The Stability Of Nonline Impulsive Dynamic Systems On Time Scales

In this paper, we mainly study the stability properties of the following two nonlinearimpulsive switched systems on time scales:Impulsive dynamic systems on time scales, usually contains some continuous dynamicsubsystems on time scales and given switched mapping, and switches at the impulsivetime.Impulsive switched system is a type of hybrid systems which has the closest rela-tionship with modern control theory, and its application background is wide, for instance,aerospace, transportation, neural networks, secure communication and so on. In recentyears, there has been a growing interest in resereching impulsive switched system, andmany stability results has been obtained. However, the stability results for impul-sive switched system on time scales are still few.Impulsive dynamic systems on time scales can better describe the development ofthings and productive process, which widely exist in the mathmatical model of problemsin several morden science areas. So the study of nonlinear impulsive dynamic systemson time scales has gained wide application background and vital practical significance.In recent years, there are more and more results on the stability of impulsive dynamicsystems on time scales[16-19], but the are few results on the exponential stsbility of thesystem[43]. In chapter one, firstly, we introduce the basic concepts of time scale calculus. sec-ondly, we establish a comparison principle of impulsive switched system on time scales. Atlast, using the comparison principle, we study the stability of impulsive switched systemon time scales (I) and obtain some results, such as (h0, h)?stability, (h0, h)-asymptoticstability, (h0, h)-practical stability, (h0, h)?strictly stability, and an example is givento illustrate the application of the stability theorem. It should be mentioned that thecomparison system can be a impulsive dynamic systems and we can obtain the directresults of stability in terms of two measures.In chapter two, firstly, we introduce the basic concepts of exponential function ontime scales. secondly, we study the exponential stability of impulsive dynamic systemson time scales(II), and obtain some stability criterion of exponential stability. Sincethe time scale theory is the unificaton of discrete and continuous, the stability researchfor impulsive dynamic systems on time scales include the existing exponential stabilityresults. In the end, an example is given to illustrate the application of the theorem.