The Bipartite Consensus for Multi-Agent Systems With Matrix-Weight-Based Signed Network

This brief focuses on the consensus problem of multi-agent systems (MASs) consisting of friends and enemies in a matrix-weight-based signed topological network. To highlight the effects of matrix coupling, we analyze the integrator model in a competitive-cooperative coexistence network. Unlike scalar-weight-based topological networks, the phenomenon of clustering in matrix-weight-based networks naturally exists, which means the important role of matrix coupling in convergence. Hence, different form existing results, depending on matrix coupling, the research shows bipartite consensus can be achieved in an unbalanced situation. Algebraic conditions are proposed for achieving a bipartite consensus and our results on structural unbalanced graph are shown to be more universality. Finally, some simulation results are given to vindicate the analysis.