Event-triggering mechanism to damp the linear wave equation

TL;DR

This paper introduces an event-triggering mechanism for the wave equation that ensures stability and avoids Zeno behavior, with theoretical conditions and numerical validation.

Contribution

It provides a novel matrix inequality condition for global exponential stability of wave equations with event-triggered damping.

Findings

Global exponential stability under the proposed mechanism

Avoidance of Zeno behavior with regular initial data

Numerical simulations demonstrating effectiveness

Abstract

This paper aims at proposing a sufficient matrix inequality condition to carry out the global exponential stability of the wave equation under an event-triggering mechanism that updates a damping source term. The damping is distributed in the whole space but sampled in time. The wellposedness of the closed-loop event-triggered control system is shown. Furthermore, the avoidance of Zeno behavior is ensured provided that the initial data are more regular. The interest of the results is drawn through some numerical simulations.