不动点定理和时滞微分系统的渐近稳定性  

The Fixed Point Theorem and Asymptotic Stability of a Delay-differential System

作　　者：丁黎明[1,2] 全建兵[3] 张颖[4] 李志祥[2] 

机构地区：[1]空军雷达学院黄陂校区,武汉430019 [2]国防科学技术大学理学院,长沙410073 [3]解放军信息工程大学电子技术学院,广州510510 [4]空军雷达学院基础部,武汉430019

出　　处：《空军雷达学院学报》2009年第3期203-204,209,共3页Journal of Air Force Radar Academy

摘　　要：通过一个限制函数和线性系统的矩阵测度满足的几个不等式,利用概念和压缩映射原理研究了一类时滞微分系统的零解的渐近稳定性,将已有的一维扰动方程的稳定性结果推广到了高维系统,补充了该领域研究的某些成果.最后给出了一个例子,且与Liapunov方法的相应结果作了比较.The asymptotic stability of the zero solution of a delay-differential system was investigated by means of the matrix measure and the contraction mapping principle through a restriction function and several inequalities satisfied with the matrix measure of a linear system. The result of one-dimensional perturbed equation was generalized to the multi-dimensional system, some research results obtained in the field was supplemented. Finally, an example was given to illustrate the result and make a comparison with the result of Liapunov method.

关 键 词：不动点 时滞微分系统 渐近稳定 矩阵测度 压缩映射原理 

分 类 号：O175.1[理学—数学]