The impulsive hybrid differential system studied in this paper is a special but important case of impulsive differential systems with variable structure , its characteristic is that its equations in different time periods may be different and the equation in the latter depends on the former 本文所讨论的脉冲混合微分系统是一类特殊的但很重要的具有可变结构的脉冲微分系统，它的特点就是不同时间段内微分系统可以不同，并且后一时间段的系统依赖于前一时间段。
Base on this idea , we give a series of sufficient conditions to determine stability properties of impulsive differential systems . firstly , we discuss stability of impulsive hybrid system . then we obtained the comparison results on stability and eventually uniform stability in terms of two measures for the above system 基于这些思想，本文给出了一系列充分条件以判别脉冲混合微分系统的稳定性以及结合比较定理给出了系统关于两个测度的稳定性和最终稳定性结果。
So far , the results about its stability and boundedness are few . in this paper , we apply lyapunov ' s direct method and comparison principle in impulsive hybrid differential systms to get some new results about practical stability , integral stability and boundedness in terms of two measures 到目前为止，有关该系统的稳定性和有界性结果并不多见，本文把lyapunov直接方法和比较方法应用到脉冲混合系统上得到了该系统关于两个测度的实际稳定性、积分稳定性和有界性结果。
In this dissertation , we study some stability properties for two impulsive differential systems employing lyapunov ' s second method : one system is impulsive hybrid differential system : the other is differertial system with impulses at variable time : herein these stability results do not require a lyapunov function to have a negative definite first derivative along trajectories of the system , further we may not require its derivative to restrict the function increasing growth ; and we do not give conditions on continuous portion or discrete portion of the systems respective ! } " , hence we can give mixing conditions on them 在这篇硕士学位论文中，我们主要借助lyapunov第二方法的思想，讨论了两类脉冲微分系统：脉冲混合微分系统和具有依赖于状态脉冲的微分系统的稳定性问题。不同于以往的研究，本文所找的lyapunov函数沿系统轨线的一阶导数不再局限于常负或定负，甚至不用其导数来限制其增长速度；不再局限于对离散或连续部分分别设置条件，而是对其离散和连续部分设置混合条件。
