Consensus with relative-state-dependent noises in time-varying networks

This paper studies the consensus problem of discrete-time multi-agent systems with relative-state-dependent (RSD) measurement noises. Firstly, consensus is analyzed for noise-free systems under the switching topologies. Then, under a martingale-difference assumption on the noises, it is proved that, by giving a small distributed control gain, the mean square (m.s.) and almost sure (a.s.) consensus can be obtained for a class of switching topology satisfying the uniformly rooted (UR) and “period” assumption. Besides, a sufficient condition to guarantee the m.s. and a.s. consensus is given if the switching topology is UR and union-mode-finite (UMF). We also analyze the statistic properties of the final consensus point. Numerical examples are given to illustrate the effectiveness of the results.