Stability Analysis of Infinite-dimensional Event-triggered and Self-triggered Control Systems with Lipschitz Perturbations

TL;DR

This paper investigates the stability of infinite-dimensional control systems under event/self-triggered mechanisms with Lipschitz perturbations, providing conditions for stability in both bounded and unbounded control operator cases.

Contribution

It offers new stability conditions for infinite-dimensional systems with Lipschitz perturbations, including cases with unbounded control operators and periodic event-triggering.

Findings

Exponential stability under bounded control operators with appropriate event mechanisms.

Stability results for unbounded control operators with periodic event-triggering.

Guarantees strict positive inter-event times and solution existence under Lipschitz perturbations.

Abstract

This paper addresses the following question: "Suppose that a state-feedback controller stabilizes an infinite-dimensional linear continuous-time system. If we choose the parameters of an event/self-triggering mechanism appropriately, is the event/self-triggered control system stable under all sufficiently small nonlinear Lipschitz perturbations?" We assume that the stabilizing feedback operator is compact. This assumption is used to guarantee the strict positiveness of inter-event times and the existence of the mild solution of evolution equations with unbounded control operators. First, for the case where the control operator is bounded, we show that the answer to the above question is positive, giving a sufficient condition for exponential stability, which can be employed for the design of event/self-triggering mechanisms. Next, we investigate the case where the control operator is unbounded and prove that the answer is still positive for periodic event-triggering mechanisms.