Controllability of fractional-order multi-agent systems with single leader

This paper proposes a new model of multi-agent systems with fractional-order and single leader, and investigates the controllability of fractional-order multi-agent systems with single leader based on undirected networks. It is shown that the controllability of fractional-order multi-agent systems with single leader depends on the information from the leader to followers. Some sufficiency and necessity results are obtained. Moreover, it is proved that the fractional-order multi-agent systems is controllable by PBH rank test. Finally, numerical examples are given to test the theoretical results.