Topology-based Conditions for Multiconsensus under the Signed Friedkin-Johnsen Model

Abstract: In this paper, we address the multiconsensus problem in networked systems, where agents are partitioned into disjoint subgroups and the states of agents within a subgroup are driven to consensus. Our objective is to present a distributed control law that leads to multiconsensus in signed digraphs. To this end, we examine the convergence of opinions under the opposing rule-based signed Friedkin-Johnsen (SFJ) model and present conditions that lead to multiconsensus under this model. Interestingly, the proposed conditions depend only on graph topology and signed interactions and not on the edge weights of the network. Consequently, the proposed SFJ-based control law relaxes the in-degree balance and homogeneity of trust-distrust, frequently assumed in the literature. Finally, we add simulation results to demonstrate the proposed conditions for multiconsensus.