一类混合系统不变集的LMI方法求解  

LMI Solution to Invariant Set in a Class of Hybrid System

作　　者：李坚强[1] 裴海龙[1] 袁玲[1] 

机构地区：[1]华南理工大学自动化科学与工程学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2008年第9期140-144,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60374036;60574004;60736024);高校博士点基金资助项目(20040561031);广东省自然科学基金资助项目(20040561031)

摘　　要：为了解决混合系统不变集的存在性问题,针对一类含有摄动干扰的混合系统,首先通过公共李雅谱诺夫函数判断不变集的存在性;然后通过构造李雅谱诺夫函数,利用线性矩阵不等式(LMI)的方法求得不变集的存在性,得出混合系统的切换规律以及子系统所对应的子空间,并进一步求得混合系统不变集的范围;最后通过一个混合系统数值仿真例子证明了该方法的可行性与有效性.In order to solve the problem of existence of the invariant sets in hybrid systems, a class of hybrid system with perturbed disturbance is investigated. By proposing a common Lyapunov function, the existence of invariant set is proved. Moreover, by constructing a Lyapunov function, the existence is calculated based on the linear matrix inequality （LMI） method, the switch laws and sub-system domains of the hybrid system are obtained, and the do- main of the invariant set is further computed. A numerical example is finally presented to confirm the feasibility and effectiveness of the proposed method.

关 键 词：混合系统 不变集 李雅谱诺夫函数 线性矩阵不等式 

分 类 号：TP332.1[自动化与计算机技术—计算机系统结构]