Stabilization of a class of slow-fast control systems at non-hyperbolic points

In this document, we deal with the local asymptotic stabilization problem of a class of slow fast systems (or singularly perturbed Ordinary Differential Equations). The systems studied here have the following properties: (1) they have one fast and an arbitrary number of slow variables, and (2) they have a non-hyperbolic singularity at the origin of arbitrary degeneracy. Our goal is to stabilize such a point. The presence of the aforementioned singularity complicates the analysis and the controller design. In particular, the classical theory of singular perturbations cannot be used. We propose a novel design based on geometric desingularization, which allows the stabilization of a non-hyperbolic point of singularly perturbed control systems. Our results are exemplified on a didactic example and on an electric circuit. (C) 2018 Elsevier Ltd. All rights reserved