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Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties

Author

Listed:
  • Khalid A. Alattas

    (Department of Computer Science and Artificial Intelligence, College of Computer Science and Engineering, University of Jeddah, Jeddah 23890, Saudi Arabia)

  • Ardashir Mohammadzadeh

    (Independent Researcher, Baku AZ1000, Azerbaijan)

  • Saleh Mobayen

    (Future Technology Research Center, National Yunlin University of Science and Technology, Douliu 64002, Taiwan)

  • Hala M. Abo-Dief

    (Department of Chemistry, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Abdullah K. Alanazi

    (Department of Chemistry, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Mai The Vu

    (School of Intelligent Mechatronics Engineering, Sejong University, Seoul 05006, Korea)

  • Arthur Chang

    (Bachelor Program in Interdisciplinary Studies, National Yunlin University of Science and Technology, Yunlin 64002, Taiwan)

Abstract

The Markov jump systems (MJSs) are a special case of parametric switching system. However, we know that time delay inevitably exists in many practical systems, and is known as the main source of efficiency reduction, and even instability. In this paper, the stochastic stable control design is discussed for time delay MJSs. In this regard, first, the problem of modeling of MJSs and their stability analysis using Lyapunov-Krasovsky functions is studied. Then, a state-feedback controller (SFC) is designed and its stability is proved on the basis of the Lyapunov theorem and linear matrix inequalities (LMIs), in the presence of polytopic uncertainties and time delays. Finally, by various simulations, the accuracy and efficiency of the proposed methods for robust stabilization of MJSs are demonstrated.

Suggested Citation

  • Khalid A. Alattas & Ardashir Mohammadzadeh & Saleh Mobayen & Hala M. Abo-Dief & Abdullah K. Alanazi & Mai The Vu & Arthur Chang, 2022. "Automatic Control for Time Delay Markov Jump Systems under Polytopic Uncertainties," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:187-:d:720049
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    References listed on IDEAS

    as
    1. Ruofeng Rao & Jialin Huang & Xinsong Yang, 2021. "Global Stabilization of a Single-Species Ecosystem with Markovian Jumping under Neumann Boundary Value via Laplacian Semigroup," Mathematics, MDPI, vol. 9(19), pages 1-11, October.
    2. Vasile Drăgan & Ivan Ganchev Ivanov & Ioan-Lucian Popa & Ovidiu Bagdasar, 2021. "Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games," Mathematics, MDPI, vol. 9(21), pages 1-15, October.
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    Cited by:

    1. Arpad Gellert & Stefan-Alexandru Precup & Alexandru Matei & Bogdan-Constantin Pirvu & Constantin-Bala Zamfirescu, 2022. "Real-Time Assembly Support System with Hidden Markov Model and Hybrid Extensions," Mathematics, MDPI, vol. 10(15), pages 1-21, August.

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