KMS Of Academy of mathematics and systems sciences, CAS
WAVE EQUATION STABILIZATION BY DELAYS EQUAL TO EVEN MULTIPLES OF THE WAVE PROPAGATION TIME | |
Wang, Jun-Min1; Guo, Bao-Zhu2,3,4; Krstic, Miroslav5 | |
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. |
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