Research On Dissipative Control Of TS Fuzzy System With Time Delay

Time delays,nonlinearity and uncertainty can be found in all kinds of systems,and they can seriously affect the performance of the system,especially the stability of the system.The method based on the T-S model has been proved to be a universal approximation model.It can approximate many nonlinear systems with arbitrary precision,which provides a powerful research tool for the study of nonlinear systems.Therefore,the influence of these factors on the system must be taken into consideration when designing the system controller.On the other hand,in recent years,designing many important systems has involved the theory of dissipative concepts.This theory is understood from the engineering practice.However,in the actual system operation process,the system is often too complex and can not be accurately expressed,and there are many factors that affect the system uncertainty.Therefore,the research on the problem of robust dissipation control for T-S fuzzy systems with time-delay It has great practical significance.Based on the Lyapunov stability theorem,parallel distributed compensation(PDC)algorithm,robust control theory,dissipative control theory and LMI method,the paper is robust to the uncertainties of T-S fuzzy systems with time-delay.Problems such as dissipative control were studied in depth.The parameter uncertainty involved in this paper is a norm bounded uncertainty or its generalized form.The T-S fuzzy model with this parameter uncertainty can approximate the nonlinear parameter uncertain system with arbitrary precision.The main work and research results of this paper include the following aspects:(1)The robust dissipativity of a class of uncertain T-S fuzzy systems with interval time-varying delays is analyzed.System uncertainties are assumed to be norm bounded uncertainties.Based on the Lyapunov stability theory,using the LMI method,combined with the convex optimization method and the new integral inequality,a sufficient condition for the robust stability and strict dissipation of closed-loop systems is obtained in the form of linear matrix inequalities.The corresponding state dissipation controller.By solving the linear matrix inequality,the controller gain matrix is obtained.(2)The robust dissipativity of uncertain T-S fuzzy systems with time delay is analyzed.The system uncertainty is assumed to be linear fractional uncertainty,and the system state time-varying delay is a random delay.Using statistical research methods to deal with random time-delay terms of the system,a T-S fuzzy system model with random time-delay is obtained.Based on the Lyapunov stability theory,using the linear matrix inequality(LMI)method,the delay-dependent condition of the closed-loop system satisfying the dissipative index is given.And the problem of designing the controller is transformed into the problem of solving the LMI.By solving the linear matrix inequality,the controller gain matrix is obtained.