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SOS Approach for Practical Stabilization of Tempered Fractional-Order Power System

Author

Listed:
  • Hamdi Gassara

    (Laboratory of Sciences and Technich of Automatic Control and Computer Engineering, National School of Engineering of Sfax, University of Sfax, PB 1173, Sfax 3038, Tunisia)

  • Dhouha Kharrat

    (Modeling, Information, and Systems Laboratory, University of Picardie Jules Verne, UFR of Sciences, 33 Rue St Leu, 80000 Amiens, France)

  • Abdellatif Ben Makhlouf

    (Department of Mathematics, Faculty of Sciences, Sfax University, BP 1171, Sfax 3038, Tunisia)

  • Lassaad Mchiri

    (ENSIIE, University of Evry-Val-d’Essonne, 1 Square de la Résistance, 91025 Évry-Courcouronnes, CEDEX, France)

  • Mohamed Rhaima

    (Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia)

Abstract

Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying the practical stability of a general class of tempered fractional-order (TFO) nonlinear systems, with broad applicability and potential for expanding its applications. Afterward, a polynomial controller is designed to guarantee the practical stability of the PS, encompassing the standard constant controller as a specific instance. The design conditions for this controller are resolved using the sum of squares (SOS) approach, a powerful technique for guaranteeing stability and control design. To showcase the practical value of the analytical findings, simulations of the PS are conducted utilizing SOSTOOLS.

Suggested Citation

  • Hamdi Gassara & Dhouha Kharrat & Abdellatif Ben Makhlouf & Lassaad Mchiri & Mohamed Rhaima, 2023. "SOS Approach for Practical Stabilization of Tempered Fractional-Order Power System," Mathematics, MDPI, vol. 11(13), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:3024-:d:1188940
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    References listed on IDEAS

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    1. Emad A. Mohamed & Mokhtar Aly & Masayuki Watanabe, 2022. "New Tilt Fractional-Order Integral Derivative with Fractional Filter (TFOIDFF) Controller with Artificial Hummingbird Optimizer for LFC in Renewable Energy Power Grids," Mathematics, MDPI, vol. 10(16), pages 1-33, August.
    2. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Shah, Kamal & Khalil, Hammad & Khan, Rahmat Ali, 2015. "Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 240-246.
    4. Jingwei Deng & Weiyuan Ma & Kaiying Deng & Yingxing Li, 2020. "Tempered Mittag–Leffler Stability of Tempered Fractional Dynamical Systems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, May.
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    Cited by:

    1. Zitane, Hanaa & Torres, Delfim F.M., 2023. "Finite time stability of tempered fractional systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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