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IMA Journal of Mathematical Control and Information Advance Access originally published online on March 13, 2006
IMA Journal of Mathematical Control and Information 2006 23(4):475-484; 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.

Boundary feedback stabilization of coupled sine-Gordon equations

Toshihiro Kobayashi** and Tetsuzo Sakamoto***

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

** Email: koba{at}cntl.kyutech.ac.jp

*** Email: sakamoto{at}cntl.kyutech.ac.jp

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.

Received on 1 December 2004. accepted on 14 October 2005.


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