Stabilization of nonlinear stochastic systems via event-triggered impulsive control

This paper addresses the problem of stabilizing nonlinear stochastic systems using an event-triggered impulse mechanism (ETIM) and control theory. Sufficient criteria for achieving asymptotic stability (AS), finite-time stability (FTS), and finite-time contraction stability (FTCS) are obtained. In the ETIM, respectively, the timer threshold and free-control indexes are introduced to effectively prevent Zeno behavior and unnecessary impulses, thus conserving control resources. Furthermore, the impulse policy is formulated by considering both the current state and past information of the system, resulting in the generation of impulses that encompass both common and delay-dependent characteristics. The research findings reveal that the stability of the system is influenced by the stochastic system, impulse strength, time delay, and the ETIM. It is demonstrated that the impulse strength and the impulse sequence are the primary factors contributing to system stability, while time delay in impulse has a negative impact. The obtained criteria are applied to a stochastic network system, and the validity of the results is supported through illustrative examples and numerical simulations.