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

Lucie Baudouin; Sylvain Ervedoza

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arXiv · 2508.06144

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

Lucie Baudouin·Sylvain Ervedoza

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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.

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BibTeX RIS

Lucie Baudouin, Sylvain Ervedoza. 2025-08-08. Event triggered control and exponential stability for infinite dimensional linear systems $\star$. https://arxiv.org/abs/2508.06144

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