Output Feedback Control For T-S Fuzzy System With Unknown Premise Variables

With the development of science and technology,the higher control performance is required by flourishing various new nonlinear systems in the industrial field,so how to deal with the nonlinear characteristics of the systems is particularly important.T-S fuzzy system is combined by sub-linear systems and membership functions,it can approximate nonlinear systems with arbitrary accuracy.Then abundant mature linear control methods can be applied on nonlinear systems through T-S fuzzy approach.Therefore,the research of T-S fuzzy system is very important.This thesis will focus on the output feedback control of T-S fuzzy system and related issues,the main contributions are listed below:For the stabilization problem of T-S fuzzy system with unknown premise variables,the observer-based controller design approach is proposed.Firstly,the terms caused by the unknown premise variables(UVP)in observer error equations are restricted by the Lipschitz conditions.Secondly,the system stability conditions are obtained based on the Lyapunov function method,to convert the bilinear matrix inequalities into LMI form,an eigenvalue matrix scaling method and a fuzzy Lyapunov function high gain observer method are proposed.Finally,based on the above two approaches,vessel dynamic positioning simulation results are compared and analyzed,which shows the effectiveness of the proposed methods.For the output feedback control problem of continuous-time UPV T-S fuzzy systems with unknown external disturbance,an H_∞observer-controller design method in low frequency domain is proposed.Firstly,an observer-controller structure is given,the terms caused by the unknown premise variables in observer error equations are restricted by the Lipschitz conditions.Then the stability conditions of the undisturbed augmented error system is given.To achieve better control performance of the system in low frequency,the H_∞index for attenuating the unknown low frequency disturbance is guaranteed by generalized Kalman-Yakubovich-Popov lemma.Secondly,the stability and robustness conditions are converted into linear matrix inequality forms which can be solved directly by convex optimization technique.Finally,in simulation section,a vessel dynamic positioning task is carried out to show the effectiveness of the proposed method.