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Convergence rate of leader-following consensus of networks of discrete-time linear agents in noisy environments

A mean square leader-following consensus protocol is proposed for discrete-time linear multi-agent systems with communication noises. To attenuate the noise's effect, a specific class of time-varying consensus gains are applied to the noise-corrupted relative states between agents. The distinguished feature of the proposed protocol is that each agent can have its own noise-attenuation gain. Both the steady-state performance and the transient performance of the closed-loop multi-agent system are analyzed. The convergence rates of the mathematical expectation and the second-moment of the leader-following consensus error are explicitly presented.