Robust consensus of multi‐agent systems with multiplicative uncertainties and its application in time synchronization

Abstract This article first studies the robust consensus problem of discrete‐time single‐integrator multi‐agent systems (MASs) with multiplicative uncertainties in switching networks. Under the assumption that the uncertainty is polynomially decaying, we prove that the consensus of the MAS can be achieved by adopting the decaying gain protocol if the switching network is uniformly strongly connected (USC). The convergence rate is quantified in terms of the decay rate of uncertainties. Then, we use the consensus conclusion studying the convergence analysis problem of a typical time synchronization algorithm (the LSTS algorithm proposed in Tian [IEEE Trans Automat Contr. 2017;62(10):5445–5450]) in wireless sensor networks. We prove that the LSTS algorithm can still achieve the bounded time synchronization even if the switching network is USC, a more general topology condition compared with existing convergence results in Tian (IEEE Trans Automat Contr. 2017;62(10):5445–5450). Simulation results are given to verify the correctness of both the consensus conclusion for MASs and convergence conclusion for LSTS algorithm.