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Stability Theory for Hybrid Dynamical Systems

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Abstract

This entry provides a short introduction to modeling of hybrid dynamical systems and then focuses on stability theory for these systems. It provides definitions of asymptotic stability, basin of attraction, and uniform asymptotic stability for a compact set. It points out mild assumptions under which different characterizations of asymptotic stability are equivalent, as well as when an asymptotically stable compact set exists. It also summarizes necessary and sufficient conditions for asymptotic stability in terms of Lyapunov functions.

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References

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Author information

Authors and Affiliations

  1. Electrical and Computer Engineering Department, University of California, Santa Barbara, CA, USA

    Andrew R. Teel

Authors
  1. Andrew R. Teel
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Corresponding author

Correspondence to Andrew R. Teel .

Editor information

Editors and Affiliations

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

    John Baillieul

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

    Tariq Samad

Section Editor information

  1. Laboratoire des Signaux et Systèmes, CNRS, Gif-sur-Yvette, France

    Francoise Lamnabhi-Lagarrigue

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Teel, A.R. (2020). Stability Theory for Hybrid Dynamical Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_99-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_99-2

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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Chapter history

  1. Latest

    Stability Theory for Hybrid Dynamical Systems
    Published:
    16 January 2020

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_99-2

  2. Original

    Stability Theory for Hybrid Dynamical Systems
    Published:
    03 April 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_99-1

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