How natural is the definition of the Filippov vector field?

Tomoharu Suda

Published 2019-01-18Version 1

Filippov's method is widely used in the literature to define vector fields on a discontinuity set of piecewise-continuous vector fields. However, it is not the only definition that has been proposed, and its naturalness is not well understood. In this paper, we first provide a general formulation of sliding vector fields and then characterize the Filippov vector field in terms of geometric and dynamical conditions. Our results show that the Filippov vector field follows from natural requirements, and eliminates many possible choices for the definition of the sliding vector field.