H ∞ Dynamic Output Feedback Consensus Control for Discrete-Time Multi-Agent Systems with Switching Topology

Abstract

In this paper, we consider distributed H∞ consensus problem for multi-agent systems with discrete-time high-dimensional linear coupling dynamics subjected to external disturbances. The interaction topology among the agents is assumed to be switching and undirected. To achieve consensus, a neighbor-based dynamic output feedback protocol is proposed for each agent. By using Schur orthogonal transformation, the considered multi-agent H∞ consensus control problem is converted into H∞ control problem of a discrete-time switching subsystem. Based on graph theory and common Lyapunov function method, a sufficient condition in terms of linear matrix inequalities is established to solve H∞ consensus problem of the considered multi-agent systems. Moreover, the feedback gain matrix can be obtained from the feasible solution to the linear matrix inequalities. Finally, a simulation example is given to illustrate our established theoretical result.