Leader-Following Consensus of One-Sided Lipschitz Multi-Agent Systems with Delay and Stochastic Perturbation

This paper is concerned with the leader-following consensus of time-delay multi-agent systems (MASs) with stochastic perturbation over a directed network. Different from existing literature subject to the conventional Lipschitz condition, the one-sided Lipschitz nonlinear MASs with delay are discussed. First, to address the challenge, in combination with current and delay information, the composite control law is constructed. By employing the Lyapunov function and using the Itô formula, this proves that the followers can eventually track the leader. Second, in the presence of external disturbance, sufficient conditions are established for the H-infinity leader-following consensus of one-sided Lipschitz nonlinear stochastic MASs. Further, the method to handle the one-sided Lipschitz nonlinearities is directly applicable to the stochastic MASs with conventional Lipschitz nonlinear dynamics, and the corresponding results are easily obtained. Finally, the relationship between one-sided Lipschitz scalars and time-delay parameters are presented, and the simulation results are given to verify the theoretical algorithms.