Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 356124, 11 pages
Research Article

LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems

A. Hmamed,1 M. Alfidi,1 A. Benzaouia,2 and F. Tadeo3

1Laboratoire d'Electronique, Signaux, Systemes et Informatique (LESSI), Département de Physique, Faculté des Sciences Dhar El Mehraz, B.P. 1796, 30000 Fes-Atlas, Morocco
2Research Unit, Constrained and Robust Regulation, Department of Physics, Faculty of Sciences Semlalia, B.P. 2390, 40000 Marrakech, Morocco
3Departamento de Ingenieria de Sistemas y Automática, Universidad de Valladolid, 47005 Valladolid, Spain

Received 11 May 2007; Revised 1 October 2007; Accepted 8 February 2008

Academic Editor: Pramod Khargonekar

Copyright © 2008 A. Hmamed et al. 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.


Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results.