Boundary Control of Coupled Wave Systems with Spatially-Varying Coefficients

doi:10.1007/s11424-021-0214-1

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (4): 1310-1329.DOI: 10.1007/s11424-021-0214-1

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Boundary Control of Coupled Wave Systems with Spatially-Varying Coefficients

FENG Xiaodan^1,2, ZHANG Zhifei^1,2

1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China

Received:2020-09-10 Revised:2021-04-17 Online:2022-08-25 Published:2022-08-02
Supported by:
This research was supported by the National Science Foundation of China under Grant No. 61473126 and the Fundamental Research Funds for the Central Universities

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FENG Xiaodan, ZHANG Zhifei. Boundary Control of Coupled Wave Systems with Spatially-Varying Coefficients[J]. Journal of Systems Science and Complexity, 2022, 35(4): 1310-1329.

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.

Key words: Backstepping, boundary control, coupled wave systems, exponential stabilization, spatiallyvarying coefficients

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