The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag

This paper is concerned with the exponential stability of singularly perturbed delay differential equations with a bounded (state-independent) lag. A generalized Halanay inequality is derived in Section 2, and in Section 3 a sufficient condition will be provided to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is exponentially stable uniformly for sufficiently small ε>0. This type of exponential asymptotic stability can obviously be applied to general delay differential equations with a bounded lag.