  In this paper we consider the problem of determining the stability
properties, and in particular assessing the exponential stability, of a
singularly perturbed linear switching system. One of the challenges of this
problem arises from the intricate interplay between the small parameter of
singular perturbation and the rate of switching, as both tend to zero. Our
approach consists in characterizing suitable auxiliary linear systems that
provide lower and upper bounds for the asymptotics of the maximal Lyapunov
exponent of the linear switching system as the parameter of the singular
perturbation tends to zero.
