Research On Robus H_? Control Method Based On T-S Fuzzy System Model Reconstruction

Fuzzy control theory has developed rapidly since Zadeh put forward the concept of fuzzy set,drawing a huge number of researchers to perform in-depth study in this area.Fuzzy control theory in the model construction,controller design,and stability analysis aspects are continuously maturing,systematic,and the actual industrial application possibilities are becoming more evident,thanks to the combined efforts of these researchers.For T-S fuzzy systems,reducing conservatism in design conditions is a hot academic issue,one of the main reasons for conservatism is that less membership function information is used in system stability conditions.How to effectively introduce membership function information,obtain low conservative results,so as to enlarge the application range of practical engineering,is a problem worthy of further study.In this paper,a membership function dependent stability analysis method is proposed for the state feedback control of T-S fuzzy systems.Firstly,the nonlinear membership function is approximated to linear form by using piecewise linear approximation theory.Then,Lyapunov stability analysis method is used to derive numerically solvable stability conditions to calculate the control gain matrix.Compared with previous methods,this method can introduce more membership function information by increasing the number of segments,so as to obtain low conservative results.Finally,a two-rule inverted pendulum model is used to further illustrate the usefulness of this method.According to the above results,a model reconstruction method is proposed to analyze the stability and robustness by using the membership function information more effectively.Based on piecewise linear approximation theory and sector nonlinear modeling principle,the membership function approaching error related items are used as new premise variables to construct a new T-S fuzzy form model.By using the new T-S fuzzy model and considering the fuzzy Lyapunov function,the stability conditions of the numerical solvable closed-loop system are obtained.Compared with the previous results,this technique may introduce more approximation error information into the system's stability analysis.The results should also be looser because more membership information is used.Finally,the superiority of the model reconstruction method is verified by comparing with some existing results.