Applications Of Averaging Method For Some Nonlinear Differential Systems

Averaging method played an important role in many fields such as mechanics,control theory.Averaging method was still unfolding,and a lot of researches were needed.In this thesis,using averaging method,we mainly studied initial value problems and boundary value problems for several classes of nonlinear differential systems.The main content of this paper consisted of four parts.In part one,we expounded the background and development of our questions,summarized some results which current scholars had achieved in these aspects,then briefly introduced the organization of this thesis.In part two,averaging method was used to investigate a class of dynamical systems with uncertain values of parameters.Some criterions of the asymptotic stability of the system via analytical skills were obtained.Moreover,an example was given to illustrate our main results.In part three,we introduced averaging schemes for boundary value problem of set differential equations with small parameter.Secondly,we proved the asymptotical behavior between the solution of set differential equations and the solution of the associated averaged one.Finally,an example was given to illustrate the applicability of the conclusion.In part four,we substantiated the applicability of some averaging schemes to fuzzy control set differential systems with a small parameter.Thereby we expanded a circle of systems to which it was possible to apply averaging method.