Topologies construction and leaders location in multi-agent controllability

It is known that multi-agent controllability relies not only on the topology structures of communication graph but also on the location of leaders. In the paper, we study topologies construction and leaders location for multi-agent controllability based on consensus algorithm. First, topologies are designed by two constructive approaches. The results on the topologies are expressed in terms of necessary conditions. Then, connections between controllability and leaders location are presented regarding multiple eigenvalues. Finally, it is shown that leaders´ role is a determining factor for the controllability of a path graph. In all the developed results, leaders location is indicated clearly.