| 时滞随机线性大系统的指数稳定性 |
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| 引用本文： | 江明辉,沈轶,蹇继贵. 时滞随机线性大系统的指数稳定性[J]. 系统工程学报, 2005, 20(6): 564-569 |
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| 作者姓名： | 江明辉 沈轶 蹇继贵 |
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| 作者单位： | 华中科技大学系统工程研究所,湖北,武汉,430074 |
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| 基金项目： | 国家自然科学基金资助项目（60574025;60274007）;教育部高校博士点基金资助项目（20010487005）. |
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| 摘 要： | 针对一般随机线性时滞微分方程，给出了方程的平凡解的几乎必然指数稳定性的一个充分条件，由此利用时滞随机系统的比较原理建立一般时滞随机线性大系统的二阶矩指数稳定与几乎必然指数稳定新的代数判据．利用恰当的Lyapunov函数结合不等式技巧得到了这些条件．特别是用一个代数方程给出了依赖时滞的Lyapunov指数的估计．并用实例加以验证．
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| 关 键 词： | 随机大系统 指数稳定 Lyapunov函数 |
| 文章编号： | 1000-5781（2005）06-0564-06 |
| 收稿时间： | 2004-01-02 |
| 修稿时间： | 2004-01-022004-06-02 |
Exponential stability of linear stochastic large-scale system with time-delay |
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| JIANG Ming-hui,SHEN Yi,JIAN Ji-gui. Exponential stability of linear stochastic large-scale system with time-delay[J]. Journal of Systems Engineering, 2005, 20(6): 564-569 |
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| Authors: | JIANG Ming-hui SHEN Yi JIAN Ji-gui |
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| Affiliation: | Institute of Systems Engineering, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | For a class of general linear stochastic equation with time-delay, this paper presents a sufficient condition of guaranteeing the almost sure exponential stability of the trivial solution of the equation. From that, a new algebraic criterion of 2-order moment exponential stability and the almost sure exponential stability for general lineal stochastic large-scale system with time-delay is established by comparison theory. These conditions are derived by using suitable Lyapunov function method and combing with inequality technique. In particular, the Lyapunov exponent, which is depended on time-delay, is estimated by an algebraic equation . An example is given to verify the effectiveness of the results. |
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| Keywords: | stochastic large-scale systems exponential stability Lyapunov function |
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