Theory And Application Of Impulsive System

There are many systems and natural processes which display some kinds of dynamic behavior in a style of both continuous and discrete characteristics. The states of these systems are characterized by abrupt changes at certain time instants. This is the familiar impulsive phenomenon. Often, sudden and sharp changes occur instantaneously, in the form of impulses, which cannot be well described by using pure continuous or pure discrete models. The impulsive systems arisen naturally can be used as an appropriate description of these phenomena of abrupt dynamical changes of states in this kind of systems. The study of the theory for impulsive systems started from 60's of 20 century. Since recent 30 years, impulsive system has received significant attention for many mathematics and control theory researchers due to a great potential of applications in real world. Significant progress has been made in the theory of impulsive systems in recent 20 years. Since 80's of 20 century, with the rapid development of computation science, impulsive control technique based on the theory of impulsive systems has been made great progress due to simpler to implement and cheaper mechanism and that there are many cases in which impulsive control can give better performance than continuous control, which is tested by practice.Stability is the most important characteristic which should be satisfied at first. A few theorems are obtained and used here.It is realized that robustness analysis of uncertain systems is an important subject in control theory by the end of 70's of 20 century. Based on a review of its current condition of research and development home and abroad and its potential huge applications, the robustness analysis of uncertain impulsive systems and its application researches have been studied thoroughly in this dissertation.Controlability is one of the most important characteristics, while such researches for impulsive system are few up to now. Especially, the resules are confused to select which is the best. So optimization is another problem here. Controlability and optimization are studied based on home and abroad research.As the application of impulsive theory, we present an example. We first study the synchronization in chaotic system via the impulsive control. Then we make a simulation about the chaotic secure communication. The example shows the practicability, and it also validates our conclusions in the dissertation.