Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 87062, 19 pages
doi:10.1155/DDNS/2006/87062
Stabilization criteria for continuous linear time-invariant systems with constant lags
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.
Abstract
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.