Finite‐time boundedness and stabilisation of switched linear systems using event‐triggered controllers

Abstract

This study proposes a systematic control design approach to consider jointly the event-triggered communication mechanism and state-feedback control for switched linear systems. The systems determine the necessary samplings of the feedback signal by constructing predefined events that can reduce redundant signal transmission and updates. Specifically, the first main step in the design is to construct sufficient conditions for stability analysis in the form of linear matrix inequalities to utilise fully the idea of average dwell time. With the proposed event-triggering mechanism, the design renders the resulting switched closed-loop system finite-time bounded. Subsequently, the authors present the conditions for finding the parameter of the event-triggered sampling mechanism and the state-feedback sub-controller gains. Then, the results for the full state feedback control case are further extended to systems incorporating observer-based state-feedback control motivated by practical applications. For each case, an estimate of the positive lower bound on the inter-execution times is further derived to avoid Zeno behaviour. A numerical example is presented to illustrate the effectiveness of the proposed methods.