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Journal Articles Automatica Year : 2023

Input-to-state stability analysis of heat equation with boundary finite-time control

Abstract

This paper addresses the problem of input-to-state stabilization for heat equation with external input via boundary control strategy. Following [29], based on the backstepping approach, a switching boundary control law depending on the system state is designed. By estimating the upper bound of kernel functions, switching levels are determined and commutation law is further constructed. For the chosen switched control, the well-posedness property is verified. It is proved that the resulting system is input-to-state stable, and the solutions of the system will not exceed the highest admissible level dependent on the disturbance amplitude. Meanwhile, a stronger result is also obtained, that is the finite-time stability for the disturbance-free system. The numerical example is provided to support the derived result.
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Dates and versions

hal-04268174 , version 1 (02-11-2023)

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  • HAL Id : hal-04268174 , version 1

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Xin-Xin Han, Denis Efimov, Andrey Polyakov, Kai-Ning Wu. Input-to-state stability analysis of heat equation with boundary finite-time control. Automatica, inPress. ⟨hal-04268174⟩
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