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


Bayhan N. , Söylemez M. T.

INTERNATIONAL JOURNAL OF CONTROL, cilt.85, ss.26-40, 2012 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 85 Konu: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1080/00207179.2011.638324
  • Dergi Adı: INTERNATIONAL JOURNAL OF CONTROL
  • Sayfa Sayısı: ss.26-40

Özet

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.