Stability Analysis And Stabilization Of TS Fuzzy Systems With Time Delays

In practical engineering systems,time delay and nonlinear phenomena often appears and it is the main reason of instability and oscillation.As a result,the study of time-delay dynamic systems has been gained considerable attention.However,T-S fuzzy model is the link between the nonlinear systems and the linear systems,so the study of time-delay and T-S fuzzy system is particularly important.For the study of time delay and T-S fuzzy systems,Lyapunov functional method has been one of the powerful tools.Due to this method is simple and clear and can be used to obtain tractable linear matrix inequality(LMI)conditions,it has received widespread application.Based on the current research findings for the studied systems,this thesis utilizes Lyapunov functional method and various inequalities to investigate the stability of linear system with time-varying delay and the stability and stabilization of time-delay T-S fuzzy systems,and develop new delay-dependent stability criteria and control design scheme with less conservatism.The main contents of this thesis are presented as follows:1.The problems of stability analysis of linear systems with time-varying delay are studied.This thesis proposes new integral inequality and appropriate LK functional to investigate the stability of the studied system in order to enlarge the feasible region for checking the maximum delay upper bound,which can guarantee system is asymptotically stable.Based on above two aspects and the Lyapunov stability theory,the delay-dependent stability conditions are obtained in terms of linear matrix inequality.Compared with the existing results,the advantages of the obtained stability criteria lie in less conservatism and decision variables and wider application.2.The problems of stability analysis of time delay T-S fuzzy systems are studied.Combining the fuzzy line integral Lyapunov functional,fuzzy-weighting-dependent augmented LK functional and relaxed Wirtinger inequality,new delay-dependent stability criteria are obtained in terms of LMI.Finally,the two numerical examples are given to illustrate the effectiveness and superiority of the obtained results.3.The problems of stabilization of time-delay T-S fuzzy systems are studied.First,a new LK functional is proposed to design the state feedback controller for the studied systems.Second,switching rules method is used to avoid the time derivative of membership functions.Finally,utilizing Lyapunov stability theory and Wirtinger inequality,new delay-dependent stabilization condition is obtained.New state feedback control scheme leads to less conservatism and less computation complexity.Two numerical examples are given to show the effectiveness and superiority of the obtained stabilization condition and controller.