Mean-square Consensus Condition for Linear Multi-agent Systems Over Random Delay Network

This paper studies the mean-square consensus problem for linear discrete-time multi-agent systems over random delay network. The channel is assumed to be symmetric and identical, and each agent adopts a convex local consensus protocol. Based on the mean-square small gain theorem, the mean-square consensus condition, both sufficient and necessary, for the multi-agent system is proposed, which results in a simultaneous performance problem. Two numerical examples are illustrated to verify the proposed results.