On the C-0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam

doi:10.1016/j.sysconle.2004.10.006

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	On the C-0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam
	Guo, BZ; Wang, JM ; Yung, SP
	2005-06-01
发表期刊	SYSTEMS & CONTROL LETTERS
ISSN	0167-6911
卷号	54 期号:6 页码:557-574
摘要	In this paper, we show that a linear unbounded operator associated with an Euler-Bemoulli beam equation under shear boundary feedback generates a C-0-semigroup in the underlying state Hilbert space. This provides an answer to a long time unsolved problem due to the lack of dissipativity for the operator. The main steps are a careful estimation of the Green's function and the verification of the Riesz basis property for the generalized eigenfunctions. As a consequence, we show that this semigroup is differentiable and exponentially stable, which is in sharp contrast to the properties possessed by most feedback controlled beams based on a passive design principle. © 2005 Elsevier B.V. All rights reserved.
关键词	Riesz basis C-0-semigroup differentiable semigroup stability
DOI	10.1016/j.sysconle.2004.10.006
语种	英语
WOS研究方向	Automation & Control Systems ; Operations Research & Management Science
WOS类目	Automation & Control Systems ; Operations Research & Management Science
WOS记录号	WOS:000229108400005
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2280
专题	系统科学研究所
通讯作者	Guo, BZ
作者单位	1.Acad Sinica, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China 2.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Wits, South Africa 3.Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Guo, BZ,Wang, JM,Yung, SP. On the C-0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam[J]. SYSTEMS & CONTROL LETTERS,2005,54(6):557-574.
APA	Guo, BZ,Wang, JM,&Yung, SP.(2005).On the C-0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam.SYSTEMS & CONTROL LETTERS,54(6),557-574.
MLA	Guo, BZ,et al."On the C-0-semigroup generation and exponential stability resulting from a shear force feedback on a rotating beam".SYSTEMS & CONTROL LETTERS 54.6(2005):557-574.