Study On Robust Control Method For T-S Fuzzy Systems

T-S fuzzy system have the property of representing or approximating non-linear systems with arbitrary accuracy.The system consists of a series of membership functions and linear subsystems,so that lots of linear control theories are applied to the control process of nonlinear system.This paper studies the analysis methods to reduce conservatism and enhance robustness for the control system synthesis issue of T-S fuzzy system.The specific con-tents are as follows:First of all,for the robust tracking control task of T-S fuzzy systems,an improved non-uniform piecewise method of membership functions is pro-posed based on the traditional uniform piecewise method to enhance robust-ness.Firstly,the nonlinear membership functions are approximated by a se-ries of decoupled polynomials functions based on the famous least-square method.Then,the non-uniform piecewise vertices are obtained by a newly proposed derivative-integral non-uniform division approach.For different forms of external disturbances,robust L_?and robust H_?control methods are designed respectively,and a series of convex robustness conditions are ob-tained by piecewise linear approximation method.Finally,the comparisons between the proposed method and the uniform piecewise method in simula-tion examples show that the proposed scheme is able to effectively improve the robustness.Secondly,in view of the traditional uniform division approach of member-ship function,a membership functions integral involving method is proposed to reduce the conservatism and enhance the robustness.Firstly,the general-ized expression of indefinite integr al of membership function and its fuzzy summation are obtained.Then a fuzzy controller and a fuzzy-liked Lyapunov function with membership functions integral are designed.Through the piecewise linear approximation method,the numerical information of both membership functions themselves and their integral is involved in the stabil-ity analysis process of stabilization control and robust H_?control,respec-tively.Finally,the comparisons between the proposed method and the existing methods in simulation examples show that the proposed scheme is able to ef-fectively improve the robustness.