Leader–Follower Consensus Problems of Multi-agent Systems with Noise Perturbation and Time Delays

In light of the stability theory for stochastic differential delay equations, the leader–follower consensus problem with noise perturbation and communication time delays is investigated. Communication among agents is modelled as a weighted directed graph and the weights are stochastically perturbed with white noise. It is analytically proven 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