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Reduced-Order H ∞ Filters for Uncertain 2-D Continuous Systems, Via LMIs and Polynomial Matrices

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Abstract

This paper deals with designing H ∞ filters of reduced order for two dimensional (2-D) continuous systems described by Roesser models, with uncertain state space matrices. These filters are characterized in terms of linear matrix inequalities (LMI), to minimize a bound on the H ∞ noise attenuation, by using homogeneous polynomially parameter-dependent matrices of arbitrary degree. The methodology is also particularized for full order and zero order (static) filters, where more simple LMI conditions are derived. Numerical examples are presented to illustrate the proposed methodology.

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Acknowledgements

This work is funded by AECI A/030426/10, AP/034911/11 and MiCInn DPI2010-21589-c05-05.

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Authors and Affiliations

  1. Department of Physics, Faculty of Sciences Dhar El Mehraz, LESSI, BP 1796, Fes-Atlas, Morocco

    Chakir El-Kasri & Abdelaziz Hmamed

  2. Department of Systems Engineering and Automatic Control, University of Valladolid, 47005, Valladolid, Spain

    Fernando Tadeo

Authors
  1. Chakir El-Kasri
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  2. Abdelaziz Hmamed
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  3. Fernando Tadeo
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Correspondence to Fernando Tadeo.

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El-Kasri, C., Hmamed, A. & Tadeo, F. Reduced-Order H ∞ Filters for Uncertain 2-D Continuous Systems, Via LMIs and Polynomial Matrices. Circuits Syst Signal Process 33, 1189–1214 (2014). https://doi.org/10.1007/s00034-013-9689-x

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  • DOI: https://doi.org/10.1007/s00034-013-9689-x

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