Global asymptotic stability analysis by the localization method of invariant compact sets
- 作者: Krishchenko A.P.1,2
-
隶属关系:
- Bauman Moscow State Technical University
- Institute for Systems Analysis
- 期: 卷 52, 编号 11 (2016)
- 页面: 1403-1410
- 栏目: Ordinary Differential Equations
- URL: https://journal-vniispk.ru/0012-2661/article/view/154145
- DOI: https://doi.org/10.1134/S0012266116110021
- ID: 154145
如何引用文章
详细
We study the asymptotic stability and the global asymptotic stability of equilibria of autonomous systems of differential equations. We prove necessary and sufficient conditions for the global asymptotic stability of an equilibrium in terms of invariant compact sets and positively invariant sets. To verify these conditions, we use some results of the localization method for invariant compact sets of autonomous systems. These results are related to finding sets that contain all invariant compact sets of the system (localizing sets) and to the behavior of trajectories of the system with respect to localizing sets. We consider an example of a system whose equilibrium belongs to the critical case.
作者简介
A. Krishchenko
Bauman Moscow State Technical University; Institute for Systems Analysis
编辑信件的主要联系方式.
Email: apkri@bmstu.ru
俄罗斯联邦, Moscow; Moscow
补充文件
