Output regulation of anti-stable coupled wave equations via the backstepping technique

Jian-Jun Gu; Jun-Min Wang; Ya-Ping Guo

Output regulation of anti-stable coupled wave equations via the backstepping technique

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Author(s): Jian-Jun Gu^{1, 2} ; Jun-Min Wang¹ ; Ya-Ping Guo³
- Affiliations: 1: School of Mathematics and Statistics, Beijing Institute of Technology , Beijing 100081 , People's Republic of China ;
  2: School of Mathematics and Statistics, Changshu Institute of Technology , Jiangsu 215500 , People's Republic of China ;
  3: School of Mathematical Sciences, Shanxi University , Taiyuan, Shanxi 030006 , People's Republic of China
Source: Volume 12, Issue 4, 06 March 2018, p. 431 – 445
DOI: 10.1049/iet-cta.2017.0677 , Print ISSN 1751-8644, Online ISSN 1751-8652

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Received 21/06/2017, Accepted 11/12/2017, Revised 29/09/2017, Published 12/12/2017

This study is concerned with the output regulation of an anti-stable system of coupled wave equations with external disturbances. A state-feedback regulator is designed to force the output of the coupled wave equations to track the reference signal, which is generated by an exosystem. Moreover, the tracking error decays exponentially at a prescribed rate. The design is based on backstepping approach and relies on solving the regulator equations. The solvability condition of the regulator equations is characterised by the transfer matrix of the coupled wave equations and eigenvalues of the exosystem. An output-feedback regulator is then constructed by developing an observer. Finally, the numerical simulations are demonstrated for the effectiveness of the theoretical results.

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Output regulation of anti-stable coupled wave equations via the backstepping technique

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