非线性脉冲微分系统解的几类ψ0-稳定性.pdfVIP

摘 要 摘 要 本文主要利用锥值Lyapunov 函数和比较方法来研究非线性脉冲微分系统零解的 稳定性, 并取得了几种 -稳定性的结果, 使该系统的稳定性理论更加丰富, 体系更加完 0 整.全文共分为五章. 第一章给 出了引言和预备知识, 简述了脉冲微分系统的课题意义和研究现状, 并 简单介绍了本文的主要内容.本章是全文内容的基础. 第二章选择适当的锥, 利用锥值 Lyapunov 函数和比较方法讨论了脉冲微分系统零解的两度量完全 -稳定. 第三章选择 0 适当的锥, 利用锥值Lyapunov 函数和比较方法讨论了脉冲微分系统零解的两度量严格 实用 -稳定和积分 -稳定. 第四章选择适当的锥, 利用锥值分段连续Lyapunov 函数, 0 0 Razumikhin 技巧和比较方法, 并用实例证明了含上确界的脉冲微分系统零解的两度量积 分 -稳定. 第五章对本篇论文的主要内容进行了简单的总结. 0 关键词 脉冲微分系统 -稳定性 完全稳定性 实用稳定性 积分稳定性 0 I Abstract Abstract This paper mainly uses the cone valued Lyapunov functions and comparison method to study the nonlinear impulsive differential system, and obtains several -stability results, the 0 stability theory of the system is more rich, more complete system. This paper is composed of five chapters. The first chapter gives the introduction and prepare knowledge, this paper expounds the subject of impulsive differential system significance and research status, and simple introduced the main content of this article. This chapter is the basis of the full text. The second chapter select proper cone, by using the cone valued Lyapunov functions and comparison method to discuss the total -stability of zero solution of two measures of the impulsive differential sys- 0 tem. The third chapter select proper cone, by using the cone valued Lyapunov functions and comparison method to discuss the strict practical -stability of zero solution of two measures