Arbitrary precision computation of the set of stabilising gains for time-delay LTI systems

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Bayhan N., Söylemez M. T.

INTERNATIONAL JOURNAL OF CONTROL, vol.85, no.1, pp.26-40, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 85 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.1080/00207179.2011.638324
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.26-40
  • Istanbul Technical University Affiliated: Yes


A new method is proposed to calculate the set of proportional controllers stabilising a given linear time-invariant system with a fixed time-delay. The method is based on the utilisation of Pade approximations for the time-delay, Lam's studies on the convergence of Pade approximations and a generalisation of the Nyquist theorem applicable to quasi-polynomials. The method allows determination of the closeness of the resulting set to the exact set of stabilising gains by tracing the uncertainty introduced by the Pade approximation. As a result, it is possible to approximate the resulting set arbitrarily close to the exact stabilising set.