| 基于参数相关Lyapunov泛函不确定时滞系统的鲁棒稳定性 |
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| 作者姓名： | 夏元清 韩京清 |
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| 作者单位： | 中国科学院数学与系统科学研究院系统科学研究所, 北京 100080 |
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| 基金项目： | 国家自然科学基金资助项目(60 1740 2 7) |
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| 摘 要： | 研究了含多面体不确定性的时滞系统的鲁棒稳定性问题。利用参数相关的Lyapunov泛函,得到了基于LMI的时滞系统时滞相关的鲁棒稳定的充分条件。在该条件中不确定系统在多面体不同的顶点用不同的Lyapunov阵判断其稳定性,而已有的结果为在所有的顶点用一个共同Lyapunov阵分析。进一步,将确定系统稳定的最大时滞问题转化为求广义特征值的拟凸优化问题。最后数值例子说明了该方法有较小的保守性
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| 关 键 词： | 时滞系统 多面体不确定性 鲁棒稳定性 LMI |
| 收稿时间： | 2002-06-27 |
| 修稿时间： | 2002-09-27 |
Robust Stability of State Delayed Systems with Ploytopic Type Uncetainties Via Parameter-Dependent Lyapunov Functionals |
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| Authors: | XIA YuanQing HAN JingQing |
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| Institution: | Institute of Systems Science, Academy of Mathematica and Systems Science, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | The problem of robust stability for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty is considered.First of all, for robust stability, new matrix inequalities characterization of delay-dependent quadratic stability results were exploited to demonstrate that it allows the use of parameter-dependent Lyapunov functionals in comparison to the classical one,whose drawback stands in the use of a single Lyapunov function to assess the stability over the whole uncertainty domain.Next, the problem of determining the maximum time-delay under which the system will remain stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques.Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method. |
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| Keywords: | time-delay systems uncertain systems robust stability LMI |
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