Study On The Design And Analysis Of Fuzzy Controller Via Fuzzy Model

The problems of fuzzy control for several classes of uncertain nonlinear dynamic systems based on Takagi-Sugeno (T-S) fuzzy model are studied in this paper. Using linear matrix inequalities (LMI) technique and Lyapunov stability theory, some control schemes are proposed to ensure stability of the closed-loop systems. The details are summarized as follows.Firstly, the issue of designing a stabilizing fuzzy controller is discussed for a class of nonlinear uncertain time-delay discrete systems based on T-S fuzzy model. It is assumed that the state variables are measurable, sufficient conditions are derived for robust stabilization in the sense of Lyapunov stability and are formulated in the format of linear matrix inequalities. The controller that ensures the robust stability of the closed-loop system is acquired through the numerical solution of a set of linear matrix inequalities. The simulation results demonstrate the effectiveness of the proposed methods.Secondly, it is assumed that the state variables are not measurable, the fuzzy observer is designed for a class of nonlinear uncertain time-delay discrete systems based on T-S fuzzy model. Sufficient conditions are derived for robust stabilization in the sense of Lyapunov stability and are formulated in the format of linear matrix inequalities. Based on the fuzzy observer, the controller that ensures the robust stability of the closed-loop system is derived through the numerical solution of a set of linear matrix inequalities.Thirdly, a class of nonlinear uncertain continuous systems with time-delay based on T-S fuzzy model is discussed. Considering the external disturbances and using LMI technique and Lyapunov stability theory, a set of LMIs is derived. Using sliding-mode control theory, sliding surface is designed by solving a set of linear matrix inequalities. The controller that ensures the robust stability of the closed-loop system is developed. The numerical examples illustrate the effectiveness of the proposed methods.Finally, a class of nonlinear continuous time systems based on T-S fuzzy model with time-delay is studied. At first, it is assumed that the external disturbances and modeling errors do not exist, a novel scheme of sliding-mode controller is designed based on the principle of sliding-mode control and LMI technique. Further, when external disturbances and modeling errors occur, using neural networks to approximate the modeling errors, an adaptive sliding-modecontroller is designed with robust control term. The states of the closed-loop control system are proven to be stable. The numerical examples show the effectiveness of the proposed approaches.