Fuzzy Control For Nonlinear Systems With Time-delay

Time-delay phenomenon universally exists in almost control systems, which makes it more complicated and difficult to analyse and synthesis the systems, it is also the cause of unstability and less effectiveness of the systems. The discussion of systems with time-delay is a hotspot in control theory and control engineering during these years. At the same time, contorl systems are getting more and more complicated , they lack of accurate maths models and possess high nonlinearity and uncertainty, meanwhile, time-delay phenomenon is the inherent character of control systems. The research of nonlinear systems is very meaningful. As an effective control method based fully using the artificial intelligence, fuzzy control turns the logic languages with certain rules into correlative controlling measures, which provides a base for classical fuzzy control, it is an effective way of modeling and controling for nonlinear systems.The corresponding questions of fuzzy control for nonlinear systems with time-delay are dicussed in this paper. Based on the T-S fuzzy model, application is taken into nonlinear systems with time-delay by using the way of certainty analysis and synthesis in linear systems control theory. Lyapunov method, parallel distributing compensate arithmetic(PDC), linear matrix inequality(LMI) method are all adopted to analyse the fuzzy control for continuous fuzzy systems with time-delay, fuzzy control for discrete fuzzy systems with time-delay and output feedback control for uncertain systems with time-delay. Main contents are as follows:In the first chapter, the background of this paper, the development of fuzy control and the state of study in the nonlinear systems with time-delay are presented. In the second chapter, the corresponding preliminary knowledge is given. In the third chapter, fuzzy control for continous fuzzy systems with time delay is studied. Based on the Lyapunov stability theory and parallel distributing compensate arithmetic(PDC), a sufficient condition for the asymptotical stability for the system is presented and a method is demonstrated via numerical examples. In the forth chapter, fuzzy control for discrete systems with time delay is studied. Through constructing proper Lyapunov fuc- tion, state feedback control and output feedback control are studied so that the discrete closed-loop system is asymptotically stable. In the last chapter, the stability condition of T-S fuzzy model with time-delay is given via constructing a Lyapunov fuction. And more relaxed conditions are given. At last, this paper is summarized and some expectations of the fuzzy control for nonlinear systems with time-delay are given.