Multidim Syst Sign Process DOI 10.1007/s11045-013-0242-7 Robust H ∞ filtering for uncertain two-dimensional continuous systems with time-varying delays Chakir El-Kasri · Abdelaziz Hmamed · El Houssaine Tissir · Fernando Tadeo Received: 4 June 2012 / Revised: 12 July 2013 / Accepted: 15 July 2013 © Springer Science+Business Media New York 2013 Abstract This paper deals with the problem of delay-dependent robust H ∞ filtering for uncertain two-dimensional (2-D) continuous systems described by Roesser state space model with time-varying delays, with the uncertain parameters assumed to be of polytopic type. A sufficient condition for H ∞ noise attenuation is derived in terms of linear matrix inequalities, so a robust H ∞ filter can be obtained by solving a convex optimization problem. Finally, some examples are provided to illustrate the effectiveness of the proposed methodology. Keywords 2-D continuous systems · Uncertainty · Delayed states · H ∞ filtering · Linear matrix inequality (LMI) 1 Introduction The noise filtering problem is known to play an important role in signal processing and other applications (Feng et al. 2012; Idczak and Majewski 2012; Klamka 1997a,b). In the last few years, delay-dependent and delay-independent designs for filters have been proposed: see, This work is funded by AECI AP/034911/11 and MiCInn DPI2010-21589-c05. C. El-Kasri · A. Hmamed · E. H. Tissir LESSI, Department of Physics, Faculty of Sciences Dhar El Mehraz, BP 1796, Fes, Atlas, Morocco e-mail: chakir_elkasri@yahoo.fr A. Hmamed e-mail: hmamed_abdelaziz@yahoo.fr E. H. Tissir e-mail: elh_tissir@yahoo.fr F. Tadeo (B ) Department of Systems Engineering and Automatic Control, University of Valladolid, 47005 Valladolid, Spain e-mail: fernando@autom.uva.es 123