Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Observers in Linear Systems Theory

  • A. Astolfi
  • Panos J. Antsaklis
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_197


Observers are dynamical systems which process the input and output signals of a given dynamical system and deliver an online estimate of the internal state of the given system which asymptotically converges to the exact value of the state. For linear, finite-dimensional, time-invariant systems, observers can be designed provided a weak observability property, known as detectability, holds.


Linear systems Observers Reduced orderobserver State estimation 
This is a preview of subscription content, log in to check access.


  1. Antsaklis PJ, Michel AN (2007) A linear systems primer. Birkhäuser, BostonGoogle Scholar
  2. Brockett RW (1970) Finite dimensional linear systems. Wiley, LondonGoogle Scholar
  3. Luenberger DG (1963) Observing the state of a linear system. IEEE Trans Mil Electron 8:74–80Google Scholar
  4. Trentelman HL, Stoorvogel AA, Hautus MLJ (2001) Control theory for linear systems. Springer, LondonGoogle Scholar
  5. Zadeh LA, Desoer CA (1963) Linear system theory. McGraw-Hill, New YorkGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • A. Astolfi
    • 1
    • 2
  • Panos J. Antsaklis
    • 3
  1. 1.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK
  2. 2.Dipartimento di Ingegneria Civile e Ingegneria InformaticaUniversità di Roma Tor VergataRomaItaly
  3. 3.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA