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

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 A novel consensus protocol based on outdated states is proposed for multi‐agent systems.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.