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

Time-delay often occurs in many dynamic systems and this phenomenon may lead the deterioration of system's performance and even instability.On the other hand,the T-S fuzzy systems can combine the flexible fuzzy logic theory and the fruitful linear system theory to research the complex nonlinear systems.Therefore,the stability analysis of T-S time-delay systems has received many attention in recent years.Although many effort have been made in this field,there is still plenty room to study.Therefore,this paper first focuses on the analysis of linear systems.Then,T-S fuzzy model will be used to analyze the nonlinear time-delay systems and to design the controller.In this paper,the following aspects will be studied:Firstly,based on the Lyapunov stability theory,an augmented Lyapunov-Krasovskii functional is constructed.When dealing with the derivative of the L-K functional,a new method named free-matrix-based integral inequality is used.Then a stability criterion with less conservatism is given.Besides,system with uncertainties is considered,and the robust stability of this system is studied.Two numerical examples are included to show the effectiveness of these results.Secondly,the case of nonlinear time-delay systems is considered based on the T-S fuzzy model methods.By using decomposing approach,a L-K functional which is different from the one in chapter three is given.An approach to deal with a mistake in some papers will be given.Two numerical examples are given to demonstrate the effectiveness of this result.The fifth chapter considers the system with external disturbance.When constructing the L-K functional,augmented L-K functional is constructed in order to obtain a better result.When dealing with the derivative of the L-K functional,another method is used to deal with the result which is too complex obtained in the chapter four,and then a method to design a H? controller is given.Finally,by comparing with the relative papers and simulation,the validity of the obtained results are verified.