Impulsive Fuzzy Modeling Of Nonlinear System And Its Stability

Since 1980s fuzzy control technique has largely been devoloped with respect to its theory and engineering application because it has many merits, such as control design simple, suiting for many nonlinear systems, robust strongly, etc.. Among fuzzy control techniques, the most important fuzzy control model is Takagi-Sugeno (T-S) one. In the framework of T-S model, the control issues of fuzzy system are redued to the stability of Ordinal Differential Equation. However, there are much problem if the T-S model is directly employed for reprezenting the system with impulsive effectness, such as complexty engnineering control system, biology system, neural network system. The major reasons are that their mathematical model is impulsive differential equation. Meanwhile, the impulsive control technique have generally been used for the domians, such as mechanics system, optimal control of spacecraft, chaos control, neural network, because impulsive control technique is ease to implementation and less cost. But, it is starting stage to introduce the impulsive control technique into the complex system represented by the T-S mode.Therefore, the traditional T-S model is extented and has the more abroad applicability by impulsive control technique in this thesis. The subsystems of the established impulsive fuzzy system model are the impulsive linear system, and this is the most important feature of the impulsive fuzzy system. Then, the merits of impulsive control can be used for the control of fuzzy system, and the traditional T-S model is extented. The system model is transformed into the impulsive differential equation by defuzzying technique. So, this thesis focuses the stability and controllability of the impulsive fuzzy system throughout using impulsive differential equation basic theorem and Lyapunov stability theorem, and robust stability of the time-delay and uncertain nonlinear system is investiged. Meanwhile, the stability and synchronization of chaotic system are investiged by impulsive fuzzy control method.Thus, this thesis establishes the theorem framework of fuzzy system based on impulsive control technique, and expandes and riches the fuzzy system theorem based on T-S model.