Consensus in noisy environments with switching topology and time-varying delays

In this paper, the leader-following consensus problem of noise perturbed multi-agent systems with time-varying delays is investigated. We analyze two different cases of coupling topologies: fixed topology and switching topology. Based on the Lyapunov functional and combining with the linear matrix inequality (LMI) approach, it is analytically proved that the consensus could be achieved almost surely with the perturbation of noise and communication time delays. Furthermore, numerical examples are provided to illustrate the effectiveness of the theoretical results. The simulation results show that the speed of convergence in environments with relatively strong noise intensity is lower than that in environments with relatively weak noise intensity.