Controllability of Multi-agent Systems with Multiple Leaders and Switching Topologies

This paper studies the controllability of multi-agent systems with multiple leaders and switching topologies. In this case, we introduce the concept of union graph and reveal that the multi-agent system with switching topologies is controllable if the corresponding system with union graph is controllable. Moreover, we obtain a necessary and sufficient condition for structural controllability of multi-agent systems with multiple leaders and switching topologies. With these conclusions respect to the union graph, some sufficient conditions for controllability of the switching multi-agent systems are shown based on the properties of controllability of multi-agent systems with fixed topology. Three computational tests and an application example are given to demonstrate the effectiveness and the practicability of the results.