Exponentially weighted input-to-state stability of stochastic differential systems via event-triggered impulsive control

This paper investigates the stabilization of stochastic differential systems with exogenous disturbance inputs by employing an event-triggered impulsive control (ETIC) strategy. Firstly, an event-triggered mechanism (ETM) is put forward consisting of an exponentially decreasing function and exogenous disturbance terms. Moreover, through the incorporation of a state-dependent waiting time, Zeno phenomenon in the system can be completely avoided. Then sufficient conditions for exponentially weighted input-to-state stability (e(lambda l)-ISS) of systems can be obtained based on Lyapunov function method and Ito's formula under some reasonable criteria. Specifically, theoretical results establish a relationship between waiting time and trigger parameters. By altering the value of trigger parameters, it becomes feasible to adjust event-triggered time and control the frequency of activated impulses accordingly. In the end, two numerical examples are given to demonstrate the feasibility of devised ETIC strategy.