In the latter part of this paper , by using lyapunov direct method and adding some conditions on the controlling function of the derivate of lyapunov function , we get some sufficient conditions of stability and unstability for impulsive differential system 后半部分主要运用了李雅普诺夫直接方法，并对李雅普诺夫函数导数的控制函数加以限制，得到了脉冲微分系统稳定性及不稳定性的若干充分条件
Using variational lyapunov method and comparison principle , some results of ultimate stability of perturbed differential systems through the corresponding ultimate stability properties of the unperturbed differential systems and the comparative system are gotten 摘要变分李雅普诺夫函数方法和比较原则相结合，利用无摄动脉冲微分系统和比较系统的最终稳定性性质得到了脉冲摄动微分系统最终稳定的若干结果。
In the former part of this paper , mainly by virtue of variational lyapunov method , under the comparison theorem , we discuss the boundedness and stability in terms of two measures of the perturbed differential equations with impulsive effects and establish some criteria on the properties of solutions of the perturbed differential equations with impulsive effects , such as boundedness in terms of two measures , stability in terms of two measures )两个测度的有界性和稳定性，建立了一些关于有界性，稳定性的判别准则文章的前半部分我们主要借助于变分李雅普诺夫函数方法的思想，在比较定理的基础上讨论了脉冲摄动微分系统( 1 )两个测度的有界性和稳定性。
Finally , in the fourth chapter , by constructing liapunov functional , we study a discrete two - dimensional predator prey - system with a finite number of delay , the similar conclusions to the continuous case are obtained . that is , the time delays are harmless for permanence of the solution of the system 在第四章，通过构造李雅普诺夫函数，我们研究了在有限滞量背景下的二维离散食饵-捕食者系统，得到了与连续情形类似的结论，即我们证明了时滞对所研究系统解的持久性没有影响。
In this dissertation , we discuss the perturbed differential system with impulsive effects as follows : mainly by using variational lyapunov method and lyapunov direct method , we discuss the boundedness and stability in terms of two measures of the perturbed impulsive differential equations ( 1 ) and establish some criteria on boundedness and stability 在这篇论文中，我们主要研究如下脉冲摄动微分系统：文中主要利用变分李雅普诺夫函数方法和李雅普诺夫直接方法的思想，讨论了脉冲摄动微分系统(
Based on this characterization , we improve the theoretic result which is the foundation of lyapunov backstepping design . the problem that how to construct a control lyapunov function from a weak lyapunov function is a significant one , because the successful reconstruction implies that robust analysis and design can be probed in depth . for affine nonlinear systems , we present a sufficient reconstruction condition and interpretate the constructing procedure by typical examples 刻画一类存在半正定弱李雅普诺夫函数的全局渐近稳定系统，并用所得结果改进了李雅普诺夫递推设计的一个重要理论依据；如何由弱李雅普诺夫函数重构控制李雅普诺夫函数，是一个十分重要的问题，因为成功的重构意味着可以进行深入的鲁棒分产摘要析与设计，针对仿射系统我们给出了可以重构的充分条件，并用典型例子说明了构造过程
Since sontag - type control based on control lyapunov function is an important control law in robust stabilization of affine systems , we point out that is a kind of variable structural control in essence . due to this recognition and the fact that control lyapunov functions are difficult to be constructed , we propose the concept of weak control lyapunov function and then prove the stabilizing property and the robustness of sontag - type control . using the way of proposing the control lyapunov function and the special structure of sontag - type control , we investigate the dissipassivation control of a kind of perturbed nonlinear systems 基于控制李雅普诺夫函数的sontag - type控制，是仿射系统鲁棒镇定研究中一种非常重要的控制律，通过研究我们发现，该控制律实质上是一种变结构控制；基于这一认识，也考虑到控制李雅普诺夫函数难于构造，我们抽象出弱控制李雅普诺夫函数概念，并证明了基于弱控制李雅普诺夫函数的sontag - type控制的镇定作用和优化特性；借鉴控制李雅普诺夫函数的抽象方式以及sontag - type控制的特殊结构，探讨了一类受扰系统的耗散化控制；探讨了齐性度理论与控制李雅普诺夫函数相结合的镇定设计问题。
