Geometric homogeneity with applications to finite-time stability

被引：1373

作者：

Bhat, SP ^{[1
]}

Bernstein, DS

机构：

[1] Indian Inst Technol, Dept Aerosp Engn, Bombay 400076, Maharashtra, India

[2] Univ Michigan, Dept Aerosp Engn, Ann Arbor, MI 48109 USA

来源：

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2005年 / 17卷 / 02期

关键词：

geometric homogeneity; homogeneous systems; stability; finite-time stability; Lyapunov theory;

D O I：

10.1007/s00498-005-0151-x

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper studies properties of homogeneous systems in a geometric, coordinate-free setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes it possible to extend previous results on homogeneous systems to the geometric framework. As an application of our results, we consider finite-time stability of homogeneous systems. The main result that links homogeneity and finite-time stability is that a homogeneous system is finite-time stable if and only if it is asymptotically stable and has a negative degree of homogeneity. We also show that the assumption of homogeneity leads to stronger properties for finite-time stable systems.

引用

页码：101 / 127

页数：27

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