Target Controllability of Multiagent Systems under Directed Weighted Topology

In this paper, the target controllability of multiagent systems under directed weighted topology is studied. A graph partition is constructed, in which part of the nodes are divided into different cells, which are selected as leaders. The remaining nodes are divided by maximum equitable partition. By taking the advantage of reachable nodes and the graph partition, we provide a necessary and sufficient condition for the target controllability of a first-order multiagent system. It is shown that the system is target controllable if and only if each cell contains no more than one target node and there are no unreachable target nodes, with $\delta-$reachable nodes belonging to the same cell in the above graph partition. By means of controllability decomposition, a necessary and sufficient condition for the target controllability of the system is given, as well as a target node selection method to ensure the target controllability. In a high-order multiagent system, once the topology, leaders, and target nodes are fixed, the target controllability of the high-order multiagent system is shown to be the same to the first-order one. This paper also considers a general linear system. If there is an independent strongly connected component that contains only target nodes and the general linear system is target controllable, then graph $\mathcal{G}$ is leader-target follower connected.