Multi-agent controllability with tree topology

This paper focuses on the controllability of multiagent systems with tree topology. The connection on controllability/uncontrollability between a single leader and multiple leaders is revealed, as well as the relationship between controllability and the common eigenvalues of components is analyzed. After that, a constructive approach is outlined to find out various uncontrollable subgraphs when the whole interconnection tree graph is uncontrollable, and a necessary and sufficient condition is presented for multi-agent controllability with tree topology.