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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 42489, 10 pages
http://dx.doi.org/10.1155/MPE/2006/42489

Discrete-time systems with time-varying time delay: Stability and stabilizability

Département de Génie Mécanique, École Polytechnique de Montréal, C.P. 6079, succ. Centre-Ville, Montréal, QC, Canada H3C 3A7

Received 7 December 2005; Accepted 2 January 2006

Copyright © 2006 El-Kébir 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.

Abstract

This paper deals with the class of linear discrete-time systems with varying time delay. The problems of stability and stabilizability for this class of systems are considered. Given an upper bound and a lower bound on the time-varying delay, sufficient conditions for checking the stability of this class of systems are developed. A control design algorithm is also provided. All the results developed in this paper are in the LMI formalism which makes their solvability easier using existing tools. A numerical example is provided to show the effectiveness of the established results.