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Tracking and Regulation in Linear Systems

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Encyclopedia of Systems and Control

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Abstract

Tracking and regulation refers to the ability of a control system to track/reject a given family of reference/disturbance signals modelled as solutions of a differential/difference equation. The problem can be posed as a stabilization problem with a constraint on the steady-state response of the system. For linear, time-invariant, systems the problem can be solved provided a system of linear matrix equations admits a solution. Properties of this system of equations are discussed, together with a general property of all controllers achieving tracking and regulation: the so-called internal model principle.

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Notes

  1. 1.

    (S) stands for stability and (R) for regulation.

Bibliography

  • Davison EJ (1976) The robust control of a servomechanism problem for linear time invariant multivariable systems. IEEE Trans Autom Control 21:25–34

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Author information

Authors and Affiliations

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

    Alessandro Astolfi

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

    Alessandro Astolfi

Authors
  1. Alessandro Astolfi
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Correspondence to Alessandro 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). Tracking and Regulation in 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_198-2

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_198-2

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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

    Tracking and Regulation in Linear Systems
    Published:
    06 November 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_198-2

  2. Original

    Tracking and Regulation in Linear Systems
    Published:
    18 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_198-1

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