Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 87062, 19 pages

Stabilization criteria for continuous linear time-invariant systems with constant lags

M. De La Sen

Departamento de Electricidad y Electrónica, Instituto de Investigación y Desarrollo de Procesos (IIDP), Facultad de Ciencias, Universidad del País Vasco, Leioa (Bizkaia), Aptdo, 644 de Bilbao 48080-Bilbao, Spain

Received 1 July 2005; Accepted 10 October 2005

Copyright © 2006 M. De La Sen. 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.


Some criteria for asymptotic stability of linear and time-invariant systems with constant point delays are derived. Such criteria are concerned with the properties of robust stability related to two relevant auxiliary delay-free systems which are built by deleting the delayed dynamics or considering that the delay is zero. Explicit asymptotic stability results, easy to test, are given for both the unforced and closed-loop systems when the stabilizing controller for one of the auxiliary delay-free systems is used for the current time-delay system. The proposed techniques include frequency domain analysis techniques including the use of H norms.