On the relation between stability of continuous- and discrete-time evolution equations via the Cayley transform

doi:10.1007/s00020-003-1350-9

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	On the relation between stability of continuous- and discrete-time evolution equations via the Cayley transform
	Guo, BZ ; Zwart, H
	2006-03-01
发表期刊	INTEGRAL EQUATIONS AND OPERATOR THEORY
ISSN	0378-620X
卷号	54 期号:3 页码:349-383
摘要	In this paper we investigate and compare the properties of the semigroup generated by A, and the sequence A(d)(n), n is an element of N, where A(d) = (I + A)(I - A)(-1). We show that if A and A(-1) generate a uniformly bounded, strongly continuous semigroup on a Hilbert space, then Ad is power bounded. For analytic semigroups we can prove stronger results. If A is the infinitesimal generator of an analytic semigroup, then power boundedness of A(d) is equivalent to the uniform boundedness of the semigroup generated by A.
关键词	abstract differential equations infinite-dimensional systems discrete time continuous time stability Lyapunov equations
DOI	10.1007/s00020-003-1350-9
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000236243500004
出版者	BIRKHAUSER VERLAG AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3567
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, BZ
作者单位	1.Acad Sinica, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Univ Twente, Dept Appl Math, NL-7500 AE Enschede, Netherlands
推荐引用方式 GB/T 7714	Guo, BZ,Zwart, H. On the relation between stability of continuous- and discrete-time evolution equations via the Cayley transform[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY,2006,54(3):349-383.
APA	Guo, BZ,&Zwart, H.(2006).On the relation between stability of continuous- and discrete-time evolution equations via the Cayley transform.INTEGRAL EQUATIONS AND OPERATOR THEORY,54(3),349-383.
MLA	Guo, BZ,et al."On the relation between stability of continuous- and discrete-time evolution equations via the Cayley transform".INTEGRAL EQUATIONS AND OPERATOR THEORY 54.3(2006):349-383.