Poincaré-Hopf theorem for hybrid systems
arXiv:2108.07434v12 citations
Originality Incremental advance
AI Analysis
This work provides a theoretical foundation for analyzing hybrid systems, which are incremental but important for control theory and engineering applications.
The authors tackled the problem of extending the Poincaré-Hopf index theorem to hybrid dynamical systems, achieving a generalization that relaxes assumptions on guard sets, mode dimensions, and resets.
A generalization of the Poincaré-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).