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Mathematical Problems in Engineering
Volume 2017, Article ID 7354654, 25 pages
Review Article

Recent Progress in Stability and Stabilization of Systems with Time-Delays

Systems Engineering Department, KFUPM, P.O. Box 5067, Dhahran 31261, Saudi Arabia

Correspondence should be addressed to Magdi S. Mahmoud; as.ude.mpufk@duomhamsm

Received 8 November 2016; Accepted 7 March 2017; Published 13 June 2017

Academic Editor: Sabri Arik

Copyright © 2017 Magdi S. Mahmoud. 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 overviews the research investigations pertaining to stability and stabilization of control systems with time-delays. The prime focus is the fundamental results and recent progress in theory and applications. The overview sheds light on the contemporary development on the linear matrix inequality (LMI) techniques in deriving both delay-independent and delay-dependent stability results for time-delay systems. Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. Key technical bounding lemmas and slack variable introduction approaches will be presented. The results will be compared and connections of certain delay-dependent stability results are also discussed.