Consensus of Switched Linear Multi-agent Systems Under Arbitrary Switching Signal

This paper studies the consensus problem of homogeneous multi-agent systems (MASs), in which each agent is governed by the switched linear dynamics. It is assumed that the switching between the subsystems of the agents is arbitrary, and the communication topology contains a directed spanning tree. By utilizing the incidence matrix of a directed spanning tree to construct a transformation matrix, we make an equivalent transformation from the globally uniformly asymptotic consensus problem of the MAS to the globally uniformly asymptotic stability (GUAS) problem of a switched linear system. Then we derive some linear matrix inequalities (LMIs) based sufficient conditions for ensuring the globally uniformly asymptotic consensus of the MAS, by employing the common Lyapunov function method. Furthermore, the agent agreed state value is also developed. We finally give several numerical examples to verify the correctness of the theoretical results.