Event-triggered tracking control for heterogeneous multi-agent systems with Markov communication delays

In this paper, we investigate the consensus problem of a set of discrete-time heterogeneous multi-agent systems with random communication delays represented by a Markov chain, where the multi-agent systems are composed of two kinds of agents differed by their dynamics. First, distributed consensus control is designed by employing the event-triggered communication technique, which can lead to a significant reduction of the information communication burden in the multi-agent network. Then, the mean square stability of the closed loop multi-agent systems is analyzed based on the Lyapunov functional method and the Kronecker product technique. Sufficient conditions are obtained to guarantee the consensus in terms of linear matrix inequalities (LMIs). Finally, a simulation example is given to illustrate the effectiveness of the developed theory.