Mathematical Problems in Engineering
Volume 2003 (2003), Issue 4, Pages 137-152

Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

D. Mehdi1 and E. K. Boukas2

1Laboratoire d'Automatique et d'Informatique Industielle LAII-ESIP, Université de Poitiers, 40 avenue du Recteur Pineau, Poitiers Cedex 86022, France
2Départment de Génie Mecanique, École Polytechnique de Montréal, C.P. 6079 Succursale Centre-Ville, Montréal H3C 3A7, Québec, Canada

Received 13 June 2002; Revised 13 January 2003

Copyright © 2003 D. Mehdi and E. K. Boukas. 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 class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.