Unknown Input Proportional Integral Observer Design for Chaotic TS Fuzzy Models

  • T. Youssef
  • Mohammed Chadli
  • Ivan Zelinka
  • M. Zelmat
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 210)


In this paper, the chaos synchronization problem is treated by an unknown input proportional integral observer (PIO) for a Takagi-Sugeno (TS) fuzzy chaotic model subject to unknown input and unmeasurable decision variables. This unknown input is considered like a message to encode by a chaotic system then to decode or to reconstruct by the PIO after to be transmitted by a public transmission canal in order to a secure communication system. In our case, the unknown input affects both state and output of the chaotic system. The synthesis conditions of this PIO are based on the hypothesis that the unknown input is under polynomial form with its kth derivative zero. At the end the measurable decision variables are also considered in this work like a particular case. The Lyapunov theory is used to develop the stability conditions of the unknown input PIO in LMIs formulation. A simulation example is proposed through a TS fuzzy chaotic model to validate the proposed design.


TS fuzzy models Unmeasurable decision variables Unknown input reconstruction Proportional Integral Observer Synchronization Chaotic system 


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • T. Youssef
    • 2
  • Mohammed Chadli
    • 1
  • Ivan Zelinka
    • 3
  • M. Zelmat
    • 2
  1. 1.The Laboratory of Modeling, Information & Systems (MIS)University of Picardie Jules Verne (UPJV)Amiens Cedex 1France
  2. 2.The Laboratory of Automatic Applied (LAA)M’hamed Bougara University of Boumerdés (UMBB)BoumerdesAlgeria
  3. 3.Department of Computer Science, Faculty of Electrical Engineering and Computer ScienceVSB-TUOOstrava-PorubaCzech Republic

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