Leader-following consensus with directed switching topologies

This paper studies the leader-following consensus problem of multi-agent systems with directed switching topologies. Some algebraic properties for a kind of digraph are derived firstly. With the assumption that all the agents are jointly linked to the considered leader across the time interval with some given length, a sufficient condition is given to make all the agents follow the considered leader by means of matrix theory and algebraic graph theory. A simulation example is given to illustrate the theoretical results.