Event-triggered impulsive control of delayed discrete-time stochastic systems with applications to complex network synchronization

This study investigates the stability properties of discrete-time nonlinear stochastic systems featuring time delays, subject to an event-triggered impulsive control strategy. To reduce redundant impulses in conventional periodic schemes, an event-triggered impulsive mechanism with checking intervals is proposed. Timer thresholds, free checking intervals, and a control-free criterion are used to determine impulsive instants, where early triggering, terminal safeguarding, and control-free skipping jointly balance necessary intervention and redundant impulsive executions; the resulting positive inter-event lower bound naturally excludes Zeno behavior. Based on the Lyapunov method and stochastic stability theory, sufficient criteria are established to guarantee asymptotic stability, finite-time stability, as well as finite-time contractive stability. Furthermore, the obtained results are utilized to address the synchronization problem of stochastic complex networks, where the control gains are determined by solving linear matrix inequalities. Finally, the effectiveness of the proposed approach is validated through two illustrative examples, namely, cooperative formation synchronization of multiple unmanned aerial vehicles and formation convergence of unmanned ground vehicles.