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Stability: Lyapunov, Linear Systems

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Encyclopedia of Systems and Control

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Abstract

The notion of stability allows to study the qualitative behavior of dynamical systems. In particular it allows to study the behavior of trajectories close to an equilibrium point or to a motion. The notion of stability that we discuss has been introduced in 1882 by the Russian mathematician A.M. Lyapunov in his doctoral thesis; hence it is often referred to as Lyapunov stability. In this article we discuss and characterize Lyapunov stability for linear systems.

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References

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Author information

Authors and Affiliations

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

    A. Astolfi

  2. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, Roma, Italy

    A. Astolfi

Authors
  1. A. Astolfi
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Correspondence to A. Astolfi .

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. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA

    Panos J. Antsaklis

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Astolfi, A. (2020). Stability: Lyapunov, Linear Systems. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_194-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_194-2

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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: Lyapunov, Linear Systems
    Published:
    07 January 2020

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_194-2

  2. Original

    Stability: Lyapunov, Linear Systems
    Published:
    05 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_194-1

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