Leader-following consensus for second-order multi-agent systems with directed switching topologies

This paper studies the leader-following consensus problem for second-order multi-agent systems with nonlinear dynamics and time-varying coupling delay. To be more practical we consider general network whose coupling topology is directed and arbitrarily switching among a finite set of topologies. Based on the common Lyapunov theory and combining with linear matrix inequality (LMI) approach, we give a class of sufficient leader-following consensus criterion under the assumption that the topology among the followers is balanced and there is a directed path from the leader to each follower. Moreover, the derivative of the time-varying communication delay is not required to be less than 1 in this paper.