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 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 infinity 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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, the exponential stabilization problem of a heat-wave coupled system under boundary control and collocated observation is considered. Two kinds of feedback strategies, namely static negative proportional feedback and dynamic feedback, are designed. The exponential stabilities of the closed-loop systems under different feedbacks are verified using the Lyapunov function direct method. The H infinity robustness is further analyzed and related sufficient conditions are developed. Additionally, the closed-loop systems are discretized into semi-discrete systems using a new finite difference method, and the uniform exponential stabilities of the discrete systems are established using an approach paralleling the continuous counterpart.