A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems

作者：Fioravanti Andre Ricardo^*; Bonnet Catherine; Ozbay Hitay; Niculescu Silviu Iulian

来源：Automatica, 2012, 48(11): 2824-2830.

DOI：10.1016/j.automatica.2012.04.009

• Delay effects
• Fractional systems
• Neutral systems
• Root-locus

This paper aims to provide a numerical algorithm able to locate all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by giving the asymptotic position of the chains of poles and the conditions for their stability for a small delay. When these conditions are met, the root continuity argument and some simple substitutions allow us to determine the locations where some roots cross the imaginary axis, providing therefore the complete characterization of the stability windows. The same method can be extended to provide the position of all unstable poles as a function of the delay.

• 出版日期2012-11
• 单位INRIA