Event-triggered damping stabilization of a linear wave equation

Lucie Baudouin; Swann Marx; Sophie Tarbouriech

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arXiv · 1901.01009

Event-triggered damping stabilization of a linear wave equation

Lucie Baudouin·Swann Marx·Sophie Tarbouriech

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Abstract

The paper addresses the design of an event-triggering mechanism for a partial differential wave equation posed in a bounded domain. The wave equation is supposed to be controlled through a first order time derivative term distributed in the whole domain. Sufficient conditions based on the use of suitable Lyapunov functional are proposed to guarantee that an event-triggered distributed control still ensures the exponential stability of the closed-loop system. Moreover, the designed event-triggering mechanism allows to avoid the Zeno behavior. The 'existence and regularity' prerequisite properties of solutions for the closed loop system are also proven.

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Lucie Baudouin, Swann Marx, Sophie Tarbouriech. 2019-01-04. Event-triggered damping stabilization of a linear wave equation. https://arxiv.org/abs/1901.01009

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