| 引用本文: | 李亚军,邓飞其,彭云建.具概率分布变时滞随机系统鲁棒稳定性[J].控制理论与应用,2011,28(7):1015~1020.[点击复制] |
| LI Ya-jun,DENG Fei-qi,PENG Yun-jian.Robust delay-probability-distribution stability of linear stochastic systems with time-varying delay[J].Control Theory and Technology,2011,28(7):1015~1020.[点击复制] |
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| 具概率分布变时滞随机系统鲁棒稳定性 |
| Robust delay-probability-distribution stability of linear stochastic systems with time-varying delay |
| 摘要点击 1925 全文点击 808 投稿时间：2009-12-16 修订日期：2010-10-12 |
| 查看全文 查看/发表评论 下载PDF阅读器 |
| DOI编号 10.7641/j.issn.1000-8152.2011.7.CCTA091627 |
| 2011,28(7):1015-1020 |
| 中文关键词 变时滞概率分布 不确定随机系统 自由权矩阵 鲁棒稳定 线性矩阵不等式 |
| 英文关键词 varying delay-probability-distribution uncertain stochastic system free weight matrix robust stability linear matrix inequality(LMI) |
| 基金项目 国家自然科学基金资助项目(60874114). |
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| 中文摘要 |
| 文研究了一类有非线性时变随机时滞的线性不确定系统的鲁棒稳定性. 其中时变随机时滞表征为伯努利随机过程, 具有已知的概率分布和变化范围. 通过构造新泛函, 建立了基于线性矩阵不等式的鲁棒均方指数稳定的充分条件, 此条件易于用MATLAB工具箱来验证. 本文所获得结果的主要特征是稳定性条件依赖时滞的概率分布和时滞导数的上界. 同时也证明了允许时变随机时滞的时滞比之传统的确定性时滞有更大的变化范围, 因此我们的条件比确定性时滞更为保守. 算例表明了文中所提方法的有效性. |
| 英文摘要 |
| This paper is concerned with the robust stability of a class of linear uncertain stochastic systems with nonlinear time-varying stochastic time-delay which is characterized by a Bernoulli stochastic process with given distribution probability in a given variation range. By constructing a new Lyapunov-Krasovskii functional, we derive for the system the sufficient conditions of mean-square exponential stability in terms of the linear matrix inequalities(LMIs), which can be checked readily by using MATLAB toolbox. The feature of our results is the conclusion of stability conditions being dependent not only on the probability distribution of the time-delay, but also on the upper bound of the its derivative. Meanwhile, we also show that the allowable variation range of the time-varying stochastic time-delay can be greater than that of a deterministic time-delay in ensuring the same stability; this demonstrates the less conservativeness of our requirements than the traditional ones. An example is given to illustrate the effectiveness of the proposed method. |