A stability study on first-order neutral systems with three rationally independent time delays

Abstract

First-order linear time invariant and time-delayed dynamics of neutral type is taken into account with three rationally independent delays. There are two main contributions of this study. (a) It is the first complete treatment in the literature on the stability analysis of systems with three delays. We use a recent procedure, the cluster treatment of characteristic roots (CTCR), for this purpose. This procedure results in an exact and exhaustive stability tableau in the domain of the three delays. (b) It provides a proof of a complex concept called the delay-stabilisability (also known as strong stability) as a by-product of CTCR. Furthermore, we deploy a numerical method (infinitesimal generator approach) to approximate the dominant characteristic roots of this class of systems, which concur with the stability outlook generated by CTCR.

Keywords:

• asymptotic stability
• feedback control
• time-delay systems
• linear systems
• multiple delays

Acknowledgement

This research has been supported in part by the awards from DoE (DE-FG02-04ER25656) and NSF (CMS-0439980) and (DMI-0522910).