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Mathematical Problems in Engineering
Volume 2012, Article ID 521675, 15 pages
Research Article

Robust 𝐻 Filtering of 2D Roesser Discrete Systems: A Polynomial Approach

1Laboratory of Electronics, Signal-Systems and Information Science (LESSI), Department of Physics, Faculty of Sciences Dhar El Mehraz, P.O. Box 1796, Fes-Atlas 30000, Morocco
2Department of Systems Engineering and Automatic Control, University of Valladolid, 47005 Valladolid, Spain

Received 5 October 2011; Accepted 23 November 2011

Academic Editor: J. Rodellar

Copyright © 2012 Chakir El-Kasri 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.


The problem of robust 𝐻 filtering is investigated for the class of uncertain two-dimensional (2D) discrete systems described by a Roesser state-space model. The main contribution is a systematic procedure for generating conditions for the existence of a 2D discrete filter such that, for all admissible uncertainties, the error system is asymptotically stable, and the 𝐻 norm of the transfer function from the noise signal to the estimation error is below a prespecified level. These conditions are expressed as parameter-dependent linear matrix inequalities. Using homogeneous polynomially parameter-dependent filters of arbitrary degree on the uncertain parameters, the proposed method extends previous results in the quadratic framework and the linearly parameter-dependent framework, thus reducing its conservatism. Performance of the proposed method, in comparison with that of existing methods, is illustrated by two examples.