Slow–fast systems and sliding on codimension 2 switching manifolds

Abstract

ABSTRACTIn this work, we consider piecewise smooth vector fields X defined in , where Σ is a self-intersecting switching manifold. A double regularization of X is a 2-parameter family of smooth vector fields , satisfying that converges uniformly to X in each compact subset of when . We define the sliding region on the non-regular part of Σ as a limit of invariant manifolds of . Since the double regularization provides a slow–fast system, the GSP-theory (geometric singular perturbation theory) is our main tool.