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IMA Journal of Mathematical Control and Information Advance Access published online on March 13, 2006
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnl006
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received December 1, 2004
Accepted October 14, 2005

Article

Boundary feedback stabilization of coupled sine-Gordon equations

Toshihiro Kobayashi 1 * and Tetsuzo Sakamoto 1

1 Department of Mechanical and Control Engineering, Faculty of Engineering Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan

* To whom correspondence should be addressed.
Toshihiro Kobayashi, E-mail: koba{at}cntl.kyutech.ac.jp


  Abstract

This paper is concerned with global stabilization of the system governed by coupled sine-Gordon equations without damping. A stabilizer is constructed by boundary velocity feedback. The closed-loop system is shown to be well posed by the non-linear semigroup approach. Moreover, using a multiplier method, global exponential stabilization of the closed-loop system is proved.

Keywords: coupled sine-Gordon equations; global asymptotic stabilization; boundary control; multiplier method.
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