The Moments Sliding Vector Field on the Intersection of Two Manifolds

In this work, we consider a special choice of sliding vector field on the intersection of two co-dimension 1 manifolds. The proposed vector field, which belongs to the class of Filippov vector fields, will be called moments vector field and we will call moments trajectory the associated solution trajectory. Our main result is to show that the moments vector field is a well defined, and smoothly varying, Filippov sliding vector field on the intersection Σ of two discontinuity manifolds, under general attractivity conditions of Σ. We also examine the behavior of the moments trajectory at first order exit points, and show that it exits smoothly at these points. Numerical experiments illustrate our results and contrast the present choice with other choices of Filippov sliding vector field.