This paper investigates the exponential attracting sets of discrete-time Markovian jump delay systems (MJDSs) with stochastic disturbances (SDs) via impulsive control (IC). By virtue of the Lyapunov-Razumikhin technique, we derive several sufficient criteria on the pth moment exponential attracting sets of the impulsive controlled discrete-time MJDSs with SDs and the estimation of the attracting sets is also given. It is shown that IC could make both unbounded and bounded impulsive-free discrete-time MJDSs with SDs into the bounded ones. Examples are presented to illustrate the effectiveness of the proposed theoretical results.

中文翻译：

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通过脉冲控制吸引具有随机干扰的离散时间马尔可夫跳跃时滞系统

本文通过脉冲控制（IC）研究了具有随机扰动（SD）的离散时间马尔可夫跳跃延迟系统（MJDS）的指数吸引集。利用Lyapunov-Razumikhin技术，我们推导了带有SD的脉冲控制离散时间MJDS的p阶指数吸引集的几个充分判据，并且给出了吸引集的估计。结果表明，IC可以将带有SD的无界和有界的无脉冲离散时间MJDS都做成有界的。举例说明了所提出理论结果的有效性。