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H∞ observer-based controller synthesis for fractional order systems over finite frequency range

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  • Zhang, Xuefeng
  • Lv, Yuanda
  • Zhang, Jin-Xi

Abstract

This paper focuses on the H∞ observer-based control problem for fractional order systems (FOSs) over finite frequency range. Firstly, as an extension to the KYP lemma, the structure singular value–μ and its upper bound are analyzed and determined. The necessary and sufficient conditions of the H∞ performance for FOSs over finite frequency range are given through the generalized μ analysis method. This method is different from the traditional μ-analysis method, which is only suitable for integer order systems. Secondly, according to these obtained LMI-based criteria for H∞ performance index and a key projection lemma, we design an H∞ observer-based controller to stabilize the estimation error and decrease the H∞ norm for the FOS simultaneously. With the help of the matrix congruence transformation, the feedback gain matrix is parameterized by a scalar matrix. Thirdly, to deal with the nonlinear terms in matrix inequalities, an iterative linear matrix inequality (ILMI) algorithm is developed. Finally, two numerical examples are provided to explain the correctness of the established results.

Suggested Citation

  • Zhang, Xuefeng & Lv, Yuanda & Zhang, Jin-Xi, 2024. "H∞ observer-based controller synthesis for fractional order systems over finite frequency range," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    • Handle: RePEc:eee:apmaco:v:474:y:2024:i:c:s0096300324001681
    DOI: 10.1016/j.amc.2024.128696
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    References listed on IDEAS

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    1. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. He Li & Guang-Hong Yang, 2020. "Fault estimation for fractional-order linear systems with polytopic uncertainties in the finite frequency domain," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(2), pages 389-403, January.
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