International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 64, Pages 3445-3467

On the uniform exponential stability of linear time-delay systems

M. de la Sen1 and Ningsu Luo2

1Departamento de Ingeniería de Sistemas y Automática, Instituto de Investigación y Desarrollo de Procesos (IIDP), Facultad de Ciencias, Universidad del País Vasco, Leioa (Bizkaia), Aptdo. 644 de Bilbao, Bilbao 48080, Spain
2Departamento de Electronica, Informatica y Automática, Escuela Politecnica Superior, Universidad de Girona, Campus Montilivi, Edificio P4, Girona 17071, Spain

Received 24 September 2003

Copyright © 2004 M. de la Sen and Ningsu Luo. 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 deals with the global uniform exponential stability independent of delay of time-delay linear and time-invariant systems subject to point and distributed delays for the initial conditions being continuous real functions except possibly on a set of zero measure of bounded discontinuities. It is assumed that the delay-free system as well as an auxiliary one are globally uniformly exponentially stable and globally uniform exponential stability independent of delay, respectively. The auxiliary system is, typically, part of the overall dynamics of the delayed system but not necessarily the isolated undelayed dynamics as usually assumed in the literature. Since there is a great freedom in setting such an auxiliary system, the obtained stability conditions are very useful in a wide class of practical applications.