Stability and robust stabilization to linear stochastic systems described by differential equations with markovian jumping and multiplicative white noise
Stability and robust stabilization to linear stochastic systems described by differential equations with markovian jumping and multiplicative white noise
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DOI：
10.1081/sap-120002421
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发表时间：
2002-03
影响因子：
1.3
通讯作者：
V. Drăgan;T. Morozan
中科院分区：
文献类型：
--
作者：
V. Drăgan;T. Morozan
本文研究了同时受到白色噪声干扰和马尔可夫跳变的线性受控随机系统。我们的目的是提供一个数学背景，以统一的方法来解决一类与线性控制系统相关的问题，同时受到乘性白色噪声扰动和马尔可夫跳跃。首先证明一个伊藤型公式。本文的结果推广了文献[24]的结果，推广到随机过程x（t）的矩不全有界的情形。给出了一类带乘性白色噪声和马尔可夫跳变的线性随机系统零解均方指数稳定的充要条件。给出了仿射随机系统解的一些估计，并给出了随机可镇定和随机可检测的充要条件。证明了一个随机形式的有界真实的引理，并研究了一类带有乘性白色噪声和马尔可夫跳变的线性系统的状态反馈鲁棒镇定问题。
In this paper we consider linear controlled stochastic systems subjected both to white noise disturbance and Markovian jumping. Our aim is to provide a mathematical background in order to give unified approach for a large class of problems associated to linear controlled systems subjected both to multiplicative white noise perturbations and Markovian jumping. First we prove an Itô type formula. Our result extends the result of Ref. [24], to the case when the stochastic process x(t) has not all moments bounded. Necessary and sufficient conditions assuring the exponential stability in mean square for the zero solution of a linear stochastic system with multiplicative white noise and Markovian jumping are provided. Some estimates for solutions of affine stochastic systems are derived, and necessary and sufficient conditions assuring the stochastic stabilizability and stochastic detectability are given. A stochastic version of Bounded Real Lemma is proved and several aspects of the problem of robust stabilization by state feedback for a class of linear systems with multiplicative white noise and Markovian jumping are investigated.