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Mathematical Problems in Engineering
Volume 2008, Article ID 875609, 15 pages
Research Article

Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

1Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), Campus Divinópolis, Rua Monte Santo 319, Divinópolis 35502-036, MG, Brazil
2Colégio Técnico (COLTEC), Universidade Federal de Minas Gerais (UFMG), Av. Antônio Carlos 6627, Belo Horizonte 31270-901, MG, Brazil

Received 29 June 2007; Revised 17 November 2007; Accepted 4 February 2008

Academic Editor: T. Runolfsson

Copyright © 2008 Valter J. S. Leite and Márcio F. Miranda. 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.


Sufficient linear matrix inequality (LMI) conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.