# Poincar'e-Bendixson Theorem for Hybrid Systems

arXiv: https://arxiv.org/abs/1801.09014 · HTML: https://mlsanity.com/paper/1801.09014/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2018.

## Built on by (most cited first, 1 of 1)

- [Hybrid Systems Neural Control with Region-of-Attraction Planner](https://mlsanity.com/paper/2303.10327/) (2023)

## Abstract (arXiv)

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.