Stability of stochastic time-delay systems involving delayed impulses?

In this paper, the pth moment exponential stability is investigated for impulsive stochastic time-delay systems (STDS) with random impulsive delay. A novel concept of average random delay in impulses is introduced to deal with the pth moment exponential stability of STDS, which provides a new idea for the study of the stochastic delay in impulses from a holistic perspective. Considering the impulsive effect, the destabilizing and stabilizing delayed impulses are studied, respectively. It is revealed that the random delay in impulses plays a significant role on the stability of the system, which may not only destabilize a stable system but also stabilize an unstable system. In particular, our results allow the delays in continuous dynamics and impulsive dynamics to exceed the length of the impulsive interval, which are more general than previous results. Finally, some numerical simulations are presented to illustrate our proposed results.(c) 2023 Elsevier Ltd. All rights reserved.