Consensus of discrete-time multi-agent systems with multiplicative uncertainties and delays

This paper studies the consensus problem of discrete-time single-integrator multi-agent systems with multiplicative uncertainties and bounded communication delays in switching networks. Some sufficient conditions for non-stochastic consensus are obtained by adopting the constant-gain protocol. For the case that the uncertainty is exponentially decaying (i.e. is $ O(\gamma ^k) $ O(γk) with $ \gamma \in (0,1) $ γ∈(0,1)), it is proved for any bounded delays, the consensus can be achieved if the switching topology is uniformly rooted. For the case that the uncertainty is polynomially decaying (i.e. is $ O( {\frac {1}{(1+k)^\mu }} ) $ O(1(1+k)μ) with $ \mu \gt 0 $ μ>0), under a precondition that the system state is bounded, a similar conclusion is also obtained. The convergence rate of the consensus protocol is quantified in terms of the decay rate of uncertainties. Simulation results are given to verify the correctness of the conclusion.