Basis property and stabilization of a translating tensioned beam through a pointwise control force

doi:10.1016/j.camwa.2004.04.023

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	Basis property and stabilization of a translating tensioned beam through a pointwise control force
	Guo, BZ; Xie, Y
	2004-04-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	47 期号:8-9 页码:1397-1409
摘要	Introducing a recently developed powerful method, Riesz basis method as it is called, and applying it to the stabilization of a translating tensioned beam through a pointwise control force are the two purposes of the paper. An asymptotic analysis, which is different from the one in treating the same problem in literature, is used to get a complete asymptotic expansion of the eigenvalues and eigenfunctions for the beam. The controlled system is written as an evolution equation in a state Hilbert space whose energy norm (induced by inner product) is the total energy of the beam. The spectrum-determined growth condition is obtained by showing that there is a set of generalized eigenfunctions of the system, which forms a Riesz basis for the state space. As a consequence, the stability, particularly the exponential stability of the system, is developed. The analysis used here can be extended to other distributed systems and the results significantly improve that in [1]. (C) 2004 Elsevier Ltd. All rights reserved.
关键词	beam equation Riesz basis stability
DOI	10.1016/j.camwa.2004.04.023
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000222231500023
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19388
专题	系统科学研究所
通讯作者	Guo, BZ
作者单位	Acad Sinica, Acad Math & Syst Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Guo, BZ,Xie, Y. Basis property and stabilization of a translating tensioned beam through a pointwise control force[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2004,47(8-9):1397-1409.
APA	Guo, BZ,&Xie, Y.(2004).Basis property and stabilization of a translating tensioned beam through a pointwise control force.COMPUTERS & MATHEMATICS WITH APPLICATIONS,47(8-9),1397-1409.
MLA	Guo, BZ,et al."Basis property and stabilization of a translating tensioned beam through a pointwise control force".COMPUTERS & MATHEMATICS WITH APPLICATIONS 47.8-9(2004):1397-1409.