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Feedback Stabilization of Nonlinear Systems

Encyclopedia of Systems and Control

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Abstract

We consider the simplest design problem for nonlinear systems: the problem of rendering asymptotically stable a given equilibrium by means of state feedback. For such a problem, we provide a necessary condition, known as Brockett condition, and a sufficient condition, which relies upon the definition of a class of functions, known as control Lyapunov functions. The theory is illustrated by means of a few examples. In addition, we discuss a nonlinear enhancement of the so-called separation principle for stabilization by means of partial state information.

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Imperial College London, London, UK

    A. Astolfi

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  1. A. Astolfi
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Correspondence to A. Astolfi .

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Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2013 Springer-Verlag London

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Astolfi, A. (2013). Feedback Stabilization of Nonlinear Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_85-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_85-1

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  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Feedback Stabilization of Nonlinear Systems
    Published:
    03 January 2020

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_85-2

  2. Original

    Feedback Stabilization of Nonlinear Systems
    Published:
    15 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_85-1

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