Leader-Following consensus of nonlinear multi-agent systems with hybrid delays: Distributed impulsive pinning strategy

The leader-following consensus problem of a type of nonlinear multi-agent systems with both general time-varying delay and distributed time-varying delay is investigated in this paper. To realize the global and exponential consensus, a kind of effective distributed impulsive pinning control strategy is proposed. Adequate conditions are derived to assure the consensus by applying the average impulsive interval, the comparison principle with hybrid time-varying delays, and the method of parametric variation. Considering that the impulse could not only be beneficial but also be adverse to the final consensus, the positive and negative impulsive effects are studied in detail, respectively, and the larger ranges of impulsive effects are obtained. Correspondingly, by considering the impulsive effects in different situations, different convergence rates are accurately calculated. In addition, the validity of the control strategy proposed in this paper is verified based on the simulation examples.