Research On Finite Frequency Domain Output Feedback Control Method For T-S Fuzzy System With Unknown Premise Variables

Nonlinear control methods have made great progress in recent years.A T-S fuzzy system concept proposed by Takagi and Sugeno in 1985 can transform complex nonlinear systems into fuzzy systems composed of membership functions and multiple linear models.In actual control system design,it is usually hoped to find a suitable controller so that the system can meet the stability requirements and robustness requirements and robustness performance indexes.However,considering the characteristics of the controlled object and the spectral characteristics of the input signal,the system needs to meet different specified indexes in different frequency domains.And many systems only work in a specific frequency band.Therefore,it is of great significance to study the finite frequency control method with T-S fuzzy system.This paper mainly discusses the observer-controller problem for the above problems:When the premise variables and disturbance of a T-S fuzzy system are unknown,an H_?observer-controller design method in finite frequency domain is proposed.Firstly,the observer-controller structure is given,then through Lipschitz condition it is proved that the error term generated by the unknown premise variables is limited,then the stability condition of the system is obtained by the negativity of the real part of the eigenvalue.In order to obtain better system control performance in finite frequency domain,the generalized(Kalman-Yakubovich-Popov,KYP)lemma is used to ensure the robustness of the system.Then the stability and robustness conditions are transformed into a linear matrix inequality(LMI)form,which is then solved using a convex optimization method Finally,the effectiveness of the method is verified by a system simulation example.Based on the above research contents,in order to further reduce the conservativeness of the control system,a new stability analysis method with piecewise membership function under the condition that the premise variables are completely unknown is proposed.Firstly,the stability and robustness conditions in LMI form are obtained by using the H_?observer-controller design method in finite frequency domain.Then,by introducing membership function information into the stability condition,the conservativeness of the control system is further reduced.Based on the traditional uniform points selection method of membership function,a non-uniform point selection method that converts multi-dimensional variables into a single dimension is proposed without increasing the LMI solving burden.Finally,the effectiveness of the method is verified by simulation.