Delay Ts Fuzzy Systems With Time Delay

With the development of technology and industrial production,practical systems often possess complex characteristics,such as high orders,nonlinearity and time delays.This makes the analysis and synthesis of the systems become more complex and difficult.So it is difficult to design and achieve the effective control using classic control theory and modern control methods.In view of the above problems,this thesis studies time-delay nonlinear systems through T-S fuzzy time-delay model approach. The problems of stability analysis and stabilization via state feedback are addressed for this class of systems by combining Lyapunov stability theories,the free-weighting matrix technique and LMI approach.The thesis studies the delay-dependent method, which is less conservative than delay-independent ones,especially when the size of delay is small.The main content contains two parts as follows:Firstly,based on T-S fuzzy systems with time delay,we employ the information on the delay-related terms,and adopt appropriate Lyapunov functionals and free-weighting matrix method to improve the stability conditions of T-S fuzzy systems with time delay.A numerical example is given to illustrate the effectiveness and the advantage of the present results.Secondly,when the premise variables of the fuzzy system are not achieved online,we can only adopt different fuzzy weighting functions.We consider the stabilization problem for T-S fuzzy systems with time-varying delays and give sufficient conditions for the design of stabilizing controllers via state feedback.The problem studied in this thesis is more general due to the consideration of different fuzzy weighting functions in controllers.Improvement on stability of T-S fuzzy systems with time-varying delay is owing to the employment of additional delay information and the convex combination technique.Numerical examples are used to show the effectiveness of the method proposed in this thesis.Finally,the conclusion and perspective are given at the end of the thesis.