Complete Stability Analysis of Neutral‐Type First Order Two‐Time‐Delay Systems with Cross‐Talking Delays

Abstract

The stability robustness of first order linear time invariant dynamics of neutral type with multiple time delays against delay uncertainties is taken into consideration. We depart from a simpler investigation of Hale and Huang [J. Math. Anal. Appl., 178 (1993), pp. 344–362], which studies the same problem for retarded‐type systems. On this basis we further introduce two challenging features by including (a) terms that add neutral dynamics and (b) an additional term that introduces cross‐talk between the multiple delays. To the best of the authors’ knowledge, the stability posture of this class of systems can be treated only by a unique procedure. It is known as cluster treatment of characteristic roots (CTCR), which was recently developed for retarded‐type dynamics. We first show the applicability of CTCR to the stability analysis of neutral‐type multiple‐delay dynamics. Next, we prove the well‐known “small‐delay” phenomenon for the dynamics at hand, interestingly, as a natural by‐product of the CTCR paradigm. Finally, we present several case studies to display the steps and the strengths of CTCR. This deployment is scalable to treat similar problems with higher order dynamics, which have direct ramifications to some practical control applications.