研究了一类Markov切换的脉冲随机偏泛函微分方程的均方稳定性问题. 首先, 利用脉冲时滞微分不等式技巧和随机分析理论, 建立了一类Markov切换的脉冲随机偏泛函微分方程的比较原理. 然后, 应用比较原理得到了这类方程的几个新的稳定性判据. 最后, 通过实例验证了所提出的结果的有效性.

This paper investigates the mean square stability problem for a class of stochastic partial functional differential equations with Markovian switching. By employing impulsive delay differential inequality technique and stochastic analysis theory, comparison principle for a class of stochastic partial functional differential equations with Markovian switching is firstly established. Then, the comparison principle is applied to obtain several novel stability criteria of such equation. Finally, an example is provided to show the effectiveness of the proposed results.