基于模糊Lyapunov函数方法的模糊广义系统H∞控制  

H_∞Control for Fuzzy Descriptor Systems Based on Fuzzy Lyapunov Function Approach

作　　者：袁宇浩[1] 张庆灵[1] 陈兵[2] 刘超[1] 

机构地区：[1]东北大学系统科学研究所,沈阳110004 [2]青岛大学复杂性科学研究所,青岛266071

出　　处：《自动化学报》2008年第8期929-936,共8页Acta Automatica Sinica

基　　金：国家自然科学基金(60574011)资助~~

摘　　要：研究一类T-S模糊广义系统的容许性条件和H_∞控制问题.首先将原系统表示成增广系统,进而基于新的模糊Lyapunov函数和模糊控制器得到容许性条件.所得开环容许条件不要求子系统是容许的;闭环容许条件中不含有控制输入矩阵与控制增益矩阵的乘积项.对于H_∞控制问题,利用隶属度函数的性质对H_∞控制条件进行了放宽,并得到了改进的严格线性矩阵不等式(LMI)形式的H_∞控制条件.数值算例表明所得结论较已有文献具有较小的保守性.The admissible conditions and H∞ control problem of T-S fuzzy descriptor systems are introduced. The original systems can be generalized to augmented systems, then some admissible conditions for fuzzy descriptor systems are obtained based on a new fuzzy Lyapunov function and new fuzzy controller. For the admissible conditions of open-loop systems, the subsystems are not required to be admissible, nor the multiplied term of input control matrix by control gain matrix has to be considered in the admissible conditions of closed-loop systems. By virtue of the property of membership function, the H∞ control conditions are improved. Furthermore, some strict linear matrix inequalities （LMIs） are obtained. At last, some examples are given to illustrate that the obtained sufficient conditions are less conservative than the results given by previous literature.

关 键 词：T-S模糊广义系统 模糊LYAPUNOV函数 容许性条件 H∞控制 严格线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]