Journal Article

Adaptive stabilization of infinite‐dimensional semilinear second‐order systems

Toshihiro Kobayashi

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 20, issue 2, pages 137-152
Published in print June 2003 | ISSN: 0265-0754
Published online June 2003 | e-ISSN: 1471-6887 | DOI:
Adaptive stabilization of infinite‐dimensional semilinear second‐order systems

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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

Journal Article.  0 words. 

Subjects: Mathematics

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