Controllability and Stabilizability Analysis of Signed Consensus Networks

Signed networks have been a topic of recent interest in the network control community as they allow studying antagonistic interactions in multi-agent systems. Although dynamical characteristics of signed networks have been well-studied, notions such as controllability and stabilizability for signed networks for protocols such as consensus are missing in the literature. Classically, graph automorphisms with respect to the input nodes have been used to characterize uncontrollability of consensus networks. In this paper, we show that in addition to the graph symmetry, the topological property of structural balance facilitates the derivation of analogous sufficient conditions for uncontrollability for signed networks. In particular, we provide an analysis which shows that a gauge transformation induced by structural balance allows symmetry arguments to hold for signed consensus networks. Lastly, we use fractional automorphisms to extend our observations to output controllability and stabilizability of signed networks.