Analysis of coordinate and other transformations of models of dynamical systems by the reduction method

被引：0
作者：
S. N. Vassilyev
R. I. Kozlov
S. A. Ul’yanov
机构：
[1] Russian Academy of Sciences,Institute of Control Problems
[2] Siberian Branch of the Russian Academy of Sciences,Institute of System Dynamics and Control Theory
来源：
Proceedings of the Steklov Institute of Mathematics | 2010年 / 268卷
关键词：
differential equations; stability; dissipativity; reduction method; coordinate transformations; vector Lyapunov functions; group control; formation stability;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The issues of preserving dynamic properties when passing from a system of differential equations to another system obtained by a change of variables, as well as the issues of preserving the properties in the opposite direction, are considered. The potential of the reduction method, which was proposed earlier, in resolving these questions are demonstrated by the examples of such properties as stability, attraction, and dissipativity. Similar issues are investigated for the case when the second system is obtained in a way characteristic for the comparison method with vector Lyapunov functions. The application of one of the obtained dissipativity criteria to analyzing the nonlinear dynamics of a group of moving objects is considered.
引用
收藏
页码：264 / 282
页数：18
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