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Controllability of Multiagent Networks With Antagonistic Interactions

This paper addresses the controllability of a class of antagonistic multiagent networks with both positive and negative edges. All the agents of the multiagent network run a consensus algorithm using a signed Laplacian. Based on the generalized equitable partition, we propose a graph-theoretic characterization of an upper bound on the controllable subspace. Then, we provide a necessary condition for the controllability of the system and give an algorithm to compute the partition. Furthermore, we prove that for a structurally balanced network, the controllability is equivalent to that of the corresponding all-positive network, if the leaders are chosen from the same vertex set. Several examples are given to illustrate these results.