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

Mohammed Taoussi, Nabil El Akchioui, Adil Bardane, Nabil El Fezazi, Rashid Farkous, El Houssaine Tissir, Mo’tassem Al-Arydah

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageBritish English
Article number31
Issue number1
StatePublished - Jan 2023


  • discrete time system
  • disturbances
  • finite time
  • reduced order controller
  • robustness


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