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Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables

Author

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  • Abdelghani Djeddi

    (Department of Electrical Engineering, Larbi Tebessi University, Tebessa 12002, Algeria
    These authors contributed equally to this work.)

  • Djalel Dib

    (Department of Electrical Engineering, Larbi Tebessi University, Tebessa 12002, Algeria
    These authors contributed equally to this work.)

  • Ahmad Taher Azar

    (College of Engineering, Robotics and Internet-of-Things Lab (RIOTU), Prince Sultan University, Riyadh 12435, Saudi Arabia
    Faculty of Computers and Artificial Intelligence, Benha University, Benha 13511, Egypt
    These authors contributed equally to this work.)

  • Salem Abdelmalek

    (Department of Mathematics, Larbi Tebessi University, Tebessa 12002, Algeria
    These authors contributed equally to this work.)

Abstract

This paper presents a new procedure for designing a fractional order unknown input observer (FOUIO) for nonlinear systems represented by a fractional-order Takagi–Sugeno (FOTS) model with unmeasurable premise variables (UPV). Most of the current research on fractional order systems considers models using measurable premise variables (MPV) and therefore cannot be utilized when premise variables are not measurable. The concept of the proposed is to model the FOTS with UPV into an uncertain FOTS model by presenting the estimated state in the model. First, the fractional-order extension of Lyapunov theory is used to investigate the convergence conditions of the FOUIO, and the linear matrix inequalities (LMIs) provide the stability condition. Secondly, performances of the proposed FOUIO are improved by the reduction of bounded external disturbances. Finally, an example is provided to clarify the proposed method. The obtained results show that a good convergence of the outputs and the state estimation errors were observed using the new proposed FOUIO.

Suggested Citation

  • Abdelghani Djeddi & Djalel Dib & Ahmad Taher Azar & Salem Abdelmalek, 2019. "Fractional Order Unknown Inputs Fuzzy Observer for Takagi–Sugeno Systems with Unmeasurable Premise Variables," Mathematics, MDPI, vol. 7(10), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:984-:d:277260
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    References listed on IDEAS

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    1. Shulan Kong & Mehrdad Saif & Guozeng Cui, 2018. "Estimation and Fault Diagnosis of Lithium-Ion Batteries: A Fractional-Order System Approach," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-12, October.
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    3. Zhu, Qiao & Xu, Mengen & Liu, Weiqun & Zheng, Mengqian, 2019. "A state of charge estimation method for lithium-ion batteries based on fractional order adaptive extended kalman filter," Energy, Elsevier, vol. 187(C).
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    1. Ahmad Taher Azar & Farah Ayad Abdul-Majeed & Hasan Sh. Majdi & Ibrahim A. Hameed & Nashwa Ahmad Kamal & Anwar Jaafar Mohamad Jawad & Ali Hashim Abbas & Wameedh Riyadh Abdul-Adheem & Ibraheem Kasim Ibr, 2022. "Parameterization of a Novel Nonlinear Estimator for Uncertain SISO Systems with Noise Scenario," Mathematics, MDPI, vol. 10(13), pages 1-17, June.

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