Stability And Application Of Discrete Impulsive Systems

In the recent years, with development of human's congnitive ability and computer science, the varies complex systems are studied. These systems exist in nature science and human society. On one hand, we can enhance cognitive ability of such systems, and make use of these systems. On the other hand, some characteristics of these systems , such as chaos, have vast application.Impulsive system become an important study area, since it can describe system that has impulsive changes. At the same time, hybrid systems gain more and more attentions. These two area attract scientist from applied mathematics, computer science, system engineering and so on.For these reason, uncertain discrete impulsive systems and switched systems are studied in this paper.Robust stability of uncertain discrete impulsive systems are studied. Criterion for robust stability and robust control of the uncertain linear discrete impulsive systems and a type of uncertain unlinear discrete impulsive systems are obtained by using Lyapunov direct method with careful estimation.Robust stability and robust control of linear uncertain discrete impulsive switched systems are studied. We first establish criterion for a general systems. Length of impuse interval is considered in these criterion. Then, we get some Criterion for linear uncertain discrete impulsive systems by using these criterion. These criterion are describe using LMIs which can be easily calculated and testified in MATLAB and other software. We also give out the construction method of the feedback controller which guarantee the robust stabiliy of the system. The method dependent on a series LMIs and can be easil solved in mathematical software. This make the theorem easy to use.A type of unlinear uncertain discrete impulsive switched systems is also studied in this paper.The criterion are derived.Robust H_∞control are studied in this paper. We also design a feedback controller to guarantee the robust stablity and performance index of the system. Impusive synchronization of discrete chaotic systems are also studied in this paper for the reason that it can be used in secure communication. Exponential stability are studied , and criterion are obtained.A new synchronization strategy for discrete chaos are introduced which may increase security of the comunication. We established Algorithm for discrete chaos sychronization by using such methods.