Poincaré-Hopf theorem for hybrid systems

Abstract

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).

arXiv comment6 pages, 1 figure, comments welcome. This work has been submitted to the IEEE for possible publication