Structural Controllability of Directed Signed Networks

In this article, the structural controllability of multiagent networks defined over directed signed graphs is investigated, where the agents are divided into leaders and followers, and only leaders are manipulated by the external control input directly. The communication digraph contains positive and negative edges, which represent cooperative and antagonistic interactions between agents, respectively. First, a graph-theoretic necessary and sufficient condition for structural controllability of multiagent networks is derived, that is, a multiagent network is structurally controllable if and only if the communication digraph is leader–follower connected. Next, the minimal controllability problem is studied. It is shown that the minimal controllability problem is solvable, and a method of polynomial complexity to accomplish minimal structural controllability is developed. In addition, the structural controllability of specified Cartesian product networks is discussed and a necessary and sufficient condition concerning the factor networks for the structural controllability is established. The application of the theoretical results is demonstrated by several practical examples.