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Sliding Mode Observers for Time-Dependent Set-Valued Lur’e Systems Subject to Uncertainties

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  • Ba Khiet Le

    (Ton Duc Thang University)

Abstract

Designing observers for dynamical systems plays an important role in the modern control theory due to the lack of full information in measured outputs. The current paper proposes a sliding mode observer for a general class of Lur’e systems subject to uncertainties where feedbacks involve time-dependent set-valued mappings. To the best of our knowledge, sliding mode observers for set-valued Lur’e systems, even for the simple static case, have not been considered in the literature. Exponential convergence of the observer state and finite-time convergence of the output estimation error are guaranteed without using any linear transformations. In addition, our design can also deduce $$H^\infty $$ H ∞ observers.

Suggested Citation

  • Ba Khiet Le, 2022. "Sliding Mode Observers for Time-Dependent Set-Valued Lur’e Systems Subject to Uncertainties," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 290-305, July.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:1:d:10.1007_s10957-022-02027-w
    DOI: 10.1007/s10957-022-02027-w
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    1. Camlibel, M.K. & Schumacher, Hans, 2016. "Linear passive systems and maximal monotone mappings," Other publications TiSEM de20953c-62e8-46a6-8af4-7, Tilburg University, School of Economics and Management.
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