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

André R. Fioravanti 1, 2 Catherine Bonnet 3, 1 Hitay Ozbay 4 Silviu-Iulian Niculescu 1, 2
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
2 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
3 L2S - Laboratoire des signaux et systèmes
4 Department of Electrical and Electronics Engineering
Abstract : 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.
Keywords : Delay effects Fractional systems Neutral systems Root-locus
Document type :
Journal articles
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https://hal.inria.fr/hal-00766550
Contributor : Catherine Bonnet <>
Submitted on : Tuesday, December 18, 2012 - 2:25:59 PM
Last modification on : Tuesday, June 4, 2019 - 11:08:04 AM

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André R. Fioravanti, Catherine Bonnet, Hitay Ozbay, Silviu-Iulian Niculescu. A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems. Automatica, Elsevier, 2012, 48 (11), pp.2824-2830. ⟨hal-00766550⟩

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