Controllability and Stabilizability Analysis of Signed Consensus Networks

TL;DR

This paper investigates how structural balance and graph symmetries influence the controllability and stabilizability of signed consensus networks, extending classical graph automorphism concepts to signed systems.

Contribution

It introduces the use of structural balance and gauge transformations to analyze controllability and stabilizability in signed networks, filling a gap in existing literature.

Findings

Structural balance facilitates controllability analysis in signed networks.

Gauge transformations enable symmetry-based controllability conditions.

Fractional automorphisms extend analysis to output controllability and stabilizability.

Abstract

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.