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Impulsive Time Window Based Quasi-Consensus on Stochastic Nonlinear Multi-Agent Systems

This paper investigates the global and exponential quasi-consensus for a kind of nonlinear multi-agent systems with time-varying delay and stochastic disturbance. In light of the significant difficulty to precisely determine the impulsive sequence in advance, the conception of impulsive time window is introduced. Correspondingly, the discrete Lyapunov function method is utilized to deal with the divided impulsive intervals caused by the impulsive time window. An effective distributed impulsive pinning (DIP) control strategy is proposed, which could economize the control execution time and save the energy consumption. Sufficient conditions for quasi-consensus are derived based on the parametric variation method and the extended delayed comparison principle. Additionally, the range of impulsive effects is further discussed by taking the positive and negative roles into consideration, respectively. Furthermore, the convergence rates and the consensus error levels corresponding to different impulsive effects are calculated accurately. At last, the rationality of the main results is illustrated clearly by some numerical examples.