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Robust H∞-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation

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  • Fiuzy, Mohammad
  • Shamaghdari, Saeed

Abstract

This paper deals a type of H∞ proportional–integral–derivative (PID) control mechanism for a type of structural uncertain fractional order linear systems by convex Polytopic and two-norm bounded uncertainties subject to input saturation which mainly focuses on the case of a fractional order α such that 0<α<1. The Gronwall–Bellman lemma and the sector condition of the saturation function are investigated for system stability analysis and stabilization. The main strategy of the presented strategy is to restore fractional order PID controller design under input saturation problem from static output feedback controller design. Unlike existing strategies, non-iterative strategy is used to get optimal output feedback based on the LMI. On the premise of a linear matrix inequality algorithm, the SOF control laws can be obtained. After that, the fractional-order PID controller is recovered from the SOF controller. A numerical example is provided in order to show the validity and superiority of the proposed method.

Suggested Citation

  • Fiuzy, Mohammad & Shamaghdari, Saeed, 2023. "Robust H∞-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 550-581.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:550-581
    DOI: 10.1016/j.matcom.2023.01.025
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    References listed on IDEAS

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    1. Xing, Sheng Yan & Lu, Jun Guo, 2009. "Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1163-1169.
    2. Ricardo Enrique Gutiérrez & João Maurício Rosário & José Tenreiro Machado, 2010. "Fractional Order Calculus: Basic Concepts and Engineering Applications," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-19, May.
    3. Margarita Rivero & Sergei V. Rogosin & José A. Tenreiro Machado & Juan J. Trujillo, 2013. "Stability of Fractional Order Systems," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-14, May.
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