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Computation of Upper Bounds for the Solution of Continuous Algebraic Riccati Equations

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Abstract

This paper is considered with the computation of upper bounds for the solution of continuous algebraic Riccati equations (CARE). A parameterized upper bound for the solution of CARE is proposed by utilizing some linear algebraic techniques. Based on this bound, more precise estimation can be achieved by means of carefully choosing the bound’s parameters. Iterative algorithm is also developed to obtain more sharper solution bounds. Comparing with some existing results in the literature, the proposed bounds are less restrictive and more effective. The effectiveness and advantages of the proposed approach are illustrated via a numerical example.

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Acknowledgements

The authors would like to thank the associate editor and the anonymous reviewers for their helpful suggestions. This work is supported in part by the National Natural Science Foundation of China under Grant 61104140, the Natural Science Foundation of Shanghai under Grant 12ZR1412200, the Innovation Program of Shanghai Municipal Education Commission under Grant 12YZ156, the Excellent Young Teachers Program of Shanghai Higher Education under Grant shgcjs001, the Fundamental Research Funds for the Central Universities (HUST: Grant No. 2011JC055), the Research Fund for the Doctoral Program of Higher Education (RFDP) under Grant 20100142120023, and the Natural Science Foundation of Hubei Province of China under Grant 2011CDB042.

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Authors and Affiliations

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

    Wei Zhang & Jia Wang

  2. Department of Control Science and Engineering, Key Laboratory of Education Ministry for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, 430074, China

    Housheng Su

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  1. Wei Zhang
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  2. Housheng Su
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  3. Jia Wang
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Correspondence to Housheng Su.

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Zhang, W., Su, H. & Wang, J. Computation of Upper Bounds for the Solution of Continuous Algebraic Riccati Equations. Circuits Syst Signal Process 32, 1477–1488 (2013). https://doi.org/10.1007/s00034-012-9498-7

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  • DOI: https://doi.org/10.1007/s00034-012-9498-7

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