Behaviors of matrix-weighted networks with antagonistic interactions

This essay considers the bipartite consensus of matrix-weighted second-order multi-agent systems with structurally unbalanced antagonistic interactions networks. Owing to the influence of matrix -weights, bipartite consensus and cluster bipartite consensus can also be reached, which is different from the existing works on signed networks. With the assistance of Lyapunov stability and matrix -valued Gauge transformation, a condition to achieve bipartite consensus is established. Moreover, a relatively straightforward algebraic graph condition for reaching cluster bipartite consensus is attained. Finally, simulation examples are supplied to illustrate the obtained results.