Exponential stability for singularly perturbed systems with state delays

Abstract

In this paper the problem of stability of the zero solution of singularly perturbed system of linear differential equation with state delays is investigated. We show that if the zero solution of reduced subsystem and the one of the fast subsystem are exponentially stable, then the zero solution of the given singularly perturbed system of differential equations is also exponentially stable. Estimates of the block components of the fundamental matrix solution are derived. These estimates are used to obtain asymptotic expansions on unbounded interval for the solutions of this class of singularly perturbed systems.