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State feedback control of commensurate fractional-order systems

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  • Jun Shen
  • James Lam

Abstract

This article focuses on the state feedback H∞ control problem for commensurate fractional-order systems with a prescribed H∞ performance. For linear time-invariant fractional-order systems, a sufficient condition to guarantee stability with H∞ performance is firstly presented. Then, by introducing a new flexible real matrix variable, the feedback gain is decoupled with complex matrix variables and further parametrised by the new flexible matrix. Moreover, iterative linear matrix inequality algorithms with initial optimisation are developed to solve the state feedback H∞ suboptimal control problem for fractional-order systems. Finally, illustrative examples are given to show the effectiveness of the proposed approaches.

Suggested Citation

  • Jun Shen & James Lam, 2014. "State feedback control of commensurate fractional-order systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(3), pages 363-372.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:3:p:363-372
    DOI: 10.1080/00207721.2012.723055
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    Cited by:

    1. Mikhail Gomoyunov, 2020. "Solution to a Zero-Sum Differential Game with Fractional Dynamics via Approximations," Dynamic Games and Applications, Springer, vol. 10(2), pages 417-443, June.
    2. Zhang, Xuefeng & Chen, Shunan & Zhang, Jin-Xi, 2022. "Adaptive sliding mode consensus control based on neural network for singular fractional order multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    3. Roxana Motorga & Vlad Mureșan & Mihaela-Ligia Ungureșan & Mihail Abrudean & Honoriu Vălean & Iulia Clitan, 2022. "Artificial Intelligence in Fractional-Order Systems Approximation with High Performances: Application in Modelling of an Isotopic Separation Process," Mathematics, MDPI, vol. 10(9), pages 1-32, April.

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