Pinning consensus for multi-agent systems with non-linear dynamics and time-varying delay under directed switching topology

This paper studies the leader-following consensus problem in directed networks of agents with non-linear dynamics and time-varying coupling delay by using the pinning control method. The main contribution of this study is that we obtain two classes of sufficient leader-following consensus criteria without assuming that the topology among followers is strongly connected or has a spanning tree, and without assuming that the derivative of the time-varying communication delay is less than 1. In addition, to be more practical we consider the general network whose coupling topology is arbitrarily switching among a finite set of topologies. Based on the common Lyapunov theory and linear matrix inequalities approach, we prove that the leader-following consensus problem can be solved only with the assumption that the topology among the followers has p (p > 1) and there is a directed path from the leader to each follower. Two examples are presented to show the applications of the criteria obtained in this study.