Approximate Models for Linear Deterministic Systems

  • Juan I. Yuz
  • Graham C. Goodwin
Part of the Communications and Control Engineering book series (CCE)


This chapter develops various approximate discrete-time models for general linear deterministic systems. It is always possible to obtain an exact sampled models for linear systems. However, approximate models are treated here to provide insights into the structure of discrete-time models, to obtain simpler models, and to be able to construct similar approximate sampled models for nonlinear systems, later in the book. We present models based on simple Euler integration, on the inclusion of asymptotic sampling zeros, on up-sampling, on normal forms and on truncated Taylor series expansions.

Further Reading

Further information regarding corrected asymptotic sampling zeros can be found in

  1. Blachuta MJ (1999a) On approximate pulse transfer functions. IEEE Trans Autom Control 44(11):2062–2067 MathSciNetCrossRefzbMATHGoogle Scholar
  2. Blachuta MJ (1999b) On zeros of pulse transfer functions. IEEE Trans Autom Control 44(6):1229–1234 MathSciNetCrossRefzbMATHGoogle Scholar

An application of up-sampled models can be found in

  1. Cea M, Goodwin GC (2010) Up-sampling strategies in sampled data nonlinear filtering. In: 49th IEEE conference on decision and control Google Scholar

Further information regarding relative errors for approximate linear sampled-data models is given in

  1. Goodwin GC, Yuz JI, Agüero JC (2008) Relative error issues in sampled data models. In: 17th IFAC world congress, Seoul, Korea Google Scholar
  2. Yucra E, Yuz JI (2011) Frequency domain accuracy of approximate sampled-data models. In: 18th IFAC world congress, Milan, Italy Google Scholar

Normal forms for linear (and nonlinear) systems are described in detail in

  1. Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, Berlin CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Juan I. Yuz
    • 1
  • Graham C. Goodwin
    • 2
  1. 1.Departamento de ElectrónicaUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.School of Electrical Engineering & Computer ScienceUniversity of NewcastleCallaghanAustralia

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