${ {\mathcal H} }_{\infty }$ couple-group consensus of stochastic multi-agent systems with fixed and Markovian switching communication topologies

Abstract

The paper addresses the issue of couple-group consensus for a class of discrete-time stochastic multi-agent systems via output-feedback control. Both fixed and Markovian switching communication topologies are considered. By employing linear transformations, the closed-loop systems are converted into reduced-order systems and the couple-group consensus issue under consideration is changed into a stochastic control problem. New conditions for the mean-square asymptotic stability and performance of the reduced-order systems are proposed. On the basis of these conditions, constructive approaches for the design of the output-feedback control protocols are developed for the fixed communication topology and the Markovian switching communication topologies, respectively. Finally, two numerical examples are given to illustrate the applicability of the present design approaches.