Mean Square Bipartite Consensus for Multi-agent Systems with Measurement Noises and Communication Time-delays

This paper investigates the mean square bipartite consensus problem of a multi-agent system with considering measurement noises and communication time-delays. And the interaction topology of the multi-agent system (MAS) is a signed digraph. The convergence of the proposed bipartite consensus protocol with both noisy measurements and uniform communication time-delays is analyzed. Sufficient conditions on the upper bound of the time-delays are first derived to guarantee the mean square bipartite consensus for the signed digraph which is structurally balanced and has a spanning tree. Then for the signed digraph which is structurally unbalanced and strongly connected, the states of all agents achieve zero in the mean square sense under the given conditions. Finally, numerical simulation examples are provided to illustrate the obtained theoretical results.