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New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

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Abstract

This paper deals with H∞ control problem for nonlinear conformable fractional order systems. The authors first derive new sufficient condition for exponential stability of nonlinear conformable fractional order systems based on Lyapunov-like function method for conformable fractional order systems and linear matrix inequalities (LMIs) approach. Then, by introducing a new concepts of H∞ control problem for nonlinear conformable fractional order systems, the authors study H∞ performance analysis and H∞ state feedback controller design problems for the considered systems. In terms of LMIs, a sufficient condition is proposed to ensure the nonlinear conformable fractional order systems are not only exponentially stable, but also satisfy H∞ performance γ. An explicit expression for state feedback controllers is also designed to make the closed-loop system is exponentially stable with H∞ performance γ. Finally, numerical examples are given to illustrate the validity and effectiveness of the proposed results.

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Authors and Affiliations

  1. Department for Management of Science and Technology Development, Ton Due Thang University, Ho Chi Minh City, Vietnam

    Viet Thuan Mai

  2. Faculty of Mathematics and Statistics, Ton Due Thang University, Ho Chi Minh City, Vietnam

    Viet Thuan Mai

  3. Faculty of General Science, Hanoi University of Natural Resources and Environment, Hanoi, Vietnam

    Thi Huyen Thu Nguyen

  4. Faculty of Fundamental Science, Hanoi University of Industry, Ha Noi, Vietnam

    Huu Sau Nguyen

  5. Department of Mathematics and Informatics, Thainguyen University of Sciences, Thainguyen, Vietnam

    Thi Thanh Huyen Nguyen

Authors
  1. Viet Thuan Mai
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  2. Thi Huyen Thu Nguyen
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  3. Huu Sau Nguyen
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  4. Thi Thanh Huyen Nguyen
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Corresponding authors

Correspondence to Viet Thuan Mai or Thi Thanh Huyen Nguyen.

Additional information

This paper was funded by Ministry of Education and Training of Vietnam (B2020-TNA-13).

This paper was recommended for publication by Editor SUN Jian.

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Mai, V.T., Nguyen, T.H.T., Nguyen, H.S. et al. New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems. J Syst Sci Complex 34, 140–156 (2021). https://doi.org/10.1007/s11424-020-9033-z

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  • DOI: https://doi.org/10.1007/s11424-020-9033-z

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