WAVE EQUATION STABILIZATION BY DELAYS EQUAL TO EVEN MULTIPLES OF THE WAVE PROPAGATION TIME

doi:10.1137/100796261

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	WAVE EQUATION STABILIZATION BY DELAYS EQUAL TO EVEN MULTIPLES OF THE WAVE PROPAGATION TIME
	Wang, Jun-Min 1; Guo, Bao-Zhu2,3,4 ; Krstic, Miroslav 5
	2011
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	49 期号:2 页码:517-554
摘要	For a string equation with time delays in the output feedback loop, we study stability and show that the system is a Riesz spectral system and prove that the spectrum-determined growth condition holds for all delays. When the delay is equal to the even multiples of the wave propagation time, we develop the necessary and sufficient conditions for the feedback gain and time delay which guarantee the exponential stability of the closed-loop system. In particular, we show that as the delay of even multiples is increasing to infinity, the stability bound on the feedback gain decays to zero. We also show that whenever the delay is an odd multiple of the wave propagation time, the closed-loop system is unstable. The lack of robustness to a small perturbation in time delay is specifically discussed for the delay equal to two. A numerical simulation for the case of the delay equal to two is presented to illustrate the convergence. Finally, an alternative stability analysis is conducted within the framework of well-posed infinite-dimensional systems.
关键词	wave equation time delay boundary control distributed parameter system
DOI	10.1137/100796261
语种	英语
资助项目	National Natural Science Foundation of China ; Program for New Century Excellent Talents in University of China ; National Basic Research Program of China[2011CB808002] ; National Research Foundation of South Africa ; National Science Foundation (NSF)
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000289972200010
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12542
专题	系统科学研究所
通讯作者	Wang, Jun-Min
作者单位	1.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 2.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China 4.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa 5.Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA
推荐引用方式 GB/T 7714	Wang, Jun-Min,Guo, Bao-Zhu,Krstic, Miroslav. WAVE EQUATION STABILIZATION BY DELAYS EQUAL TO EVEN MULTIPLES OF THE WAVE PROPAGATION TIME[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2011,49(2):517-554.
APA	Wang, Jun-Min,Guo, Bao-Zhu,&Krstic, Miroslav.(2011).WAVE EQUATION STABILIZATION BY DELAYS EQUAL TO EVEN MULTIPLES OF THE WAVE PROPAGATION TIME.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,49(2),517-554.
MLA	Wang, Jun-Min,et al."WAVE EQUATION STABILIZATION BY DELAYS EQUAL TO EVEN MULTIPLES OF THE WAVE PROPAGATION TIME".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 49.2(2011):517-554.