Stochastic Bipartite Consensus for Multi-Agent Systems with Time-Delay and Antagonistic Information

In this paper, we investigate the stochastic bipartite consensus issue for continuous-time integrator multi-agent systems affected by communication noise with time-delays. Each agent's control input can only use it's own local state and adjacent states destroyed by white noise. In order to reduce the negative impact of communication noise on information transmission, we design a stochastic approximation protocol with time-varying gain. By combining the tools of algebraic graph theory and stochastic analysis, the convergence is analyzed, and some sufficient conditions for the mean square bipartite consensus by estimating the differential resolvent function for functional equations is given. Finally, the effectiveness of our results is demonstrated by a simulation.