T-S模糊广义系统稳定性的一个新判据  

A New Stabilization Conditions for T-S Fuzzy Descriptor System

作　　者：张双红[1,2] 任俊超[2] 

机构地区：[1]吉林师范大学数学学院,吉林四平136000 [2]东北大学系统科学研究所,辽宁沈阳110819

出　　处：《控制工程》2013年第4期598-601,606,共5页Control Engineering of China

基　　金：国家自然科学基金(61203001);中央高校基本科研业务费专项资金(N110305010);吉林省教育厅项目(2013444);吉林省四平市科技局项目(2012030)

摘　　要：以模糊模型为基础的控制技术为非线性系统的研究提供了有效的方法,而对于连续的T-S模糊系统,在对模糊Lyapunov函数求导进而研究系统的稳定性的时候,不可避免的会产生一定的保守性。基于广义系统方法研究了连续T-S广义模糊系统的稳定性问题。通过引入新的变量给出了开环模糊系统的一个宽松稳定条件。然后通过引入新的变量和使用新的松弛技术,得到了一类non-PDC(Parallel Distributed Compensation)控制器的设计方法。该方法具有比现有结果更小的保守性。所得到的定理均通过线性矩阵不等式组表出。数值算例的结果证明了结论的有效性和所得条件具有较低的保守性。Fuzzy-model-based（FMB）control approach offered a systematic ways to tackle nonlinear systems. At the same time, For continuous - time T-S fuzzy systems, a certain degree of conservativeness remains because information on the time derivative of member- ship functions is generated into the fuzzy Lyapunov function（FLF） time2derivative. In this paper, we investigated the problems of stabili- ty analysis of continuous - time T-S fuzzy descriptor systems based on the descriptor system approach. New criteria for the asymptotic stability of the T-S fuzzy descriptor systems are established. Moreover, with the usage of the non-PDC control scheme, less conservative stabilizations are attained by both introducing additional variables and applying a kind of relaxed technique. Furthermore, all the condi- tions we obtained are expressed in the terms of linear matrix inequalities. And numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed conditions.

关 键 词：模糊Lyapunov函数(FLF) 松弛稳定条件 T—S模糊广义系统 线性矩阵不等式组 

分 类 号：TP27[自动化与计算机技术—检测技术与自动化装置]