Event triggered control and exponential stability for infinite dimensional linear systems $\star$

TL;DR

This paper develops a unified framework for event-triggered control of infinite dimensional linear systems, ensuring exponential stability and avoiding Zeno behavior through Lyapunov methods.

Contribution

It introduces a novel event-triggering mechanism for infinite dimensional systems that preserves exponential stability using Lyapunov functionals.

Findings

Proves exponential stability under event-triggered control

Establishes existence and regularity of solutions

Ensures avoidance of Zeno behavior

Abstract

This article aims at providing a unified analysis of the exponential stabilization of some abstract infinite dimensional systems undergoing an event-triggering mechanism that samples the control input. The partial differential equation is supposed to be defined by a skew-adjoint operator and controlled and observed through bounded operators. The continuously controlled closed loop system is assumed to be exponentially stable and the goal is to prove that a well-designed event-triggering mechanism to rule the time updates of the sampled control will allow to keep such a stability property. The key of the proof relies on the existence of an adequate Lyapunov functional. Existence and regularity of the solution to the closed-loop event-triggered system are also proven, along with the avoidance of Zeno behavior.