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arXiv · 1801.09014

Poincar\'e-Bendixson Theorem for Hybrid Systems

William Clark·Anthony Bloch·Leonardo Colombo
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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.

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William Clark, Anthony Bloch, Leonardo Colombo. 2018-01-27. Poincar\'e-Bendixson Theorem for Hybrid Systems. https://arxiv.org/abs/1801.09014

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