中文摘要：

研究了一类具有脉冲效应和时变时滞的灰色随机系统的鲁棒稳定性问题。在给出了脉冲随机泛函微分系统随机稳定性的条件的基础上,首先利用Lyapunov-KrasoVskii泛函法和灰矩阵的连续矩阵覆盖的分解技术,得到了具有脉冲效应和时变时滞的灰色随机系统的随机鲁棒稳定性判据,进而基于所得的这个随机鲁棒稳定性判据和Dini导数,给出了该系统指数鲁棒稳定性的判据。实例表明,所得判据是有效的和实用的。

英文摘要：

In this paper, we study the robust stability for a class of grey stochastic systems with impulsive effect and time-varying delay. Based on the stochastic stability condition of impulsive stochastic functional differential systems presented by this paper, we first deduce a criterion of stochastic robust stability for such a system by using the Lyapunov-Krasovskii flmctional method and the decomposition technique of continuous matrix-covered sets of grey matrix. Then by using the obtained criterion of stochastic robust stability and Dini derivative, we give an exponential robust stability criterion for such a system. The effectiveness and practicality of the presented criteria is confirmed by a numerical example.