Non-Linear Approximation Of The T-S Fuzzy System Membership Function And Stability Analysis Method Study

With the developments need of various types of nonlinear systems in the industrial field,the control performance requirements of system are increasing,and TS fuzzy systems can provide a satisfied solution to such problems.Therefore,the study of control methods based on T-S fuzzy systems is in great importance.For this class of systems,how to reduce the conservatism in stability analysis has been a hot issue of discussion.One of the reasons for this situation is the lack of information on the membership function in the derived stability conditions.Stability analysis methods with lower conservativeness can be more widely used in practical engineering applications,so the discussion on this issue is attracting more and more attention.A new stability analysis method is proposed for the state feedback control problem of the T-S fuzzy systems.This method is applicable to the membership function without coupling items in the polynomial approximation function.Firstly,the system membership function is approximated by a series of nonlinear polynomials,and then a new polynomial transformation method is proposed for the purpose of converting the polynomial approximation function to a linear form.Compared with linear approximation,this method can achieve better approximation accuracy.Then,the information of the membership function is introduced into the stability analysis to derive the stability conditions of linear matrix inequalities.Finally,the effectiveness of the proposed method in reducing conservativeness and enhancing robustness is illustrated by simulation example.Based on the above results,a stability analysis method is proposed that can be applied to more general nonlinear membership functions.The nonlinear stability conditions containing the information of the membership function are obtained through stability analysis by approximating the membership function by means of Taylor series expansion.Subsequently,different linear transformations are performed on the coupled and uncoupled terms of the approximation function to achieve decoupling and linearization,and a series of linear stability conditions are obtained.Finally,the effectiveness of the proposed method in reducing conservativeness is illustrated by simulation example.