Area contraction in the presence of first integrals and almost global convergence

Aeyels  D; De Smet  F; Langerock  B

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Area contraction in the presence of first integrals and almost global convergence

机译：Area contraction in the presence of first integrals and almost global convergence

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摘要

We investigate the evolution of the area of multi-dimensional surfaces along the flow of a dynamical system with known first integrals, and we formulate sufficient conditions for area contraction. These results, together with known results about the Hausdorff dimension and the box-counting dimension of invariant sets, are applied to systems exhibiting almost global convergence/asymptotic stability. This leads to a generalization of a well-known result on almost global convergence of a system, based on the use of density functions. We conclude with an example.

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来源
《Discrete and continuous dynamical systems》 |2007年第1期|135-157|共23页
作者
Aeyels D; De Smet F; Langerock B;
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作者单位

Univ Ghent, Dept Elect Energy Syst & Automat, Syst Res Grp, B-9052 Ghent, Belgium;

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原文格式 PDF
正文语种英语
中图分类理论力学（一般力学）;
关键词
k-contracting vector fields; Hausdorff dimension; first integrals; almost global convergence; HAUSDORFF DIMENSION; INVARIANT-SETS;

Area contraction in the presence of first integrals and almost global convergence

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