Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Realizations in Linear Systems Theory

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_193-1


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.


Realizations Minimal order Irreducible Controllability Observability 
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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

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