Research On Robust Control For System With Time-varying Delays Based On The T-S Fuzzy Model

Time delay, nonlinearity and parameter uncertainties often appear in the actual control system, which have become the three factors to be considered in the research and analysis of modern control theory.In the last few decades, the robust control of nonlinear time delay system is always the key content of the control theory. Takagi and Sugeno(T-S) fuzzy model combined the traditional control theory and expert experience, has gradually become a very important method of the study of complex nonlinear system and attracted the attention of scholars at home and abroad.Therefore,the analysis of robust control for T-S fuzzy time-delay systems has its profound theoretical significance and good development space.On the basis of existing results at home and abroad, the robust control synthesis problem of uncertain nonlinear fuzzy systems with state delay is discussed.Robust control, robust H? control, robust H? guaranteed cost control of nonlinear uncertain T-S fuzzy systems with time delay and stability and stabilization problem of neural networks with time-varying delays are analyzed using Lyapunov theory and LMI technique.The main work and research results show as follows:1.The continuous T-S fuzzy model with interval time-varying delay is established,and the sufficient condition for the delay-dependent stability is given by using the integral inequality method, and the conservatism is lower.Based on the criteria obtained,the stabilization conditions of the fuzzy delay system are obtained by the parallel distribution compensation algorithm.The results are generalized to the fuzzy systems with uncertainties and obtain the stability criteria and the stabilization scheme for the uncertain fuzzy systems.On this basis,the problem of robust H? performance analysis and controller design for uncertain fuzzy time-delay systems is discussed.2.The problem of robust H? guaranteed cost for a class of fuzzy time-delay systems with uncertainties of parameters is studied.Some integral terms are dealt with from the process of derivation by using the integral inequality, the robust H? asymptotic stability criterion of the system is obtained, and the robust H? guaranteed cost state feedback controller for the system is designed.The correctness of the theorem is proved by using numerical examples.3.The problem of robust stability and controller design for a class of neural network systems with time-varying delays is studied.A new Lyapunov-Krasovslii functional included the upper and lower bound information of time delay is chosen,when its derivative is processed,by introducing some matrix equations containing integral terms and equaling to 0,the asymptotic stability criterion and the stabilization condition of the neural network system with time-varying delay arederived,and some conclusions are improved and extended. The feasibility of this theorem is proved by numerical simulation.4.Based on T-S fuzzy model with time delay for polypropylene tank reactor,the obtained control method is applied to solve the nonlinear problem,and robust H? fuzzy controller and robust H? fuzzy guaranteed cost controller with the less conservatism are designed.