Consensus of discrete multi-agent systems with multiplicative noises

In this paper, we consider the consensus problem of discrete multi-agent systems with multiplicative communication noises. Each agent can only receive information corrupted by noises from its neighbors. The intensities of these noises are dependent on the distance of neighbors' states. Under some mild assumptions of the noises and the structure of network, both fixed topology case and switching topology case are analyzed. By combining algebraic graph theory and martingale convergence theorem, sufficient conditions for mean square average consensus are given for both the cases. Further, it is shown that the consensus point is a random variable with bounded variance and its expectation is the average of the initial states. Two numerical examples are given to illustrate the effectiveness of our results.