A POINCARE-BENDIXSON THEOREM FOR HYBRID SYSTEMS

被引：4

作者：

Clark, William ^{[1
]}

Bloch, Anthony ^{[1
]}

Colombo, Leonardo ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA

[2] Inst Ciencias Math CSIC UAM UC3M UCM, C Nicolas Cabrera 13-15, Madrid 28049, Spain

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2020年 / 10卷 / 01期

关键词：

Poincare-Bendixson theorem; hybrid systems; hybrid flows; stability of periodic orbits; Poincare map; MECHANICAL SYSTEMS; ROBOTS;

D O I：

10.3934/mcrf.2019028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Poincare-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincare-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincare return map, a useful object for the stability analysis of hybrid systems. We also prove a Poincare-Bendixson Theorem for a class of one dimensional hybrid dynamical systems.

引用

页码：27 / 45

页数：19

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