Stability bounds of singularly perturbed delay systems

The stability problem of a linear time-invariant singularly perturbed delay system is considered. A sufficient condition is proposed to guarantee that the delay system is asymptotically stable. Both the time-varying delay and time-invariant delay are discussed. An explicit stability bound is obtained by using a state transformation and the Lyapunov direct method. A numerical example is presented to show the application of the proposed techniques.