Event-triggered boundary damping of a linear wave equation
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.
Keywords
Cite
@article{arxiv.2303.00381,
title = {Event-triggered boundary damping of a linear wave equation},
author = {Lucie Baudouin and Swann Marx and Sophie Tarbouriech and Julie Valein},
journal= {arXiv preprint arXiv:2303.00381},
year = {2023}
}