Sampled-data leader-following consensus for nonlinear multi-agent systems with Markovian switching topologies and communication delay

This paper is concerned with sampled-data leader-following consensus of nonlinear multi-agent systems with random switching network topologies and communication delay. By modeling the switching of network topologies by a Markov process and considering the effect of communication delay, a new sampled-data consensus control protocol with variable sampling period is proposed. With this protocol, the leader-following consensus problem is equivalently converted to the stability of a class of Markovian jump systems with a time-varying delay. Then, by employing Lyapunov-Krosovskii functional method and the weak infinitesimal operation, a new delay-dependent stability criterion is derived, which ensures that the leader-following consensus can be globally exponentially achieved in mean-square sense. Based on this criterion, the switching consensus controller gains are obtained by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the design method.