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.
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.
出处
《郑州大学学报(理学版)》
CAS
2007年第1期1-5,共5页
Journal of Zhengzhou University:Natural Science Edition
基金
国家自然科学基金资助项目
编号60403001
辽宁省智能信息处理重点实验室开放课题基金
辽宁省智能信息处理重点实验室博士启动基金资助项目