Robust \(H_{\infty }\) Filters for Uncertain Systems with Finite Frequency Specifications

  • Abderrahim El-amrani
  • Bensalem BoukiliEmail author
  • Abdelaziz Hmamed
  • El Mostafa El Adel


This paper deals with \(H_{\infty }\) filtering problem of linear discrete-time uncertain systems with finite frequency input signals. The uncertain parameters are supposed to reside in a polytope. By applying the generalized Kalman–Yakubovich–Popov lemma, polynomially parameter-dependent Lyapunov function and some key matrices to eliminate the product terms between the filter parameters and the Lyapunov matrices, an improved condition is obtained for analyzing the \(H_{\infty }\) performance of the filtering error system. Then sufficient condition in terms of linear matrix inequality is established for designing filters with a guaranteed \(H_{\infty }\) filtering performance level. Finally, a numerical examples are used to demonstrate the effectiveness of the proposed method.


Discrete time system Finite frequency GKYP lemma \(H_{\infty }\) Filtering Uncertain systems Linear matrix inequalities (LMIs) 


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Copyright information

© Brazilian Society for Automatics--SBA 2017

Authors and Affiliations

  • Abderrahim El-amrani
    • 1
  • Bensalem Boukili
    • 1
    Email author
  • Abdelaziz Hmamed
    • 1
  • El Mostafa El Adel
    • 2
  1. 1.Department of Physics, Faculty of Sciences Dhar El MehrazUniversity of Sidi Mohamed Ben AbdellahFez-AtlasMorocco
  2. 2.LSIS-UMR 6168University of Paul CzanneAix-MarseilleFrance

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