Asymptotic Analysis of Spectrum and Stability for One Class of Singularly Perturbed Neutral-Type Time-Delay Systems

In this study, a singularly perturbed linear time-delay system of neutral type is considered. It is assumed that the delay is small of order of a small positive parameter multiplying a part of the derivatives in the system. This system is decomposed asymptotically into two much simpler parameter-free subsystems, the slow and fast ones. Using this decomposition, an asymptotic analysis of the spectrum of the considered system is carried out. Based on this spectrum analysis, parameter-free conditions guaranteeing the exponential stability of the original system for all sufficiently small values of the parameter are derived. Illustrative examples are presented.