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A New Observer Design for the Joint Estimation of States and Unknown Inputs for a Class of Nonlinear Fractional-Order Systems

Author

Listed:
  • Chenchen Peng

    (School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China)

  • Haiyi Yang

    (School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China)

  • Anqing Yang

    (School of Information Engineering, Shandong Management University, Jinan 250357, China)

  • Ling Ren

    (School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China)

Abstract

This article designs an observer for the joint estimation of the state and the unknown input for a class of nonlinear fractional-order systems (FOSs) such that one portion satisfies the Lipschitz condition and the other does not necessarily satisfy such a condition. Firstly, by reconstructing system dynamics, the observer design is transformed equivalently into the tracking problem between the original nonlinear FOSs and the designed observer. Secondly, the parameterized matrices of the desired observer are derived by use of the property of the generalized inverse matrices and the linear matrix inequality (LMI) technique combined with the Schur complement lemma. Moreover, an algorithm is presented to determine the desired observer for the nonlinear FOSs effectively. Finally, a numerical example is reported to verify the correctness and efficiency of the proposed algorithm.

Suggested Citation

  • Chenchen Peng & Haiyi Yang & Anqing Yang & Ling Ren, 2024. "A New Observer Design for the Joint Estimation of States and Unknown Inputs for a Class of Nonlinear Fractional-Order Systems," Mathematics, MDPI, vol. 12(8), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1139-:d:1373319
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    References listed on IDEAS

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    1. Sharma, Vivek & Shukla, Manoj & Sharma, B.B., 2018. "Unknown input observer design for a class of fractional order nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 96-107.
    2. Srivastava, H.M. & Dubey, V.P. & Kumar, R. & Singh, J. & Kumar, D. & Baleanu, D., 2020. "An efficient computational approach for a fractional-order biological population model with carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Durdu, Ali & Uyaroğlu, Yılmaz, 2017. "The Shortest Synchronization Time with Optimal Fractional Order Value Using a Novel Chaotic Attractor Based on Secure Communication," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 98-106.
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