Poincar\'{e}-Hopf theorem for hybrid systems
Dynamical Systems
2024-10-28 v1 Robotics
Algebraic Topology
Abstract
A generalization of the Poincar\'{e}-Hopf index theorem applicable to hybrid dynamical systems is obtained. For the hybrid systems considered, guard sets are not assumed to be smooth; distinct "modes" are not assumed to have constant dimension; and resets are arbitrary multivalued maps (relations).
Keywords
Cite
@article{arxiv.2108.07434,
title = {Poincar\'{e}-Hopf theorem for hybrid systems},
author = {Matthew D. Kvalheim},
journal= {arXiv preprint arXiv:2108.07434},
year = {2024}
}
Comments
6 pages, 1 figure, comments welcome. This work has been submitted to the IEEE for possible publication