Mean Square Average Consensus of Multi-Agent Systems Under Matrix-Valued Weighted Topologies

Abstract

In this paper, average-consensus problem of multi-agent systems with measurement noise is studied under matrix-valued weighted topologies. To reduce the interference of noise, a time-varying control gain is introduced, and then a distributed protocol is proposed for each agent. With the help of Lyapunov function the closed-loop system is analyzed and sufficient conditions for ensuring unbiased mean square average-consensus under matrix-valued weighted topologies are given. It is proven that the state of each agent converges in mean square sense to a common Gaussian random vector, whose mathematical expectation is the mean of the initial states of all agents. In particular, the matrix-valued weighted topology here is always supposed to be balanced, which plays a vital role in achieving mean square average consensus.