Stabilization of stochastic systems: event-triggered impulsive control

This paper systematically establishes criteria for ensuring $r$-th moment asymptotic stability and $r$-th moment exponential stability in stochastic systems via an event-triggered impulsive control (ETIC) strategy, considering both scenarios with and without impulsive delay. By constructing appropriate Lyapunov functions and applying stochastic analysis methods, the intrinsic relationships among event-triggered parameters, impulsive control (IC) strength, and system stability are established. Moreover, this paper thoroughly investigates how the selection of event-triggered parameters, the length of the inspection interval, and the magnitude of impulsive delay influence the convergence rate of the system. Finally, two numerical examples are presented to verify the effectiveness of the proposed ETIC method, one of which focuses on the consensus problem of stochastic multi-agent systems.