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1、?2009020887 ? ? ?15966332156 Email:kdong1987 ? 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?2012?2012? 1 ?10445 ?2009020887 ?O175.21 ? ? ? ? ? ?2012? ? ?. 1 ?. 3 ?. 5 ?. 7 1.1?. 7 1.2?.7 1.3?Lyapunov?.9 1.4?.16 ?. 25 2.1?. 25 2.2?. 25 2.3?. 26 ?h?.41 3.1?. 41 3.2?. 41 3.3h?.43 ?. 55 ?. 56 ?. 60 1 ? ?
2、? (?250014) ? ? x(t) = f(t,x),t t0,t 6= tk,t T x(t+ k) = x(tk) + Ik(x(tk), k = 0,1,2, x(t+ 0) = x0, t0 0,t0 T. (I) ? ? ? ? ? ? ? ? ? ? ?Lyapunov? ? ? Lyapunov? ?Lipschtiz? ? ? ? ? ?Lya- punov?(h0,h)? ?(h0,h)? ? ? ?Lyapunov? ?V? ? ? ? 1 ? ? ? ? ? ? ? ? ? ?h?Lyapunov? ?h?V? ? ? ?Lyapunov?(h0,h) ?(h0,h
3、)?h? ?O175.21 2 ? The Stability Analysis of Impulsive Dynamic Systems on Time Scales Dong Kong School of Mathematical Sciences, Shandong Normal University Jinan, Shandong, 250014, P. R. China ABSTRACT In this paper, we mainly study the stability properties of the following impulsive dynamic systems
4、on time scales: x(t) = f(t,x),t t0,t 6= tk,t T x(t+ k) = x(tk) + Ik(x(tk), k = 0,1,2, x(t+ 0) = x0, t0 0,t0 T. (I) Theory of dynamic systems on time scales,which can unify the continuous and dis- crete systems,has been and are being proved to be of great importance and protential applications in man
5、y fi elds of modern technology,such as biology,fi nancial consumption process,etc.The establishing of mathematical models on time scales gets closer to the actual.At the same time,the impulsive phenomenon widely exists in practical problems of many morden science and technology areas. So the impulsi
6、ve dynamic systems can describe the development of things and productive process better.Stability is one of the most fundamental and most important issue in the investigation of dynamic systems.It should be fi rstly considered in system analysis and control systems design.Since the gen- eral problem
7、 of the stability of motion was introduced by Soviet Union academician Lyapunov,the problem of stability has caused many mathematicians concern.With the development of technology,many new concepts of stability based on the basic stability theories were introduced,such as eventual stability,Lipschitz
8、 stability,strict stability and exponential stability.In recent years, there are more and more results on the stability of dynamic systems on time scales, but there are few results on the stability of impulsive dynamic systems on time scales. So the study of the stability of impulsive dynamic sys- tems o
