Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays
Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays
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DOI：
10.1109/tac.2010.2046114
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发表时间：
2010-03
影响因子：
6.8
通讯作者：
Zidong Wang;Yurong Liu;Xiaohui Liu
中科院分区：
文献类型：
--
作者：
Zidong Wang;Yurong Liu;Xiaohui Liu
本文研究了一类具有马尔可夫跳变参数和混合时滞的随机系统的全局指数镇定问题。混合模式相关时滞包括离散时滞和分布时滞。我们的目标是设计一个无记忆状态反馈控制器，使闭环系统在均方意义下是随机指数稳定的。首先，通过引入一个新的Lyapunov-Krasovskii功能，占模式依赖的混合时滞，随机分析进行，以获得一个标准的指数稳定性问题。然后，这样的标准的变化，以方便控制器的设计，通过使用线性矩阵不等式（LMI）的方法。最后，它表明，所需的状态反馈控制器可以明确的特点是在一组LMI的解决方案。数值仿真验证了所提方法的有效性。
In this technical note, the globally exponential stabilization problem is investigated for a general class of stochastic systems with both Markovian jumping parameters and mixed time-delays. The mixed mode-dependent time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. First, by introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem. Then, a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality (LMI) approach. Finally, it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of LMIs. Numerical simulation is carried out to demonstrate the effectiveness of the proposed methods.