Impulsive Modeling Of Nonlinear Circuit And System And Its Stability

Recently, nonlinear circuits and systems as a branch of nonlinear science attract more and more attentions from various fields of science and engineering. In this dissertation, we perform impulsive modeling and stability study on nonlinear circuits and systems. The main contents of this dissertation include: 1) Impulsive modeling of Chua's chaotic circuit and its control; 2) Stability analysis and design of impulsive control Lorenz chaotic systems family; 3) Impulsive modeling and control of Lurie systems and the nonlinear systems with time-varying delays; 4) Stability of fuzzy chaotic systems and impulsive fuzzy systems with time-delays; 5) Impulsive modeling of a class of uncertain systems with time-delays and its control.The main originality in this paper can be summarized as follows:1. The study of impulsive modeling of Chua's chaotic circuit and its controlIt's well known that Chua's circuit, Chua's oscillator and time-delayed Chua's oscillator are typical nonlinear circuits and the first chaotic systems which can be implemented by physical devices. Introducing impulse and design of its controller, we study globally exponential stability of the impulsive model of Chua's oscillator. According to the same idea of impulsive control, we still study stability, asymptotical stability and globally exponential stability of the impulsive model of time-delayed Chua's oscillator.2. Stability study of impulsive control Lorenz chaotic systems familyLorenz chaotic systems family consisting of Lorenz chaotic systems, Chen chaotic systems and Lüchaotic systems, whose mathematical models are presented by three parameters, can be modeled as a united chaotic system with one parameter. In this thesis, we formulate the impulsive model of Lorenz chaotic systems family, and further investigate asmptotical stability of a class of interrelation systems extended by the first chaotic model of Lorenz system by using the Lyapunov function method and the tool of inequalities. We derive explicit relationship between the stability of impulsive control Lorenz chaotic systems family and time-varying impulse interval. 3. Study on impulsive modeling and control of Lurie systems and the nonlinear systems with time-varying delaysWith the structure of impulsive control system, we extend the idea of impulsive control to the general nonlinear control systems with feedback named as Lurie systems and the nonlinear systems with time-varying delays. By constructing the very Lyapunov function and using comparison principle, inequality theorem and linear matrix inequalities (LMIs), we investigate impulsive control of Lurie systems and the nonlinear systems with time-varying delays, and obtain some easy-verified asymptotically stable and globally exponentially stable criteria, further derive the estimate the upper bounds of impulse intervals and time-varying delays for asymptotically stable control.4. Stability study of fuzzy chaotic systems and impulsive fuzzy systems with time-delaysNew Conceptual idea is to introduce impulse and time delay to fuzzy systems. According to the method of center-average defuzzifier and design of parallel distributed compensation (PDC), we introduce time-delayed effect to design a new fuzzy controller based on current state feedback and time-delayed state feedback. By using Lyapunov-Krasovskii functionals and LMIs, we investigate asmptotical stability of this kind of fuzzy chaotic systems. Furthermore, we consider fuzzy and impulsive hybrid modeling of the nonlinear systems, and study globally exponential stability of this kind of impulsive fuzzy system with time delays by using Lyapunov direct method and Schur complement.5. Impulsive modeling of a class of uncertain systems with time-delays and its controlBy introducing impulses to the uncertain systems with time delays, we establish the uncertain hybrid systems based on impulsive model and time-delayed effect, futher study these robust asmptotical stability by the use of Lyapunov direct method and comparison principle, and derive explicit relationship between robust stability and uncertain parameter, impulse interval and time delay. We still can spread the art of impulsive modeling and its control to apply the uncertain nonlinear systems with time-varying delays extensively.