Leader-following consensus control for linear multi-agents systems with switching directed topologies

This paper addresses the distributed leader-following consensus problem of multi-agent systems with general linear node dynamics and switching directed topologies. The possible underlying topologies consist of a null graph as well as several directed graphs with each of them containing a directed spanning trees with the leader being the root. A new kind of distributed controllers is constructed for each follower to guarantee that the states of the followers can track those of the leader asymptotically. By appropriately constructing a Lyapunov function and using tools from M-matrix theory, some sufficient conditions for achieving leader-following consensus are provided. Theoretical analysis is finally verified by performing numerical simulations.