Studies On The Stability Of Solutions For Several Kinds Of Impulsive Differential System

The paper focuses on the third-order and the forth-order impulsive differential system,by the method of constructing equivalent system and Lyapunov function,the stability for a kind of third-order and forth-order impulsive differential system at fixed times is investigated,stability is obtained for a kind of impulsive differential system at fixed times by the methods involving construction of Lyapunov function,so the drawing of a deduction when p(t)=1 is that the full condition of uniform stability for a generic impulsive differential system at fixed times,further study the impulsive effect on the stability of the system of crucial impact,finally the application of this method is illustrated with some examples.The main content is depicted as follows:1.We introduce the development and research history of the stability of impulsive differential system and the third-order and the forth-order impulsive differential system and generalize the contents of the paper.2.We introduce the concept of impulsive differential system,the definition of stability of the zero solution,the constitution of Lyapunov function and the stability of non-autonomous system which constitute the basis of this theory.3.On the basis of the existing literature,we further study a kind of third-order impulsive differential system,by the method of constructing equivalent system and Lyapunov function,and establish some sufficient conditions for the uniform stability of the zero solution of the system.Then the numerical simulations by Matlab are given to validate the effectiveness of the obtained results.4.We study a kind of forth-order impulsive differential system,by the method of constructing equivalent system and Lyapunov function,and also establish some sufficient conditions for the uniform stability of the zero solution of the system, applicable to the analysis of stability of more high-end impulsive differential system. Then the numerical simulations by Matlab are given to validate the effectiveness of the obtained results.