The Analysis of Exact Frequency Spectra and Stability of First-order Neutral Systems with Two Delays

This paper aims at the asymptotic stability analysis of a general class of first-order linear-time-invariant neutral time-delay systems (LTI-NTDS). The concept of small delay effect, which reveals the underlying difference between NTDS and retarded time-delay systems (RTDS) is firstly introduced. NTDS manifests an elusive stability property, due to this unique feature, therefore, it is proposed to address in this paper by deploying a novel frequency-domain approach called Dixon resultant theory, along with the so-called Cluster Treatment of Characteristic Roots (CTCR) paradigm. The proposed method is shown, for the first time in the literature, very effective and efficient for the stability analysis of LTI-NTDS. Finally, an example case study is presented to prove the feasibility and strength of the proposed method.