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Exponential Reduced-Order Observers for Nonlinear Systems Satisfying Incremental Quadratic Constraints

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Abstract

This paper considers the design problem of exponential reduced-order observers for nonlinear systems satisfying incremental quadratic constraints governed by an incremental multiplier matrix. Sufficient existence conditions of the exponential full-order observers are established and formulated in terms of matrix inequalities. Then, it is shown that the conditions under which an exponential full-order observer exists also guarantee the existence of an exponential reduced-order observer. Moreover, with a proper parameterization of the multiplier matrix, the design of reduced-order observers is reduced to solving linear matrix inequalities of the Lyapunov matrix and observer gain matrices. Finally, the effectiveness of the proposed design method is illustrated by an example.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 51505273, the State Key Laboratory of Robotics and System (HIT) under Grant SKLRS-2014-MS-10, the Jiangsu Provincial Key Laboratory of Advanced Robotics Fund Projects under Grant JAR201401 and the Fund of MOE Key Laboratory of Image Processing and Intelligence Control (Huazhong University of Science and Technology) under Grant No. IPIC2015-02.

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Authors and Affiliations

  1. Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Younan Zhao, Wei Zhang, Wuyang Zhang & Fang Song

  2. MOE Key Laboratory of Image Processing and Intelligence Control, Huazhong University of Science and Technology, Wuhan, 430074, China

    Younan Zhao, Wei Zhang & Wuyang Zhang

  3. State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, 150001, China

    Fang Song

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  1. Younan Zhao
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Correspondence to Wei Zhang.

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Zhao, Y., Zhang, W., Zhang, W. et al. Exponential Reduced-Order Observers for Nonlinear Systems Satisfying Incremental Quadratic Constraints. Circuits Syst Signal Process 37, 3725–3738 (2018). https://doi.org/10.1007/s00034-018-0745-4

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