Stability analysis for a class of switched systems under perturbations with applications to consensus

Abstract

This study investigates the stability problem for a class of discrete-time switched systems with stochastic or non-stochastic perturbations. Under the condition that the system matrix is weakly periodic and Hurwitz constrained, we firstly give stability analysis of the system with bounded or (exponentially) convergent perturbations. Then, for the system with perturbations containing stochastic noises, which are subject to a martingale-difference assumption, we give mean square (m.s.) and almost sure (a.s.) convergence results. Both multiplicative noises and additive noises are discussed in this paper. As applications of the stability result, we give m.s. and a.s. consensus conditions for both multi-agent systems (MASs) with relative-state-dependent noises and MASs with additive noises under the weakly periodic switching topology together with a Hurwitz constraint. Compared to the existing consensus results, we do not require the digraphs be balanced and the edge weights be non-negative. We also give a more general form of the statistic properties of the final consensus point compared with the balanced switching topology case. Some examples are given to illustrate the effectiveness of the stability results and the consensus results.