Poincar\'e-Bendixson Theorem for Hybrid Systems
Dynamical Systems
2018-01-30 v1 Systems and Control
Optimization and Control
Chaotic Dynamics
Abstract
The Poincar\'e-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 Poincar\'e-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincar\'e return map, a useful object for the stability analysis of hybrid systems. We also prove a Poincar\'e-Bendixson Theorem for a class of one dimensional hybrid dynamical systems.
Keywords
Cite
@article{arxiv.1801.09014,
title = {Poincar\'e-Bendixson Theorem for Hybrid Systems},
author = {William Clark and Anthony Bloch and Leonardo Colombo},
journal= {arXiv preprint arXiv:1801.09014},
year = {2018}
}
Comments
Comments welcome