On the stochastic finite (fixed)‐time stability for a class of stochastic nonlinear delayed systems

Abstract By developing a new approach and technology, we obtain several novel stochastic finite‐time stability (SFTS) criteria for a class of stochastic nonlinear delayed systems (SNDSs). Meanwhile, we find that when the noise term satisfies certain conditions, the stochastic nonlinear delayed system corresponding to an unstable deterministic time‐delay system is SFTS and stochastic fixed‐time stable (SFxTS). Besides, we also obtain some estimates for the stochastic settling time. Two numerical examples are provided to clarify this interesting phenomenon.