时间周期线性扰动系统零解的稳定性分析  

Stability analysis of the zero solution for time-periodic linear system with small perturbations

作　　者：李卓 李霞 LI Zhuo;LI Xia(School of Mathematics and Physics,SUST,Suzhou 215009,China)

机构地区：[1]苏州科技大学数理学院

出　　处：《苏州科技大学学报（自然科学版）》2019年第2期20-24,共5页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11471238);研究生科研创新计划项目(SKYCX16_011);研究生教育教学改革与研究项目(SKJG16_12)

摘　　要：研究周期线性扰动系统的零解稳定性。通过对周期线性系统性质的研究,可使用寻找非奇异可微周期矩阵的方法,将对周期线性系统性质的研究转化为对常系数线性系统性质的研究,并将常系数线性扰动系统的零解稳定性结论推广至周期线性扰动系统。在一定条件下,当周期线性扰动系统的扰动项是关于||x||的高阶无穷小时,周期线性扰动系统与未扰动系统的零解具有相同的稳定性。最后,给出了文中所得结果的一个应用举例。In this paper,we studied the stability of the zero solution for time-periodic linear perturbed systems. After investigating the properties of periodic linear systems,we applied the method of finding nonsingular and differentiable periodic matrices into the study of the properties of linear systems with constant coefficients. Then we extended the zero solution's stability of the constant coefficient linear system with small perturbation to the periodic linear system with small perturbations. Under the condition that the perturbation term of a periodic linear disturbance system is of a higher order than ||x||, the periodic linear disturbance system has the same stability as the zero solution of the disturbed system. Finally, the result was illustrated.

关 键 词：常系数线性扰动系统 零解稳定性 周期线性扰动系统 

分 类 号：O193[理学—数学]