Unified stability criteria for impulsive stochastic delayed systems

This paper investigates the $p$th moment exponential stability of impulsive stochastic delayed systems (ISDS). New stability criteria for ISDS are developed by applying the Razumikhin approach and a novel concept of average random impulsive estimation (ARIE). Stochastic impulsive strength, the time-varying delay in continuous dynamics, and the impulsive delay are considered simultaneously, and there are no imposed restrictions on their sizes. Utilizing ARIE, the proposed control scheme with stabilizing impulse can still ensure the stability of the whole system under the presence of impulsive perturbations at some impulsive instants, that is, it allows some impulsive intensities at impulsive instants are greater than 1 or a certain threshold which is more than 1. In addition, the requirement for the sign of time-derivative of Razumikhin function is also relaxed. Several illustrated examples are given to verify the effectiveness of our proposed results.