Mean square averaging with relative-state-dependent measurement noises and linear noise intensity functions

In this paper, we consider the distributed averaging of high-dimensional first-order agents with relative-state-dependent measurement noises. Each agent can measure or receive its neighbors´ state information with random noises, whose intensity is a linear vector-valued function of agents´ relative states. By the tools of stochastic differential equations and algebraic graph theory, we give some necessary and sufficient conditions in terms of the control gain matrix, the noise intensity function and the network topology graph to ensure mean square average-consensus. Especially, for the case with independent and homogeneous channels, if the noise intensity grows with the rate σ, then 0 <; k <; N/[(N - 1)σ²] is a necessary and sufficient condition on the control gain k to ensure mean square average-consensus.