Impulsive Consensus of Nonlinear Multi-Agent Systems with Hybrid Delays

The global and exponential consensus problem of a kind of nonlinear multi-agent systems is intensively investigated by applying a valid distributed impulsive pinning control strategy. Due to different kinds of information transmissions in some real networks and systems. In addition to the general time-varying delay, the distributed delay is also considered for the purpose of increasing the universality of the system model. Based on the theories of the parametric variation, the Lyapunov function method, the comparison principle with delay and the average impulsive interval, sufficient conditions for the global and exponential consensus of nonlinear multi-agent systems with hybrid time-varying delays are derived by considering the positive and negative impulsive effects, respectively. Correspondingly, different convergence rates are precisely calculated with thinking significantly different roles of the impulsive effects. Moreover, the sufficient rationality of the main theories are illustrated successfully according to some numerical examples.