Controllability decompositions of networked systems through quotient graphs

In this paper we study decentralized, networked systems whose interaction dynamics are given by a nearest-neighbor averaging rule. By letting one node in the network take on the role of a leader in the sense that this node provides the control input to the entire system, we can ask questions concerning the controllability. In particular, we show that the controllable subspaces associated with such systems have a direct, graph theoretic interpretation in terms of so-called quotient graphs, providing us with a smaller, approximate bisimulation of the original network.