New Results of Multi-Agent Controllability Under Equitable Partitions

This paper studies the controllability of leader-follower multi-agent systems under fixed topology. The relationship between controllability and information communication topologies is characterized by taking advantage of equitable partitions. Firstly, for one non-trivial cell taking leaders role, a graph theory method is proposed to determine the multi-agent controllability. Secondly, the controllability of undirected graphs consisting of four nodes is analyzed in detail, and the limitation of the equitable partition in controllability analysis is pointed out for the first time. Thirdly, the results of four-node graphs are extended to general topologies, by which, we reveal the relationship between the ranks of controllability matrix of the quotient graph and original graph. Finally, the effect of non-trivial cells on the controllable subspace is analyzed from the viewpoint of controllability matrix and eigenvector.