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IMA Journal of Mathematical Control and Information 2003 20(2):137-152; doi:10.1093/imamci/20.2.137
© 2003 by Institute of Mathematics and its Applications
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Adaptive stabilization of infinite-dimensional semilinear second-order systems

Toshihiro Kobayashi1

1 Department of Mechanical and Control Engineering, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 8040015, Japan

In this paper adaptive stabilization of infinite-dimensional undamped semilinear second-order systems is considered in the case of the input and output operators being collocated. The adaptive stabilizer is constructed by the concept of high-gain output feedback. An energy-like function and a multiplier function are introduced and adaptive stabilization of the semilinear second-order systems is analysed. The theories are applied to a nonlinear string system and the sine-Gordon system.

Keywords: adaptive stabilization; semilinear second-order dynamical systems; energy-like functions; multiplier functions.

Received 30 July 2002. Accepted 1 November 2002.


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