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This paper studies the consensus problem of discrete-time single-integrator multi-agent systems (MASs) with relative-state-dependent (RSD) noises in possibly unbalanced switching networks. By using a time-varying quadratic Lyapunov function, we prove that the mean square and almost sure consensus of the single-integrator MASs with RSD noises can always be achieved by adopting a constant gain protocol if the switching network is uniformly strongly connected. We also give the statistic property of the convergent random variable with respect to the initial state of the system. Simulation results are given to verify the correctness of the consensus conclusion.

Consensus in possibly unbalanced switching networks with relative-state-dependent noises