CSpace  > 系统科学研究所
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
Source PublicationSIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN0363-0129
Volume49Issue:2Pages:517-554
AbstractFor 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.
Keywordwave equation time delay boundary control distributed parameter system
DOI10.1137/100796261
Language英语
Funding ProjectNational 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 Research AreaAutomation & Control Systems ; Mathematics
WOS SubjectAutomation & Control Systems ; Mathematics, Applied
WOS IDWOS:000289972200010
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:28[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/12542
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Wang, Jun-Min]'s Articles
[Guo, Bao-Zhu]'s Articles
[Krstic, Miroslav]'s Articles
Baidu academic
Similar articles in Baidu academic
[Wang, Jun-Min]'s Articles
[Guo, Bao-Zhu]'s Articles
[Krstic, Miroslav]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Wang, Jun-Min]'s Articles
[Guo, Bao-Zhu]'s Articles
[Krstic, Miroslav]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.