线性切换系统二次稳定的一个充分条件  

Sufficient Condition for Quadratic Stability of Switched Linear Systems

作　　者：孙文安[1] 孙希明[1] 赵军[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2004年第11期1024-1026,共3页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(60274009);教育部高等学校博士学科点专项科研基金资助项目(20020145007);辽宁省自然科学基金资助项目(20032020)

摘　　要：首先构造区间矩阵,把线性切换系统转化为区间系统,利用矩阵不等式给出了在任意的切换策略下线性切换系统二次稳定性的充分条件·这个条件等价于共同二次Lyapunov函数判定条件,但共同二次Lyapunov函数判定条件需要求解若干个矩阵不等式,当子系统较多时计算量是相当大的,而这个条件只需找到一个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·最后用数值例子说明了结果的正确性·An interval matrix is constructed to transform the switched linear system into interval system. Then, a sufficient condition is presented in terms of matrix inequality for the quadratic stability of switched linear systems under any switching laws. This condition is equivalent to the critical condition for common quadratic Lyapunov function to all subsystems, while it is much simpler than the latter because it needs only one matrix inequality to solve but the latter involves several LMIs with immense computation to do if there are not a few subsystems. A numerical example illustrates the effectiveness of the method.

关 键 词：线性切换系统 二次稳定性 LYAPUNOV函数 任意切换 区间矩阵 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]