New approaches to relaxed stabilization conditions and H-infinity control designs for T-S fuzzy systems  

作　　者：Juntao PAN Shumin FEI Yudong NI Mingxiang XUE 

机构地区：[1]Key Laboratory of Measurement and Control of Complex Systems of Engineering （Ministry of Education）, Southeast University, Nanjing Jiangsu 210096, China [2]LAMIH, UMR CNRS8503, University of Valenciennes et Hainaut-Cambr6sis, Le Mont Houy, 59313 Valenciennes Cedex 9, France

出　　处：《控制理论与应用（英文版）》2012年第1期82-91,共10页

基　　金：supported by the National Natural Science Foundation of China-Key Program (No. 60835001);the National Natural Science Foundation of China (No. 61104068)

摘　　要：This paper focuses on the problem of fuzzy control for a class of continuous-time T-S fuzzy systems. New methods of stabilization design and H-infinity control are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used. Through the staircase membership functions approx- imating the continuous membership functions of the given fuzzy model, the membership functions can be brought into the design conditions of fuzzy systems, thereby significantly reducing the conservativeness in the recent fuzzy controller design methods. Unlike some previous fuzzy Lyapunov function approaches reported in the literatures, the proposed design techniques of stabilization and H-infinity control do not depend on the time-derivative of the membership functions that may be pointed out as the main source of conservatism when considering fuzzy Lyapunov functions analysis. Moreover, conditions for the solvability of the controller design given here are written in the form of linear matrix inequalities, but not bilinear matrix inequalities, which are easier to be solved by convex optimization techniques. Simulation examples are given to demonstrate the validity and applicability of the proposed approaches.This paper focuses on the problem of fuzzy control for a class of continuous-time T-S fuzzy systems. New methods of stabilization design and H-infinity control are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used. Through the staircase membership functions approx- imating the continuous membership functions of the given fuzzy model, the membership functions can be brought into the design conditions of fuzzy systems, thereby significantly reducing the conservativeness in the recent fuzzy controller design methods. Unlike some previous fuzzy Lyapunov function approaches reported in the literatures, the proposed design techniques of stabilization and H-infinity control do not depend on the time-derivative of the membership functions that may be pointed out as the main source of conservatism when considering fuzzy Lyapunov functions analysis. Moreover, conditions for the solvability of the controller design given here are written in the form of linear matrix inequalities, but not bilinear matrix inequalities, which are easier to be solved by convex optimization techniques. Simulation examples are given to demonstrate the validity and applicability of the proposed approaches.

关 键 词：T-S fuzzy systems Fuzzy Lyapunov functions Staircase membership functions Linear matrix inequalities 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] TD327.2[自动化与计算机技术—控制科学与工程]