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.
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页码：27 / 45
页数：19
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