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Consensus of discrete-time multi-agent systems with relative-state-dependent noises for a class of switching topology

This paper investigates the consensus problem of first-order discrete-time multi-agent systems with relative-state-dependent (RSD) measurement noises. Firstly, consensus is analyzed under a fixed topology and switching topology without noises. Then, under some assumptions of the noises and the structure of network, it is proved that, by giving a small distributed control gain, the weak consensus can be obtained for a class of switching topology satisfying the uniformly rooted and “period” assumption. A numerical example is given to illustrate the effectiveness of the result.