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Robust \(H_{\infty }\) Observer-Based Stabilization of Disturbed Uncertain Fractional-Order Systems Using a Two-Step Procedure

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Theoretical Developments and Applications of Non-Integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 357))

Abstract

The main objective of this work is the problem of robust \(H_{\infty }\) observer-based stabilization for a class of linear Disturbed Uncertain Fractional-Order Systems (DU-FOS) by using \(H_{\infty }\)-norm optimization. Based on the \(H_{\infty }\)-norm analysis for FOS, a new design methodology is established to stabilize a linear DU-FOS by using robust \(H_{\infty }\) Observer-Based Control (OBC). The existence conditions are derived, and by using the \(H_{\infty }\)-optimization technique, the stability of the estimation error and stabilization of the original system are given in an inequality condition, where all the observer matrices gains and the control law can be computed by solving a single inequality condition in two step. Finally, a simulation example is given to illustrate the validity of the results.

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Authors and Affiliations

  1. Centre de Recherche En Automatique de Nancy (CRAN - UMR 7039, CNRS), Université de Lorraine, IUT de Longwy, 186 rue de Lorraine, 54400, Cosnes et Romain, France

    Yassine Boukal, Michel Zasadzinski & Mohamed Darouach

  2. Faculté des Sciences Ain-Chock Laboratoire Physique et Matériaux Microélectronique Automatique et Thermique (LPMMAT), Université Hassan II, BP: 5366 Maarif, 20100, Casablanca, Morocco

    Yassine Boukal & Nour-Eddine Radhy

Authors
  1. Yassine Boukal
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  2. Michel Zasadzinski
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  3. Mohamed Darouach
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  4. Nour-Eddine Radhy
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Corresponding author

Correspondence to Michel Zasadzinski .

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Editors and Affiliations

  1. Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland

    Stefan Domek

  2. Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland

    Paweł Dworak

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Boukal, Y., Zasadzinski, M., Darouach, M., Radhy, NE. (2016). Robust \(H_{\infty }\) Observer-Based Stabilization of Disturbed Uncertain Fractional-Order Systems Using a Two-Step Procedure. In: Domek, S., Dworak, P. (eds) Theoretical Developments and Applications of Non-Integer Order Systems. Lecture Notes in Electrical Engineering, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-319-23039-9_14

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  • DOI: https://doi.org/10.1007/978-3-319-23039-9_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23038-2

  • Online ISBN: 978-3-319-23039-9

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