Boundary Control of Coupled Wave Systems with Spatially-Varying Coefficients

This paper considers the stabilization of the coupled wave systems with spatially-varying coefficients. The authors design a state feedback controller by backstepping method. In contrast to the previous work in the literature, the kernel equations become more complicated and the main difficulty lies...

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Bibliographic Details
Published in:Journal of systems science and complexity 2022-08, Vol.35 (4), p.1310-1329
Main Authors: Feng, Xiaodan, Zhang, Zhifei
Format: Article
Language:English
Subjects:
Boundary control
Coefficients
Complex Systems
Control
Control systems design
Feedback control
Kernels
Liapunov functions
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Stabilization
State feedback
Statistics
Systems Theory
Uniqueness
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Summary:This paper considers the stabilization of the coupled wave systems with spatially-varying coefficients. The authors design a state feedback controller by backstepping method. In contrast to the previous work in the literature, the kernel equations become more complicated and the main difficulty lies in proving the existence and uniqueness of the solution to the kernel equations. Firstly, using the backstepping approach, the authors verify the kernel equations, which is a system of coupled hyperbolic equations with spatially-varying coefficients. Then, the existence and uniqueness of the kernel matrices is obtained. Finally, the authors use a Lyapunov function to get the exponential stabilization of the closed-loop system. A numerical example is presented to illustrate the effectiveness of the proposed controller.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-021-0214-1