Mean Square Bipartite Consensus for Multiagent Systems With Antagonistic Information and Time-Varying Topologies

We consider the discrete-time distributed bipartite-consensus problem for multiagent systems subject to measurement noises and time-varying random networks, where the information exchange among the agents can be antagonistic and disturbed by both multiplicative and additive noises. The antagonistic information is characterized by a signed random graph. The main challenge is that the coexistence of multiplicative noise and antagonistic information does not allow the multiplicative noise term to be converted into an error equation. Based on the semi-decomposition method and Lyapunov-based technique, we derive sufficient conditions for stochastic approximation step size to assure the mean square bipartite consensus. Moreover, the convergence rate of the consensus error is explicitly formulated, which is tightly linked to the step size and the eigenvalues of the Laplacian matrix. Finally, we verify the main results via a numerical example.