Stability analysis based on nonlinear inhomogeneous approximation

被引：2
作者：
Aleksandrov, A. Yu [1 ]
Platonov, A. V. [1 ]
机构：
[1] St Petersburg State Univ, St Petersburg, Russia
来源：
MATHEMATICAL NOTES | 2011年 / 90卷 / 5-6期
基金：
俄罗斯基础研究基金会;
关键词：
asymptotic stability; Lyapunov function; nonlinear approximation; cascade system; homogeneous function; REDUCTION PRINCIPLE; SYSTEMS;
D O I：
10.1134/S0001434611110198
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The asymptotic stability of zero solutions for essentially nonlinear systems of differential equations in triangular inhomogeneous approximation is studied. Conditions under which perturbations do not affect the asymptotic stability of the zero solution are determined by using the direct Lyapunov method. Stability criteria are stated in the form of inequalities between perturbation orders and the orders of homogeneity of functions involved in the nonlinear approximation system under consideration.
引用
收藏
页码：787 / 800
页数：14
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