Event-Triggered Impulsive Control of Nonlinear Stochastic Systems With Exogenous Disturbances

In this work, the stability problem of nonlinear stochastic systems is investigated under exogenous disturbances through event-triggered impulsive control (ETIC). The ETIC strategy proposed in this paper incorporates three levels of events, taking into account four indicators: threshold, control-free index, inspection interval, and waiting time for stochastic systems, which is more practically significant and can effectively eliminate the Zeno behavior. By utilizing Lyapunov stability theory, stochastic analysis techniques, and some fundamental inequalities, sufficient conditions for the $r\text{th}$ moment input-to-state stability ($r$-ISS) and exponentially $r$-ISS of the considered system can be achieved through the implementation of the designed ETIC. Then, the theoretical results are employed in actual nonlinear stochastic systems, leading to the establishment of LMI-based criteria for exponential $r$-ISS. Ultimately, the feasibility of ETIC strategy is confirmed through two instances.