An exponential stability result for the wave equation

Date
2002
Authors
Morgül, Ö.
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Source Title
Automatica
Print ISSN
0005-1098
Electronic ISSN
Publisher
Elsevier
Volume
38
Issue
4
Pages
731 - 735
Language
English
Type
Article
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Abstract

We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize this system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function which consists of a strictly positive real function and some poles on the imaginary axis. We then show that under some conditions the closed-loop system is exponentially stable. © 2002 Published by Elsevier Ltd.

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Keywords
Control theory, Distributed parameter systems, Boundary conditions, Closed loop control systems, Control equipment, Linear equations, Stability, Transfer functions, Wave equations, Dynamic boundary controller, Distributed parameter control systems
Citation
Published Version (Please cite this version)