Research On Stability And Stabilization Of Nonlinear Impulsive Systems With Time-delay Based On T-S Fuzzy Framework

Due to the complex dynamic characteristics and brilliant application prospect of nonlinear systems,the research on fuzzy logic control of nonlinear systems based on Takagi-Sugeno(T-S)fuzzy framework has attracted extensive attention from scholars.As an important branch of nonlinear control research,fuzzy logic control based on a class of nonlinear systems is widely used in different fields such as secure communication,signal encryption,biology and information engineering.With the rapid development of science and technology,it is found that many natural phenomena can be modeled by nonlinear time-delay systems under the T-S fuzzy framework.Therefore,the study of fuzzy logic control of T-S fuzzy time-delay system has great theoretical significance and application value.This thesis aims at improving and developing new stability criteria for nonlinear delay systems with impulse effect.Starting from the analysis of system dynamics,an impule-time-dependent Lyapunov function/functional which can describe the characteristics of the model is constructed to solve the synthesis problem of fuzzy logic controller.The main work is as follows:(1)The robust stabilization problem of T-S fuzzy time-delay systems subject to impulsive perturbations is concerned.New results on robust stabilization via parallel distributed compensation(PDC)control are derived.First,based on the impulse-type Razumikhin-Lyapunov method combined with the use of an impulse-time-dependent Lyapunov function,a new exponential stability criterion for T-S fuzzy time-delay system with impulsive effects is obtained.The proposed stability criterion removes the restrictive condition on the relationship between the size of time-delay and lower bound of impulse intervals imposed by the previous results.Then,by employing a convex relaxation technique,a sufficient condition of stability criterion based on PDC controllers is presented,which is expressed in terms of linear matrix inequalities(LMIs).Next,the robust stabilization problem for the T-S system with slowly time-varying delay is studied.A different stabilization condition is derived via an impulse-time-dependent Lyapunov functional,which is less conservative than the former when the state delay is constant.Finally,an illustrative example is provided to demonstrate the effectiveness of the proposed analysis and design techniques.(2)The state feedback fuzzy controller synthesis for nonlinear neutral state-delayed systems with impulse effect is addressed.A methodology for stability analysis of the considered system is developed in the framework of system augmentation.Time-dependent Lyapunov functions based analysis techniques,including Razumikhin-type technique and Lyapunov functional technique,is developed to reduce conservativeness of stability condition.By employing an augmentation technique of matrix inequality for separating the product terms involving the control gain matrices,the fuzzy controller synthesis problem is solved in the convex optimization framework.Three illustrative examples are presented to demonstrate the novelty of the new stability criteria and the effectiveness of the proposed design method.(3)A research on the guaranteed cost fuzzy impulsive stabilization problem for nonlinear time-varying delay systems is concerned.First,by constructing the impulse-time-dependent Lyapunov function,a new result of designing fuzzy impulsive guaranteed cost controller for T-S fuzzy time-delay system with parameter uncertainty is obtained.Then,based on convex relaxation technique,a sufficient condition of stability criterion is derived.Second,the problem of guaranteed cost fuzzy impulsive stabilization of T-S system with slow time-varying delay is discussed,a conclusion that the stability criterion obtained by impulse-time-dependent Lyapunov functional is less conservative than that obtained by Razumikhin method is gained when the state delay is constant.Finally,the validity of the theoretical results is demonstrated by an illustrative example.