Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 725783, 46 pages
Review Article

A Review of Some Subtleties of Practical Relevance for Time-Delay Systems of Neutral Type

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA

Received 15 August 2012; Accepted 11 October 2012

Academic Editors: S. W. Gong and W. Yeih

Copyright © 2012 Keqin Gu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper reviews some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The framework prsented in this paper makes it possible to provide simpler formulation and strengthen, generalize, or provide alternative interpretation of the existing results.