Stability analysis of infinite-dimensional event-triggered and self-triggered control systems with Lipschitz perturbations

Abstract

This paper addresses the following question: "Suppose that a state-feedback controller stabilizes an infinite-dimensional linear continuoustime 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.

Stability of Infinite-dimensional Sampled-data Systems with Unbounded Control Operators and Perturbations

“…For infinitedimensional systems, this type of robustness has been discussed in [13][14][15]. Robustness analysis with respect to perturbations has been also developed for infinitedimensional sampled-data systems in [16,17]. Bounded control operators and unbounded perturbations have been considered in [16], while unbounded control operators and bounded nonlinear perturbations have been dealt with [17,Lemma 4.5].…”

“…Hence we provide an alternative estimate by investigating the difference between the resolvents of the nominal generator and the perturbed generator. Therefore, the proposed approach is also different from the time-domain approach used in [17,Lemma 4.5] for bounded and nonlinear perturbations.…”