Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Tracking and Regulation in Linear Systems

  • Alessandro AstolfiEmail author
Living reference work entry

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


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.


Linear systems Tracking Regulation Internal model principle 
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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK
  2. 2.Dipartimento di Ingegneria Civile e Ingegneria InformaticaUniversità di Roma Tor VergataRomaItaly

Section editors and affiliations

  • Panos J. Antsaklis
    • 1
  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA