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A Control Lyapunov Function Approach to Stabilization of Affine Nonlinear Systems with Bounded Uncertain Parameters

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Abstract

This paper considers the robust stabilization problem of a class of affine nonlinear systems with bounded uncertain time-invariant parameters. A robust control Lyapunov function (RCLF) is introduced for the considered system. Based on the RCLF, a globally asymptotically stabilizing controller is then designed. The proposed controller is robust under the variant of system parameters. As the applications of the proposed scheme, the stabilization of uncertain feedback linearizable systems and the unified chaotic system are investigated, respectively. A numerical example on the unified chaotic system is also provided to illustrate the effectiveness of the presented method.

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Acknowledgments

This work is partly supported by the National Natural Science Foundation of China under Grants 61104140 and 61374077, the Program for New Century Excellent Talents in University from Chinese Ministry of Education under Grant NCET-12-0215, the Innovation Foundation of Shanghai Municipal Education Commission under Grant 12YZ156, the Fund of SUES under Grant 2012gp45, and Shanghai Municipal Natural Science Foundation under Grant 12ZR1412200.

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Authors and Affiliations

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

    Wei Zhang

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

    Housheng Su

  3. College of Mathematics, Physics, and Information Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Xiushan Cai

  4. College of Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Hui Guo

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  1. Wei Zhang
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  2. Housheng Su
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  3. Xiushan Cai
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  4. Hui Guo
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Correspondence to Housheng Su.

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Zhang, W., Su, H., Cai, X. et al. A Control Lyapunov Function Approach to Stabilization of Affine Nonlinear Systems with Bounded Uncertain Parameters. Circuits Syst Signal Process 34, 341–352 (2015). https://doi.org/10.1007/s00034-014-9848-8

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  • DOI: https://doi.org/10.1007/s00034-014-9848-8

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