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1887

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

© The Institution of Engineering and Technology
Received 17/12/2016, Accepted 26/01/2017, Published 07/02/2017

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.

Inspec keywords: mean square error methods; matrix algebra; topology; switching systems (control); convergence of numerical methods; multi-agent systems; perturbation techniques; stability

Other keywords: stochastic noises; multiagent systems; Hurwitz constraint; multiplicative noises; system matrix; MAS; relative-state-dependent noises; discrete-time switched systems; convergent perturbations; martingale-difference assumption; mean square convergence result; nonstochastic perturbations; bounded perturbations; stability analysis; additive noises; stochastic perturbations; almost sure convergence result; consensus conditions; weakly periodic switching topology

Subjects: Time-varying control systems; Interpolation and function approximation (numerical analysis); Linear algebra (numerical analysis); Combinatorial mathematics; Stability in control theory

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