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. Each agent is allowed to have its own time-varying gain to attenuate the effect of communication noises. Therefore, the common assumption 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
$t^{-\beta}$

$(\beta\in(0,1))$
asymptotically, then the second-moment of the relative state between each follower agent and the leader agent is characterized by a function bounded above by
$t^{-\beta}$
asymptotically.