The generalised singular perturbation approximation for bounded real and positive real control systems

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The generalised singular perturbation approximation (GSPA) is considered as a model reduction scheme for bounded real and positive real linear control systems. The GSPA is a state-space approach to truncation with the defining property that the transfer function of the approximation interpolates the original transfer function at a prescribed point in the closed right half complex plane. Both familiar balanced truncation and singular perturbation approximation are known to be special cases of the GSPA, interpolating at infinity and at zero, respectively. Suitably modified, we show that the GSPA preserves classical dissipativity properties of the truncations, and existing a priori error bounds for these balanced truncation schemes are satisfied as well.
Original languageEnglish
Pages (from-to)313-350
Number of pages38
JournalMathematical Control and Related Fields
Issue number2
Early online date1 Dec 2018
Publication statusPublished - 1 Jun 2019


  • And phrases
  • Balanced truncation
  • Dissipative system
  • Linear system
  • Model reduction
  • Rational interpolation
  • Singular perturbation approximation

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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