Consensus of discrete multi-agent systems under switching topologies

In this paper, we consider a multi-agent consensus problem with discrete-time high-dimensional linear coupling dynamics. The interaction topology among the agents is assumed to be switching and undirected. To achieve consensus, a neighbor-based feedback protocol is proposed for each agent. By using Schur orthogonal transformation, the multi-agent consensus problem is converted into stability problem of a switching subsystem with special structure. Based on graph theory and common Lyapunov function method, some sufficient consensus conditions are established for the considered multi-agent systems. Moreover, we provide Riccati and linear matrix inequality based approaches to obtain feedback matrix. Finally, a simulation example is given to illustrate our obtained theoretical result.