Stability Analysis of Stochastic Time‐Varying Systems Involving Unbounded Delay and Multiple Impulses

ABSTRACT This article mainly discusses th moment exponential stability for impulsive stochastic dynamical systems with unbounded delay. By utilizing the improved Lyapunov–Razumikhin approach together with the mode‐dependent average dwell time method, some novel criteria are obtained from the perspective of impulsive perturbation and impulsive control, which specifically provide the intrinsic connection among current state, unbounded delay and multiple impulses. Compared with some existing works, it should be highlighted that our results do not require the steady state behavior of both discrete system and continuous dynamical system. Finally, two numerical examples are presented to demonstrate the validity and the distinctiveness of derived results.