Asymptotic stability of nonlinear singularly perturbed systems using higher order corrections (Q5903375)

The paper studies stability properties of nonlinear differential equations containing a small parameter \(\epsilon\) in the derivative. The aim is to establish stability criteria on the basis of the low order models obtained for \(\epsilon =0\). The main result has the following form: if the slow and the fast subsystems have appropriately coupled Lyapunov functions, then one can find \(\epsilon^*\) such that for all \(0<\epsilon \leq \epsilon^*\) the origin is a uniformly asymptotically stable equilibrium and a certain expression is a Lyapunov function for the original system. As an application, this result is adapted to a simpler system that is linear in the fast variable. Some examples show that the obtained estimation of the stability improves older results.