Controllability of discrete-time multiagent systems with switching topology

The current theoretical investigation on the controllability of switched multiagent systems mainly focuses on fixed connected topology or union graph without nonaccessible nodes. However, for discrete-time multiagent systems with switching topology, it is still unknown whether the existing results are valid or not under the condition of arbitrary topology. Based on graph distance partitions and Wonham's geometric approach, we provide the lower and upper bounds for the dimension of controllable subspaces of discrete-time multiagent systems. Unlike the existing results of controllability with switching topology, the proposed results have the advantage of being applicable to multiagent systems with arbitrary graphic topologies, union graph (strongly connected or not), and coupling weights. We also provide 2 algorithms for computing the lower and upper bounds for the dimension of controllable subspaces, respectively. Furthermore, as a remarkable application, we present how the proposed lower bound can be utilized for achieving the targeted controllability if the dimension of the controllable subspace of the switched system satisfies certain conditions.