Consensus seeking in second-order multi-agent systems with relative-state-dependent noises*

This paper studies the consensus problem of second-order discrete-time multi-agent systems with relative-state-dependent (RSD) noises. Firstly, for a fixed topology having a spanning tree, it is proved that the mean square (m.s.) and almost sure (a.s.) consensus can be guaranteed with small but constant distributed control gains. Then, if all digraphs in a switching topology are strongly connected and the corresponding Laplacian matrices have a common left eigenvector for zero eigenvalue, the m.s. and a.s. consensus can also be achieved for an arbitrary switching sequence with some constant gains. We also analyze the statistic properties of the final consensus points. Numerical examples are presented to illustrate the effectiveness of the results.