| 引用本文: | 吴立刚, 王常虹, 高会军, 曾庆双.时滞不确定随机系统基于参数依赖Lyapunov函数的稳定条件[J].控制理论与应用,2007,24(4):607~612.[点击复制] |
| WU Li-gang, WANG Chang-hong, GAO Hui-jun, ZENG Qing-shuang.Stability of uncertain stochastic systems with time-varying delays based on parameter-dependent Lyapunov functional[J].Control Theory and Technology,2007,24(4):607~612.[点击复制] |
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| 时滞不确定随机系统基于参数依赖Lyapunov函数的稳定条件 |
| Stability of uncertain stochastic systems with time-varying delays based on parameter-dependent Lyapunov functional |
| 摘要点击 1404 全文点击 1602 投稿时间：2005-06-13 修订日期：2006-02-23 |
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| DOI编号 |
| 2007,24(4):607-612 |
| 中文关键词 参数依赖Lyapunov函数 时滞相关 随机系统 凸多面体不确定性 线性矩阵不等式 |
| 英文关键词 parameter-dependent Lyapunov functional delay-dependent stochastic systems polytopic-type uncertainties linear matrix inequalities (LMIs) |
| 基金项目 国家自然科学基金资助项目(69874008). |
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| 中文摘要 |
| 针对一类具有凸多面体参数不确定性的时滞随机系统, 研究了其鲁棒稳定性问题. 通过引入适当的加权矩阵变量来寻找Leibniz-Newton公式各项之间的关系, 从而直接地处理系统中的时滞状态项, 避免了常规的应用Leibniz-Newton公式来进行模型变换的间接方法所带来的较大保守性. 采用参数依赖Lyapunov函数方法, 推导了此类系统鲁棒稳定的时滞相关的充分条件. 本文所得条件为线性矩阵不等式形式, 便于借助于内点算法进行求解. 仿真实例证明了本文所提出的稳定条件具有较低的保守性. |
| 英文摘要 |
| The robust stability analysis for a class of linear stochastic systems with polytopic-type uncertainties and time-varying delays is considered in this paper. By introducing some slack matrices, and finding the relation between the terms in the Leibniz-Newton formula, a sufficient delay-dependent condition is proposed for the robust asymptotic stability of such a system by applying the parameter-dependent Lyapunov functional approach. In contrast to the traditional method of using model transformation to derive the delay-dependent condition, this new stability condition is less conservative. The resultant stability condition is in the form of linear matrix inequalities (LMIs), which can be solved via efficient interiorpoint algorithms. A numerical example is also presented to illustrate the less conservative properly of the proposed stability condition. |
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