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H \(\infty \) observer-based sliding mode control for singularly perturbed systems with input nonlinearity

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Abstract

This paper considers the problem of \(H \infty \) observer-based sliding mode control for singularly perturbed systems with input nonlinearities. First, a proper observer is designed such that the observer error system with disturbance attenuation level is asymptotically stable. Then, an observer-based sliding surface is constructed under which a criterion for the input-to-state stability (ISS) of the sliding mode dynamics with respect to the observer error is obtained via linear matrix inequality. The criterion presented is independent of the small parameter, and the upper bound for ISS can be obtained efficiently. In addition, a sliding mode control law is synthesized to guarantee the reachability of the sliding surface in the state estimation space. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theoretical results.

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Acknowledgments

This paper is supported by the National Natural Science Foundation of China (11171113, 11471118), the Research Foundation of the Henan Higher Education Institutions of China (16A110006) and the Science and Technology Planning Project of Henan Province of China (162102310619).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001, China

    Wei Liu & Yanyan Wang

  2. Center for Applied and Multidisciplinary Mathematics, Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Wei Liu & Zhiming Wang

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  1. Wei Liu
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  2. Yanyan Wang
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  3. Zhiming Wang
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Correspondence to Wei Liu.

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Liu, W., Wang, Y. & Wang, Z. H \(\infty \) observer-based sliding mode control for singularly perturbed systems with input nonlinearity. Nonlinear Dyn 85, 573–582 (2016). https://doi.org/10.1007/s11071-016-2707-3

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