φ₀-Stability Of Solutions Of Nonlinear Impulsive Differential System

This paper mainly uses the cone valued Lyapunov functions and comparison method tostudy the nonlinear impulsive differential system, and obtains several ??0-stability results, thestability theory of the system is more rich, more complete system. This paper is composed offive chapters.The first chapter gives the introduction and prepare knowledge, this paper expounds thesubject of impulsive differential system significance and research status, and simple introducedthe main content of this article. This chapter is the basis of the full text. The second chapterselect proper cone, by using the cone valued Lyapunov functions and comparison method todiscuss the total ??0-stability of zero solution of two measures of the impulsive differential sys-tem. The third chapter select proper cone, by using the cone valued Lyapunov functions andcomparison method to discuss the strict practical ??0-stability of zero solution of two measuresof the impulsive differential system and integral ??0-stability of zero solution of this system. Thefourth chapter select proper cone, by using the cone valued piecewise continuous Lyapunovfunctions, Razumikhin technique and comparison method to discuss the integral ??0-stability ofzero solution of two measures of the impulsive differential systems with “supremum” and anexample is provided to illustrate our results. The fifth chapter, the main contents of this thesisare summarized.