The exponential stabilization of a heat-wave coupled system and its approximation

In this paper, we consider exponential stabilization for a heat-wave coupled system under boundary control and collocated observation. It is known that the system is polynomially stable without control. Two kinds of feedback strategies namely static negative proportional feedback and dynamic feedbac...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2023-05, Vol.521 (1), p.126927, Article 126927
Main Authors: Zheng, Fu, Zhang, Sijia, Wang, Huakun, Guo, Bao-Zhu
Format: Article
Language:English
Subjects:
[formula omitted] robustness
Collocated observation and control
Exponential stabilization
Heat-wave coupled equation
Semi-discretization
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Summary:In this paper, we consider exponential stabilization for a heat-wave coupled system under boundary control and collocated observation. It is known that the system is polynomially stable without control. Two kinds of feedback strategies namely static negative proportional feedback and dynamic feedback are designed. By the Lyapunov function direct method, the exponential stabilities of the closed-loop systems under different two feedbacks are firstly verified. Secondly, the H∞ robustness is further analyzed and the related sufficient conditions are developed. Furthermore, the closed-loop systems are discretized into semi-discrete systems by a new finite difference method, and the uniform exponential stabilities of the discrete systems are established by the approach paralleling to the continuous counterpart.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126927