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Realizations in Linear Systems Theory

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 refers to the following: 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 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 controllable and observable. Realizations in both the continuous-time and discrete-time systems are discussed.

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Authors and Affiliations

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

    P. 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

    P. J. Antsaklis

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

Correspondence to P. J. Antsaklis .

Editor information

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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© 2014 Springer-Verlag London

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Antsaklis, P.J., Astolfi, A. (2014). 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_193-1

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

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  • Publisher Name: Springer, London

  • 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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