Stability of impulsive stochastic nonlinear systems involving random delays

This article is dedicated to investigation of the stability for impulsive stochastic nonlinear systems involving random delays. By utilizing the stochastic analysis approach together with impulsive delayed differential inequality, we obtain some novel criteria of global weak stochastic exponential stability for addressed systems. Different from the majority of previous works that focused on the constant/time-dependent delay, delay in the continuous dynamical system is state-dependent, which is in fact a random variable for any fixed time and its range is exactly unknown. Additionally, delays in impulses depend on the integral of a piecewise continuous and sign-changing function over the interval between two adjacent impulse instants and they can be flexible enough, i.e., sufficiently large or small. Finally, two numerical examples with simulations are given to support the usefulness and the novelty of the derived results.