Paper Info
Title
Wave Equation Stabilization by Delays Equal to Even Multiples of the Wave Propagation Time
Abstract
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.
Year
DOI
Venue
2011
10.1137/100796261
SIAM J. Control and Optimization
Keywords
Field
DocType
exponential stability,feedback gain decay,wave equation stabilization,alternative stability analysis,wave propagation time,output feedback loop,riesz spectral system,well-posed infinite-dimensional system,time delay,feedback gain,closed-loop system,delays equal,distributed parameter system,wave equation,wave propagation
Convergence (routing),Mathematical optimization,Computer simulation,Control theory,Mathematical analysis,Group delay and phase delay,Feedback loop,Exponential stability,Distributed parameter system,Wave equation,Propagation time,Mathematics
Journal
Volume
Issue
ISSN
49
2
0363-0129
Citations 
PageRank 
References 
9
0.63
4
Authors
3
Name
Order
Citations
PageRank
Jun-Min Wang121929.95
Bao-Zhu Guo21178117.67
Miroslav Krstic34987553.84