Exponential consensus of non‐linear multi‐agent systems with semi‐Markov switching topologies

Abstract

This study investigates the leader-following consensus problem for non-linear multi-agent systems with semi-Markov switching topologies. The dynamics of the leader agent and the follower agents is described by a general linear system. Since the transition rates of the semi-Markov switching topologies are time-varying, they are more general and practicable than the classic Markov switching topologies. A novel consensus protocol based on outdated states is proposed for multi-agent systems. By a system transformation, the consensus problem of multi-agent systems is converted into the stability problem of semi-Markov switching systems. The controller design condition is derived utilising the semi-Markov jump system theory and algebraic graph theory, which can guarantee that the multi-agent systems achieve a consensus with an exponential decay rate. A numerical example is given to illustrate the effectiveness of the proposed method.