离散广义T-S模糊系统的稳定性分析  

Stability analysis of discrete singular T-S fuzzy systems

作　　者：杜富[1] 梁家荣[2] 张晶华[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004 [2]广西大学计算机与电子信息学院,广西南宁530004

出　　处：《控制工程》2011年第4期543-547,共5页Control Engineering of China

基　　金：国家自然基金项目(61064002);研究生创新项目(105931003061)

摘　　要：针对广义模糊系统的结构特点和技术要求,构造出离散广义分段模糊Lyapunov函数的处理技术,讨论了输入采用双交叠模糊分化的离散广义T-S模糊系统的稳定性和控制器设计问题,在分段Lyapunov函数的基础上采用并行分布补偿法设计出离散广义模糊系统的模糊控制器,得出了新的判定闭环离散T-S模糊广义系统稳定性的充分条件,即在各最大交叠规则组内寻求一个公共正定矩阵和一个对称矩阵。所提出的条件成功的运用在模糊规则数较多的模糊系统中,取得了明显的效果。数值算例说明此法的有效性。To fit the structure characteristic and requirement of singular fuzzy systems,piecewise fuzzy Lyapunov function of discrete-time singular systems is structured to study the stability of discrete singular fuzzy systems with their inputs employing two-overlapped fuzzy partition.A fuzzy controller is designed for discrete singular fuzzy systems with the method of parallel distributed compensation after the definition of a piecewise fuzzy Lyapunov function.Then a new sufficient condition that searching for a common positive-definite matrix and a symmetric matrix in each maximal overlapped-rule group is obtained to check the stability of the closed-loop discrete singular T-S fuzzy systems.This sufficient condition that is proved to provide obviously benefits has been successfully applied to fuzzy singular systems with more fuzzy rules.A numerical example is given to demonstrate the applicability of the proposed design approach.

关 键 词：分段模糊LYAPUNOV函数 稳定性分析 模糊分化 并行分布补偿法 模糊控制器 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]