Controllability of diffusively-coupled multi-agent systems with general and distance regular coupling topologies

This paper studies the controllability of linearly diffusively coupled multi-agent systems when some agents, called leaders, are under the influence of external control inputs. We bound the system´s controllable subspace using combinatorial characteristics of some partitions of the graph describing the neighbor relationships between the agents. In particular, when such graphs are distance regular, we provide a full characterization of the controllable subspace for single leader cases while for multi-leader cases, a necessary condition and a sufficient condition for controllability are given respectively. In the end, we discuss how to choose leaders among the agents to guarantee controllability when the graphs are cycles or complete graphs, which are special subclasses of distance regular graphs.