Stability of Discrete-Time Impulsive Stochastic Systems With Hybrid Nondeterministic Delays

This paper is committed to the stability analysis of discrete-time impulsive stochastic systems involving hybrid non-deterministic delays. We develop several novel criteria of weakly globally stochastically exponential stability for the suggested systems by means of delayed inequality approach under impulsive disturbance and Razumikhin method under impulsive control, respectively. It should be highlighted that different from the majority works that focused on constant delays or time-dependent delays, time delays in both the discrete-time stochastic system and the impulses are non-deterministic. Such delays should be handled with some new techniques, thus potentially leading to certain theoretical difficulties. In addition, the connection among the system state, impulses, hybrid non-deterministic delays is specifically provided and it sufficiently qualifies the positive or negative behaviours of impulses as well as delays. Finally, two numerical examples are presented to show the usefulness and the novelty of the derived results.