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Design of Finite Time Reduced Order H∞ Controller for Linear Discrete Time Systems

Author

Listed:
  • Mohammed Taoussi

    (Industrial Technologies and Services Laboratory, Higher School of Technology, Sidi Mohammed Ben Abdellah University, Fez 30000, Morocco)

  • Nabil El Akchioui

    (LRDSI Laboratory, Department of Physics, Faculty of Sciences and Technology, Abdelmalek Essaâdi University, Al Hoceima 32000, Morocco)

  • Adil Bardane

    (Department of Physics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates
    Faculty of Sciences, Ibn Tofail University, Kenitra 14000, Morocco)

  • Nabil El Fezazi

    (LISAC Laboratory, Department of Physics, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, Fez 30000, Morocco)

  • Rashid Farkous

    (LISAC Laboratory, Department of Physics, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, Fez 30000, Morocco)

  • El Houssaine Tissir

    (LISAC Laboratory, Department of Physics, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, Fez 30000, Morocco)

  • Mo’tassem Al-Arydah

    (Department of Mathematics, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates)

Abstract

The current article gives a new approach that is efficient for the design of a low-order H∞ controller over a finite time interval. The system under consideration is a linear discrete time system affected by norm bounded disturbances. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, reducing the number of variables in Linear Matrix Inequalities (LMIs). Thus, reduced order H∞ controller parameters are given to guarantee a finite time H∞ bound (FTB-H∞) for a closed-loop system. The method of the finite time stability, that is proven in this paper by the Lyapunov theory, can be applied to a wide range of process models. Numerical examples demonstrating the effectiveness of the results developed are presented at the end of this paper.

Suggested Citation

  • Mohammed Taoussi & Nabil El Akchioui & Adil Bardane & Nabil El Fezazi & Rashid Farkous & El Houssaine Tissir & Mo’tassem Al-Arydah, 2022. "Design of Finite Time Reduced Order H∞ Controller for Linear Discrete Time Systems," Mathematics, MDPI, vol. 11(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:31-:d:1010667
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