Asymptotic Sampling Zeros

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


The location of poles of sampled models depends on the poles of the underlying continuous-time system and the sampling period. However, the relation between the zeros in discrete-time and continuous-time is much more involved. The sampled model can have extra zeros which have no continuous-time counterpart. This chapter examines the asymptotic behaviour of these sampling zeros in the discrete-time model, as the sampling period goes to zero.

Further Reading

Asymptotic sampling zeros were first described in

  1. Åström KJ, Hagander P, Sternby J (1984) Zeros of sampled systems. Automatica 20(1):31–38 MathSciNetCrossRefzbMATHGoogle Scholar
  2. Mårtensson B (1982) Zeros of sampled systems. Master’s thesis, Department of Automatic Control, Lund University, Lund, Sweden. Report TFRT-5266 Google Scholar

Further results were later presented in

  1. Blachuta MJ (1999) On zeros of pulse transfer functions. IEEE Trans Autom Control 44(6):1229–1234 MathSciNetCrossRefzbMATHGoogle Scholar
  2. Hagiwara T, Yuasa T, Araki M (1993) Stability of the limiting zeros of sampled-data systems with zero- and first-order holds. Int J Control Google Scholar
  3. Weller SR, Moran W, Ninness B, Pollington AD (2001) Sampling zeros and the Euler–Fröbenius polynomials. IEEE Trans Autom Control 46(2):340–343 MathSciNetCrossRefzbMATHGoogle 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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