Stability Analysis And Controller Design For A Class Of T-S Fuzzy Time-Delay Systems

Time-delays,unavoidably existing in many practical systems such as aerospace systems,network transmissions,power systems,engineering science,are the main factor that degrades system performance and threatens system stability,which brings great difficulties to the theoretical analysis and engineering application of the control system.On the other hand,a majority of the real systems are nonlinear so that some traditional control systems are difficult to be modelled and controlled directly.However,it is possible to analyze and simulate the stability and performance of the system without establishing an accurate mathematical model by the fuzzy control theory.For this reason,A T-S fuzzy model has been widely studied in recent decades since it can effectively describe nonlinear systems by smoothly connecting a set of local linear models with fuzzy membership functions.A large number of existing less conservative results of nonlinear system based on T-S model have emerged,but there is still room for improvement.This paper focuses on the problem of delay-dependent stability and stabilization for T-S fuzzy systems with time-varying delay.The specific research contents are as follows:(1)Considering a class of nonlinear system with time-varying delay based on T-S model.An augmented Lyapunov-Krasovskii functional(LKF)containing triple integral terms independent of membership function is constructed by making full use of time-delay to reduce the conservatism of stability criteria.Then,Jensen integral inequality,Wirtinger integral inequality,Convex combination technique and the free weight matrix method are employed to handle the derivatives of the considered LKF.As a results,relaxed delay-dependent stability conditions are derived in the forms of linear matrix inequalities which are summarized as a theorem.At last,two classical numerical examples are given to illustrate the validity of the proposed results.(2)On the basis of the stability problem of T-S fuzzy time-delay system independent of the membership function,an augmented LKF with triple integral terms related to membership function is constructed to further reduce the conservatism.The switching idea is used to process the relevant terms of the membership function from the derivation of the LKF to avoid the derivative of the membership function.Then,the stability criteria of T-S fuzzy time-delay systems related to the membership function is given in the form of linear matrix inequality.To show the conservatism improvement of the proposed stability conditions regarding to previous results from the literature,comparisons are made through the stability analysis of a well known numerical example of T-S systems with time-varying delays.At the same time,the system state response curve is obtained by Simulink simulation to further verify the effectiveness of the stability criterion.(3)There are some random factors in the actual system usually,which may bring some influence on some aspects of the system.In this chapter,the random time delay is introduced into the proposed control scheme that ensures the exponential stabilization of T-S fuzzy models.In addition,stochastic variables conforming with the Bernoulli distribution are considered to depict random time delays and a new model is proposed.By applying the L-K stability theory and the parallel distributed compensation(PDC)method,the stability criteria and stabilization controller design for the T-S fuzzy system with a stochastic input delay are derived in the form of linear matrix inequality.Finally,the efficiency and benefits of the stability criterion and controller design method are illustrated by several classical numerical examples.