Lyapunov Functions for Linear Singularly Perturbed Systems with Marginally Stable Boundary Layer Systems

Singularly perturbed linear systems which have marginally stable boundary layer systems are considered. Conditions are given which assure the existence of Lyapunov functions for these systems. Based on these conditions, criteria are presented which guarantee asymptotic stability or instability for sufficiently small values of the singular perturbation parameter. The results are illustrated by application to a simple flexible mechanical system.