Sliding motion on tangential sets of Filippov systems

Abstract

We consider piecewise smooth vector fields Z = (Z + , Z − ) defined in R n where both vector fields are tangent to the switching manifold Σ along a manifold M . Our main purpose is to study the existence of an invariant vector field defined on M , that we call tangential sliding vector field. We provide necessary and sufficient conditions under Z to characterize the existence of this vector field. Considering a regularization process, we proved that this tangential sliding vector field is topological equivalent to an invariant dynamics under the slow manifold. The results are applied to study a Filippov model for intermittent treatment of HIV.