On Convergence Rate of Leader-Following Consensus of Linear Multi-Agent Systems with Communication Noises

This note further studies the previously proposed consensus protocol for linear multi-agent systems with communication noises in [15], [16]. Each agent is allowed to have its own time-varying gain to attenuate the effect of communication noises. Therefore, the common assumption in most references that all agents have the same noise-attenuation gain is not necessary. It has been proved that if all noise-attenuation gains are infinitesimal of the same order, then the mean square leader-following consensus can be reached. Furthermore, the convergence rate of the multi-agent system has been investigated. If the noise-attenuation gains belong to a class of functions which are bounded above and below by $t^{-β}$ $(β\in(0,1))$ asymptotically, then the states of all follower agents are convergent in mean square to the leader's state with the rate characterized by a function bounded above by $t^{-β}$ asymptotically.