Output Feedback Stabilization of an Unstable Wave Equation with Observations Subject to Time Delay

This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor...

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Bibliographic Details
Published inJournal of systems science and complexity Vol. 29; no. 1; pp. 99 - 118
Main Authors Yang, Kunyi, Ren, Xiang, Zhang, Jie
Format Journal Article
LanguageEnglish
Published Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.02.2016
Subjects
Complex Systems
Control
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Statistics
Systems Theory
理论
系统学
系统工程
系统科学
time delay
observability inequality
unstable boundary condition
Exponential stability
output feedback
wave equation
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Summary:This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed：The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.
Bibliography:Exponential stability observability inequality output feedback unstable boundary condition time delay wave equation
This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed：The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.
11-4543/O1
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-016-5169-2