Analysis And Design For Nonlinear Time-delay Systems Based On The T-S Model

There are many problems during the process of the systems being controlled,such as para-meter uncertainties,time delays,time-varing and uncertain external disturbance and so on.In the practical engineering application,the existence of these problems will make the system instability and performance degradation,which affect the normal operation of the system and make it difficult to maintain a stable state.As the T-S fuzzy model can be used to approximate the complex nonlinear system with the weighted sum of the form of single line subsystem.Therefore,it has profound significance and extensive application value for the stability analysis and control design of T-S fuzzy systems with time-delay.In this paper,we mainly study the robust control analysis and design method for several classes of nonlinear fuzzy systems with state time-delay and uncertain parameters.Robust control and robust H_? guaranteed cost control problem of the T-S fuzzy model with time-delay are analyzed using parallel distributed compensation(PDC)algorithm;As the T-S fuzzy time-delay model under imperfect premise matching,augmented Lyapunov-Krasovskii functional method based on an additional tripleintegral term.The stability results are obtained in a simple form and less conservative.The main result of the study are as follows:In the first part,the state feedback controller for the T-S fuzzy model with interval time-varying delay is designed,which can make the T-S fuzzy systems stable.Based on Lyapunov-Krasovskii functional method and the parallel distribution compensation algorithm,using the various integral inequality to deal with derivative generated integral,which transforme the problem of controller design into the problem of solving linear matrix inequalities,and the results are generalized to the fuzzy systems with uncertainties.Because there had no free-weighting matrix been introduced when dealing with the integral term.Therefore,the stability results are obtained in a simple form and less conservative.The feasibility of this theorem is proved by numerical simulation.In the second part.The problem of robust H_? control and guaranteed cost for a class of T-S fuzzy time-delay systems with disturbance is discussed.Firstly,based on the Lyapunov-Krasovskii functional,applying the improved integral inequality meth-od.The stabilization condition of T-S fuzzy time-delay systems with less conservatism is obtained by using linear matrix inequality(LMI).Then,the results are extended to fuzzy systems with uncertainty,a sufficient condition for the uncertain T-S fuzzy system with stability and satisfy H_? performance is obtained.Also the robust H_? guaranteed cost state feedback controller for the system is designed.The correctness of this theorem is proved by numerical examples.In the third part,T-S fuzzy control systems with time-varying delay under imperfect premise matching are investigated.The problem of delay dependent robust stability and robust stabilization of this system is studied.When the LyapunovKrasovskii functional is established,we introducing less free-weighting matrices and triple-integral term,and applying the improved integral inequality method,the controller design method under imperfect premise matching is also proposed based on the stability conditions.A simple form and less conservative results are obtained.The feasibility of this theorem is proved by numerical simulation.