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| 多胞型线性切换系统二次稳定的充要条件 | |
| 引用本文： | 孙文安,冯佳昕,张强. 多胞型线性切换系统二次稳定的充要条件[J]. 郑州大学学报(理学版), 2007, 39(1): 1-5 |
| 作者姓名： | 孙文安 冯佳昕 张强 |
| 作者单位： | 1. 大连大学信息工程学院,辽宁,大连,116622 2. 上海财经大学信息管理与工程学院,上海,200433 3. 大连大学辽宁省智能信息处理重点实验室,辽宁,大连,116622 |
| 基金项目： | 国家自然科学基金;辽宁省智能信息处理重点实验室开放课题基金;国家博士科研启动项目 |
| 摘 要： | 研究了多胞型线性切换系统在任意切换下的二次稳定性问题.首先构造区间矩阵,把多胞型线性切换系统转化为区间系统,利用Riccati不等式给出了在任意切换策略下多胞型线性切换系统二次稳定性的充要条件.这个条件等价于共同二次正定Lyapunov函数判定条件,而且该条件只需找到一组LMI的解就可以判定该系统的二次稳定性,大大降低计算工作量.最后用数值例子对所得结果加以验证,说明了结果的正确性. |
| 关 键 词： | 线性切换系统 二次稳定性 Lyapunov函数 多胞型摄动 区间矩阵 线性矩阵不等式 |
| 文章编号： | 1671-6841(2007)01-0001-05 |
| 修稿时间： | 2006-08-16 |
A Necessary and Sufficient Condition of the Quadratic Stability for Switched Linear Systems with Polytopic Perturbations |
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| SUN Wen-an,FENG Jia-xin,ZHANG Qiang. A Necessary and Sufficient Condition of the Quadratic Stability for Switched Linear Systems with Polytopic Perturbations[J]. Journal of Zhengzhou University(Natrual Science Edition), 2007, 39(1): 1-5 | |
| Authors: | SUN Wen-an FENG Jia-xin ZHANG Qiang |
| Abstract: | The quadratic stability problem of switched linear systems with polytopic perturbations under arbitrary switching laws is presented.First,To construct the interval matrix,switched linear system with polytopic perturbations is translated into interval system.Using Riccati inequality a necessary and sufficient condition for quadratic stability of switched linear systems with polytopic perturbations under arbitrary switching laws is established.This condition is equivalent to common Lyapunov function with quadratic positive-definite for all subsystems.And this condition,only by finding a set of solutions to the LMI,can determine the quadratic stability of switched linear systems.Finally,a numerical example is given to illustrate the effectiveness of the results. |
| Keywords: | switched linear system quadratic stability Lyapunov function polytopic perturbation interval matrix linear matrix inequality(LMI) |
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