  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.
