Stochastic bipartite consensus of discrete-time multi-agent systems with random link failure over signed graph

This paper investigates the stochastic bipartite consensus problem for discrete-time multi-agent systems in the presence of antagonistic interactions, noise and random link failure. First of all, we define mean square bipartite consensus and almost sure bipartite consensus for multi-agent systems with the help of stochastic theory, matrix theory and algebraic graph theory. Second, we design a cooperative protocol for stochastic bipartite consensus based on the neighbors' information on signed directed graph. Third, for the case that communication graph Gm has a directed spanning tree and is structurally balanced, stochastic bipartite consensus can be achieved for discrete-time multi-agent systems. Finally, an example is given to support our result.