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arXiv · 2303.00381

Event-triggered boundary damping of a linear wave equation

Lucie Baudouin·Swann Marx·Sophie Tarbouriech·Julie Valein
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Abstract

This article presents an analysis of the stabilization of a multidimensional partial differential wave equation under a well designed event-triggering mechanism that samples the boundary control input. The wave equation is set in a bounded domain and the control is performed through a boundary classical damping term, where the Neumann boundary condition is made proportional to the velocity. First of all, existence and regularity of the solution to the closed-loop system under the event-triggering mechanism of the control are proven. Then, sufficient conditions based on the use of a specific Lyapunov functional are proposed in order to ensure that the solutions converge into a compact set containing the origin, that can be tuned by the designer. Furthermore, as expected, any Zeno behavior of the closed-loop system is avoided.

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Lucie Baudouin, Swann Marx, Sophie Tarbouriech, Julie Valein. 2023-03-01. Event-triggered boundary damping of a linear wave equation. https://arxiv.org/abs/2303.00381

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