	space	space	NOUN
ejde-719	193	28	,	,	PUNCT
ejde-719	193	29	nonautonomous	nonautonomous	ADJ
ejde-719	193	30	dynamical	dynamical	ADJ
ejde-719	193	31	systems	system	NOUN
ejde-719	193	32	,	,	PUNCT
ejde-719	193	33	8	8	NUM
ejde-719	193	34	(	(	PUNCT
ejde-719	193	35	1	1	NUM
ejde-719	193	36	)	)	PUNCT
ejde-719	193	37	(	(	PUNCT
ejde-719	193	38	2021	2021	NUM
ejde-719	193	39	)	)	PUNCT
ejde-719	193	40	,	,	PUNCT
ejde-719	193	41	168	168	NUM
ejde-719	193	42	-	-	SYM
ejde-719	193	43	179	179	NUM
ejde-719	193	44	.	.	PUNCT
ejde-719	194	1	[	[	X
ejde-719	194	2	9	9	NUM
ejde-719	194	3	]	]	PUNCT
ejde-719	194	4	m.	m.	NOUN
ejde-719	194	5	i.	i.	PROPN
ejde-719	194	6	gil	gil	PROPN
ejde-719	194	7	’	'	PUNCT
ejde-719	194	8	,	,	PUNCT
ejde-719	194	9	on	on	ADP
ejde-719	194	10	dyson	dyson	PROPN
ejde-719	194	11	-	-	PUNCT
ejde-719	194	12	phillips	phillips	PROPN
ejde-719	194	13	type	type	NOUN
ejde-719	194	14	approach	approach	NOUN
ejde-719	194	15	to	to	ADP
ejde-719	194	16	differential	differential	ADJ
ejde-719	194	17	-	-	PUNCT
ejde-719	194	18	difference	difference	NOUN
ejde-719	194	19	equations	equation	NOUN
ejde-719	194	20	in	in	ADP
ejde-719	194	21	a	a	DET
ejde-719	194	22	banach	banach	NOUN
ejde-719	194	23	space	space	NOUN
ejde-719	194	24	,	,	PUNCT
ejde-719	194	25	discussiones	discussione	NOUN
ejde-719	194	26	mathematicae	mathematicae	VERB
ejde-719	194	27	differential	differential	ADJ
ejde-719	194	28	inclusions	inclusion	NOUN
ejde-719	194	29	.	.	PUNCT
ejde-719	195	1	control	control	NOUN
ejde-719	195	2	and	and	CCONJ
ejde-719	195	3	optimization	optimization	NOUN
ejde-719	195	4	,	,	PUNCT
ejde-719	195	5	42(2	42(2	NUM
ejde-719	195	6	)	)	PUNCT
ejde-719	195	7	(	(	PUNCT
ejde-719	195	8	2022	2022	NUM
ejde-719	195	9	)	)	PUNCT
ejde-719	195	10	,	,	PUNCT
ejde-719	195	11	1	1	NUM
ejde-719	195	12	-	-	SYM
ejde-719	195	13	8	8	NUM
ejde-719	195	14	.	.	PUNCT
ejde-719	196	1	[	[	X
ejde-719	196	2	10	10	NUM
ejde-719	196	3	]	]	PUNCT
ejde-719	196	4	m.	m.	NOUN
ejde-719	196	5	i.	i.	PROPN
ejde-719	196	6	gil	gil	PROPN
ejde-719	196	7	’	'	PUNCT
ejde-719	196	8	,	,	PUNCT
ejde-719	196	9	delay	delay	NOUN
ejde-719	196	10	-	-	PUNCT
ejde-719	196	11	dependent	dependent	ADJ
ejde-719	196	12	stability	stability	NOUN
ejde-719	196	13	conditions	condition	NOUN
ejde-719	196	14	for	for	ADP
ejde-719	196	15	differential	differential	ADJ
ejde-719	196	16	–	–	PUNCT
ejde-719	196	17	difference	difference	NOUN
ejde-719	196	18	equations	equation	NOUN
ejde-719	196	19	with	with	ADP
ejde-719	196	20	small	small	ADJ
ejde-719	196	21	commutators	commutator	NOUN
ejde-719	196	22	in	in	ADP
ejde-719	196	23	a	a	DET
ejde-719	196	24	banach	banach	NOUN
ejde-719	196	25	space	space	NOUN
ejde-719	196	26	,	,	PUNCT
ejde-719	196	27	bulletin	bulletin	NOUN
ejde-719	196	28	of	of	ADP
ejde-719	196	29	mathematical	mathematical	ADJ
ejde-719	196	30	sciences	science	NOUN
ejde-719	196	31	,	,	PUNCT
ejde-719	196	32	2350009	2350009	NUM
ejde-719	196	33	(	(	PUNCT
ejde-719	196	34	2023	2023	NUM
ejde-719	196	35	)	)	PUNCT
ejde-719	196	36	,	,	PUNCT
ejde-719	196	37	1	1	NUM
ejde-719	196	38	-	-	SYM
ejde-719	196	39	12	12	NUM
ejde-719	196	40	.	.	NOUN
ejde-719	196	41	8	8	NUM
ejde-719	196	42	m.	m.	NOUN
ejde-719	196	43	gil	gil	PROPN
ejde-719	196	44	’	'	PUNCT
ejde-719	196	45	ejde-2024/76	ejde-2024/76	PROPN
ejde-719	196	46	[	[	X
ejde-719	196	47	11	11	NUM
ejde-719	196	48	]	]	X
ejde-719	196	49	chuhu	chuhu	PROPN
ejde-719	196	50	jin	jin	PROPN
ejde-719	196	51	,	,	PUNCT
ejde-719	196	52	jiaowan	jiaowan	PROPN
ejde-719	196	53	luo	luo	PROPN
ejde-719	196	54	;	;	PUNCT
ejde-719	196	55	stability	stability	NOUN
ejde-719	196	56	of	of	ADP
ejde-719	196	57	an	an	DET
ejde-719	196	58	integro	integro	ADJ
ejde-719	196	59	-	-	PUNCT
ejde-719	196	60	differential	differential	NOUN
ejde-719	196	61	equation	equation	NOUN
ejde-719	196	62	,	,	PUNCT
ejde-719	196	63	computers	computer	NOUN
ejde-719	196	64	and	and	CCONJ
ejde-719	196	65	mathematics	mathematic	NOUN
ejde-719	196	66	with	with	ADP
ejde-719	196	67	applications	application	NOUN
ejde-719	196	68	,	,	PUNCT
ejde-719	196	69	57	57	NUM
ejde-719	196	70	,	,	PUNCT
ejde-719	196	71	(	(	PUNCT
ejde-719	196	72	2009	2009	NUM
ejde-719	196	73	)	)	PUNCT
ejde-719	196	74	,	,	PUNCT
ejde-719	196	75	1080–1088	1080–1088	NUM
ejde-719	196	76	.	.	PUNCT
ejde-719	197	1	[	[	X
ejde-719	197	2	12	12	NUM
ejde-719	197	3	]	]	X
ejde-719	197	4	s.	s.	PROPN
ejde-719	197	5	g.	g.	PROPN
ejde-719	197	6	krein	krein	PROPN
ejde-719	197	7	;	;	PUNCT
ejde-719	197	8	linear	linear	ADJ
ejde-719	197	9	equations	equation	NOUN
ejde-719	197	10	in	in	ADP
ejde-719	197	11	banach	banach	NOUN
ejde-719	197	12	spaces	space	NOUN
ejde-719	197	13	,	,	PUNCT
ejde-719	197	14	boston	boston	PROPN
ejde-719	197	15	,	,	PUNCT
ejde-719	197	16	birkhauser	birkhauser	NOUN
ejde-719	197	17	1982	1982	NUM
ejde-719	197	18	.	.	PUNCT
ejde-719	198	1	[	[	X
ejde-719	198	2	13	13	NUM
ejde-719	198	3	]	]	PUNCT
ejde-719	198	4	v.	v.	CCONJ
ejde-719	198	5	kolmanovskii	kolmanovskii	PROPN
ejde-719	198	6	,	,	PUNCT
ejde-719	198	7	a.	a.	NOUN
ejde-719	198	8	myshkis	myshki	NOUN
ejde-719	198	9	;	;	PUNCT
ejde-719	198	10	applied	apply	VERB
ejde-719	198	11	theory	theory	NOUN
ejde-719	198	12	of	of	ADP
ejde-719	198	13	functional	functional	ADJ
ejde-719	198	14	differential	differential	ADJ
ejde-719	198	15	equations	equation	NOUN
ejde-719	198	16	,	,	PUNCT
ejde-719	198	17	kluwer	kluwer	NOUN
ejde-719	198	18	,	,	PUNCT
ejde-719	198	19	dordrecht	dordrecht	PROPN
ejde-719	198	20	,	,	PUNCT
ejde-719	198	21	1999	1999	NUM
ejde-719	198	22	.	.	PUNCT
ejde-719	199	1	[	[	X
ejde-719	199	2	14	14	NUM
ejde-719	199	3	]	]	X
ejde-719	199	4	y.	y.	PROPN
ejde-719	199	5	p.	p.	PROPN
ejde-719	199	6	luo	luo	PROPN
ejde-719	199	7	,	,	PUNCT
ejde-719	199	8	f.	f.	PROPN
ejde-719	199	9	q.	q.	PROPN
ejde-719	199	10	deng	deng	PROPN
ejde-719	199	11	;	;	PUNCT
ejde-719	199	12	lmi	lmi	PROPN
ejde-719	199	13	-	-	PUNCT
ejde-719	199	14	based	base	VERB
ejde-719	199	15	approach	approach	NOUN
ejde-719	199	16	of	of	ADP
ejde-719	199	17	robust	robust	ADJ
ejde-719	199	18	control	control	NOUN
ejde-719	199	19	for	for	ADP
ejde-719	199	20	uncertain	uncertain	ADJ
ejde-719	199	21	distributed	distribute	VERB
ejde-719	199	22	parameter	parameter	NOUN
ejde-719	199	23	control	control	NOUN
ejde-719	199	24	systems	system	NOUN
ejde-719	199	25	with	with	ADP
ejde-719	199	26	time	time	NOUN
ejde-719	199	27	-	-	PUNCT
ejde-719	199	28	delay	delay	NOUN
ejde-719	199	29	.	.	PUNCT
ejde-719	200	1	control	control	NOUN
ejde-719	200	2	theory	theory	NOUN
ejde-719	200	3	and	and	CCONJ
ejde-719	200	4	applications	application	NOUN
ejde-719	200	5	,	,	PUNCT
ejde-719	200	6	23	23	NUM
ejde-719	200	7	(	(	PUNCT
ejde-719	200	8	2006	2006	NUM
ejde-719	200	9	)	)	PUNCT
ejde-719	200	10	,	,	PUNCT
ejde-719	200	11	318–324	318–324	NUM
ejde-719	200	12	.	.	PUNCT
ejde-719	201	1	[	[	X
ejde-719	201	2	15	15	NUM
ejde-719	201	3	]	]	X
ejde-719	201	4	l.	l.	PROPN
ejde-719	201	5	wang	wang	PROPN
ejde-719	201	6	,	,	PUNCT
ejde-719	201	7	y.	y.	PROPN
ejde-719	201	8	wang	wang	PROPN
ejde-719	201	9	;	;	PUNCT
ejde-719	201	10	lmi	lmi	PROPN
ejde-719	201	11	-	-	PUNCT
ejde-719	201	12	based	base	VERB
ejde-719	201	13	approach	approach	NOUN
ejde-719	201	14	of	of	ADP
ejde-719	201	15	global	global	ADJ
ejde-719	201	16	exponential	exponential	ADJ
ejde-719	201	17	robust	robust	ADJ
ejde-719	201	18	stability	stability	NOUN
ejde-719	201	19	for	for	ADP
ejde-719	201	20	a	a	DET
ejde-719	201	21	class	class	NOUN
ejde-719	201	22	of	of	ADP
ejde-719	201	23	uncertain	uncertain	ADJ
ejde-719	201	24	distributed	distribute	VERB
ejde-719	201	25	parameter	parameter	NOUN
ejde-719	201	26	control	control	NOUN
ejde-719	201	27	systems	system	NOUN
ejde-719	201	28	with	with	ADP
ejde-719	201	29	time	time	NOUN
ejde-719	201	30	-	-	PUNCT
ejde-719	201	31	varying	vary	VERB
ejde-719	201	32	delays	delay	NOUN
ejde-719	201	33	.	.	PUNCT
ejde-719	202	1	journal	journal	NOUN
ejde-719	202	2	of	of	ADP
ejde-719	202	3	vibration	vibration	NOUN
ejde-719	202	4	and	and	CCONJ
ejde-719	202	5	control	control	NOUN
ejde-719	202	6	,	,	PUNCT
ejde-719	202	7	15	15	NUM
ejde-719	202	8	(	(	PUNCT
ejde-719	202	9	2009	2009	NUM
ejde-719	202	10	)	)	PUNCT
ejde-719	202	11	,	,	PUNCT
ejde-719	202	12	1173–1185	1173–1185	NUM
ejde-719	202	13	.	.	PUNCT
ejde-719	203	1	michael	michael	PROPN
ejde-719	203	2	gil	gil	PROPN
ejde-719	203	3	’	'	PUNCT
ejde-719	203	4	department	department	PROPN
ejde-719	203	5	of	of	ADP
ejde-719	203	6	mathematics	mathematics	PROPN
ejde-719	203	7	,	,	PUNCT
ejde-719	203	8	ben	ben	PROPN
ejde-719	203	9	gurion	gurion	PROPN
ejde-719	203	10	university	university	PROPN
ejde-719	203	11	of	of	ADP
ejde-719	203	12	the	the	DET
ejde-719	203	13	negev	negev	PROPN
ejde-719	203	14	,	,	PUNCT
ejde-719	203	15	p.0	p.0	PROPN
ejde-719	203	16	.	.	PUNCT
ejde-719	203	17	box	box	PROPN
ejde-719	203	18	653	653	NUM
ejde-719	203	19	,	,	PUNCT
ejde-719	203	20	beersheva	beersheva	NOUN
ejde-719	203	21	84105	84105	NUM
ejde-719	203	22	,	,	PUNCT
ejde-719	203	23	israel	israel	PROPN
ejde-719	203	24	email	email	NOUN
ejde-719	203	25	address	address	NOUN
ejde-719	203	26	:	:	PUNCT
ejde-719	204	1	gilmi@bezeqint.net	gilmi@bezeqint.net	PROPN
ejde-719	204	2	1	1	NUM
ejde-719	204	3	.	.	PUNCT
ejde-719	204	4	introduction	introduction	NOUN
ejde-719	204	5	and	and	CCONJ
ejde-719	204	6	statement	statement	NOUN
ejde-719	204	7	of	of	ADP
ejde-719	204	8	the	the	DET
ejde-719	204	9	main	main	ADJ
ejde-719	204	10	result	result	NOUN
ejde-719	204	11	2	2	X
ejde-719	204	12	.	.	PUNCT
ejde-719	204	13	proofs	proof	NOUN
ejde-719	204	14	of	of	ADP
ejde-719	204	15	theorem	theorem	NOUN
ejde-719	204	16	?	?	PUNCT
ejde-719	204	17	?	?	PUNCT
ejde-719	205	1	and	and	CCONJ
ejde-719	205	2	corollary	corollary	ADJ
ejde-719	205	3	1.2	1.2	NUM
ejde-719	205	4	3	3	NUM
ejde-719	205	5	.	.	PUNCT
ejde-719	205	6	example	example	NOUN
ejde-719	205	7	acknowledgments	acknowledgment	NOUN
ejde-719	205	8	references	reference	NOUN