This paper presents the numerical analysis of the Nonlinear Subgrid Scale (NSGS) model for approximating singularly perturbed transport models. The NSGS is a free parameter subgrid stabilizing method that introduces an extra stability only onto the subgrid scales. This new feature comes from the local control yielded by decomposing the velocity field into the resolved and unresolved scales. Suc...

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have one fast variable and an arbitrary number of slow variables, 2) they have a non-hyperbolic singularity of the fold type at the origin. The presence of the a...

Singularly perturbed delay differential equations arising from the regularization of state dependent neutral delay equations are considered. Much insight into the solution of the regularized problem and into its limit for ε→ 0+ is obtained by the study of asymptotic expansions. Due to discontinuities in the derivative of the solution of the neutral delay equation and the presence of different t...

We treat the problem of robustness of output feedback controllers with respect to singular perturbations. Given a singularly perturbed control system whose boundary layer system is exponentially stable and whose reduced order system is exponentially stabilizable via a (possibly dynamical) output feedback controller, we present a sufficient condition which ensures that the system obtained by app...