中文摘要：

该文基于随机线性二次控制问题，讨论了多时滞、且具有马尔可夫跳变参数的微分系统的最优控制的鲁棒性及可镇定问题．应用了Lyapunov—Krasovskii型的泛函、伊藤（Ito）公式、及Schur补等工具，分析了该随机多时滞、具有马尔可夫过程的微分系统的均方指数稳定性．得到了时滞相关与时滞无关的充分性的代数判据．

英文摘要：

This paper is based on the stochastic linear quadratic control problem. The robustness of stabilizability of optimal controller for stochastic multi-time delay systems with Markovian jumping parameters is investigated. Lyapunov-Krasovskii like functional, stochastic analysis, Ito formula and Schur complement are employed to analyze the exponential stability in mean square for stochastic multi-time delay differential systems with Markovian jumping parameters. The delay dependent and delay independent algebric criteria are established.