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

Nevra Bayhan, Mehmet Turan Söylemez*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 Padé approximations for the time-delay, Lam's studies on the convergence of Padé 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 Padé approximation. As a result, it is possible to approximate the resulting set arbitrarily close to the exact stabilising set.

Original languageEnglish
Pages (from-to)26-40
Number of pages15
JournalInternational Journal of Control
Volume85
Issue number1
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • Padéapproximation
  • proportionalcontrol
  • stabilisation
  • time-delaysystems

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