# Event-triggered damping stabilization of a linear wave equation

## TL;DR

This paper develops an event-triggered control mechanism for a linear wave equation, ensuring exponential stability and avoiding Zeno behavior through Lyapunov-based conditions.

## Contribution

It introduces a novel event-triggering scheme for PDE control that guarantees stability and regularity, advancing control strategies for wave equations.

## Key findings

- Ensures exponential stability of the controlled wave system.
- Prevents Zeno behavior in event-triggered control.
- Provides conditions for solution existence and regularity.

## 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.