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

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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 \(H^\infty \) observers.

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Acknowledgements

The author would like to thank the referees and the handling editor for valuable comments and suggestions. In addition, he wants to express his gratitude to University of O’Higgins, especially to Rector Dr. R. Correa and all his colleagues for warm welcome and hospitality during the time he worked in Chile, where some parts of this manuscript were done.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Ba Khiet Le

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  1. Ba Khiet Le
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Correspondence to Ba Khiet Le.

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Communicated by Negash G. Medhin.

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Le, B.K. Sliding Mode Observers for Time-Dependent Set-Valued Lur’e Systems Subject to Uncertainties. J Optim Theory Appl 194, 290–305 (2022). https://doi.org/10.1007/s10957-022-02027-w

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