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Global stabilization of nonlinear systems: A continuous feedback framework

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Nonlinear and Adaptive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 281))

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Abstract

This article develops a continuous feedback framework for global stabilization of inherently nonlinear systems that may not be stabilized by any smooth feedback, even locally. Sufficient conditions are given for the existence of continuous but non-smooth state feedback control laws that achieve global strong stability. A systematic design method which combines homogeneous systems theory with the idea of adding a power integrator is presented for the explicit construction of C 0 globally stabilizing controllers. The significance of this new framework is illustrated by solving a variety of open nonlinear control problems that cannot be dealt with by existing methods.

This work was supported in part by the U.S. NSF under Grants ECS-9875273, ECS-9906218, and DMS-9972045. Corresponding author: Prof. Wei Lin (e-mail: linwei@nonlinear.cwru.edu)

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Author information

Authors and Affiliations

  1. The University of Texas at San Antonio, San Antonio, TX, 78249, USA

    Chunjiang Qian

  2. Case Western Reserve University, Cleveland, OH, 44106, USA

    Wei Lin

Authors
  1. Chunjiang Qian
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  2. Wei Lin
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Editor information

Editors and Affiliations

  1. Departement of AppliedMathematics, The University of Sheffield, Western Bank, Sheffield, S10 2TN, UK

    Alan Zinober

  2. Dept. of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    David Owens

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© 2003 Springer-Verlag Berlin Heidelberg

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Qian, C., Lin, W. (2003). Global stabilization of nonlinear systems: A continuous feedback framework. In: Zinober, A., Owens, D. (eds) Nonlinear and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45802-6_24

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  • DOI: https://doi.org/10.1007/3-540-45802-6_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43240-1

  • Online ISBN: 978-3-540-45802-9

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