Robust $H_{\infty}$ Asynchronous Consensus of Discrete-time Multi-Agent Systems Under Switching Topologies

In this paper, the problem of robust $H_{\infty}$ consensus is investigated for discrete-time multi-agent systems with external disturbances and time delay under switching topologies. Considering the asynchronous switching caused by the time delay of controller and topology switching, a weighted $H_{\infty}$ output feedback protocol is proposed. By transforming the model, the consensus problem of multi-agent systems is converted into the asymptotical stability of the reduced-order system. The average dwell time (ADT) method and Lyapunov-Krasovskii function method are used to solve the problems of asynchronous switching and time delay, and the sufficient conditions of the matrix inequality given by linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the proposed scheme.