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Realizations in Linear Systems Theory

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Encyclopedia of Systems and Control

Abstract

When a state variable description of a linear system is known, then its input–output behavior can be easily realized by interconnecting simpler components. The problem of realization is the inverse of this process and can be formulated as follows: given an input–output description, such as the impulse response or the transfer function in the case of time-invariant systems, find a state variable description the impulse response or transfer function of which is the given one. Existence and minimality conditions are discussed. We are interested in realizations of minimum order, which is the case when the realization is both reachable and observable. Realizations for both continuous-time and discrete-time systems are discussed.

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Author information

Authors and Affiliations

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

    Panos J. Antsaklis

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

    A. Astolfi

  3. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma Tor Vergata, Roma, Italy

    A. Astolfi

Authors
  1. Panos J. Antsaklis
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  2. A. Astolfi
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Corresponding author

Correspondence to Panos J. Antsaklis .

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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Antsaklis, P.J., Astolfi, A. (2020). Realizations in Linear Systems Theory. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_193-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_193-2

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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

    Realizations in Linear Systems Theory
    Published:
    08 January 2020

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_193-2

  2. Original

    Realizations in Linear Systems Theory
    Published:
    05 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_193-1

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