Exponential and input‐to‐state stability of the stochastic nonlinear systems with event‐triggered impulsive control

Abstract This paper studies the weakly exponential stability (WES), input‐to‐state stability (ISS), and stochastic input‐to‐state stability (SISS) of stochastic nonlinear systems through an event‐triggered impulsive control (ETIC) strategy. Two new Lyapunov‐based event‐triggered mechanisms (ETM) are designed for the stochastic nonlinear impulsive systems. According to ETIC and ETM, some sufficient conditions can be proposed to guarantee ES, ISS, and SISS in the framework of the Lyapunov approach. Due to the fact that impulses only happen when the events associated with the system state are triggered, it means that the generation of such impulses is not only random but also closely connected with the internal dynamic changes of the system and hence can reflect minor fluctuations or significant changes of state. Next, the flexible impulsive control strategies under the designed ETIC are provided. The examples are given to demonstrate the practicability and validity of the results in this paper.