Analysis And Application Of Hybrid Dynamic Systems

A complex hybrid dynamic system is made up of some continuous variable processesand some discrete event processes which occur alternately and interact. Based on switchedmodel, this thesis mainly studies some control problems of hybrid dynamic systems, such asasymptotic stability, robust stability, impulsive control, state-back control, H∞ control,controllability, observability etc. Hybrid dynamic systems are widely applied to the areas ofmanagement and control of complex systems, communication networks, artificalintelligence, numerical control systems, design of automatic driving etc. In particular, theapplication to secure communication is more and more focused on recently. Firstly, the background and basic control theories of hybrid dynamic systems aresimply introduced. A new mathematic model, named impulse switched systems, is presentedfor the systems under impulse control or accompanied with switching impulse at theswitching points. By Lyapunov function method, some sufficient conditions of asymptoticstability and robust stability of this system are obtained; By H∞ control method, the innerstability and γ performance of this system is studied and a robust controller based onMATLAB soft is designed; Some controllability and observability theories are introduced,several sufficient conditions of the controllability of this system are presented, and thensome numerical examples are worked to illustrate the efficiency of the main results. Hybriddynamic systems are a class of very complicated nonlinear systems and can generate chaosby chosen switching rules. Based on Chua's circuit, the principle of generating chaos andchaos dynamic behaviors are analyzed in detail. Then, some theories and methods of chaossynchronization are illuminated and some projects, by which the chaos synchronization canbe realized in secure communication, are introduced. Finally, the thesis simply summarizesthe research work of our laboratory on secure communication systems based on chaossynchronization. This thesis is based on the theories of switched systems and mainly studies a class ofimpulse switched systems. In the end, A brief summary has been done for all discussion inthe thesis. The farther research trend on hybrid dynamic systems is presented.