A graph theory based characterization of controllability for multi-agent systems with fixed topology

The paper studies a class of formation control problem, i.e. the controllability for multi-agent systems under leader-follower framework. A new concept leader-follower connectedness is proposed to deal with what is the desired extent of connectivity between the leader and follower subgraphs for a multi-agent system to be controllable. Analysis based on this concept yields graph theory based characterizations for the controllability of interconnection dynamic networks with fixed topologies.