ℋ∞ Consensus for Discrete-time Multi-agent Systems Subject to Distributed Delay and Switching Topologies

Abstract

This paper is concerned with the issue of weighted ${\mathcal{H}_\infty }$ consensus for discrete-time multi-agent systems with time-varying delay and switching topologies. The objective is designing a dynamic output feedback protocol in the presence of external perturbations such that the system achieves consensus in mean square and has a prescribed ${\mathcal{H}_\infty }$ performance level. Firstly, the ${\mathcal{H}_\infty }$ consensus design is converted to a standard ${\mathcal{H}_\infty }$ control problem by reconstructing the closed-loop system as a reduced-order system. Then, by means of the multiple Lyapunov-Krasovskii functional method, the delay-dependent bounded real lemma is derived to guarantee the stability of closed-loop system. Based on these, sufficient conditions for the existence of the required dynamic output feedback protocol is developed in the form of a series of solvable linear matrix inequalities. Finally, numerical example and simulation results are given to illustrate the effectiveness of the obtained results.