Pinning consensus for multi‐agent systems with non‐linear dynamics and time‐varying delay under directed switching topology. Issue 17 (1st November 2014) - Wang, Yangling; Cao, Jinde; Hu, Jianqiang
Abstract : 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.