Stability windows and unstable root-loci for linear fractionnal time-delay systems

André R. Fioravanti 1, 2 Catherine Bonnet 1, 2 Hitay Ozbay 3 Silviu-Iulian Niculescu 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
Abstract : The main point of this paper is on the formulation of a numerical algorithm to find the location of 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 the asymptotic position of the chains of poles and conditions for their stability, for a small delay. When these conditions are met, we continue by means of the root continuity argument, and using a simple substitution, we can find all the locations where roots cross the imaginary axis. We can extend the method to provide the location of all unstable poles as a function of the delay. Before concluding, some examples are presented.
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Submitted on : Wednesday, February 1, 2012 - 2:23:13 PM
Last modification on : Tuesday, June 4, 2019 - 11:08:06 AM

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André R. Fioravanti, Catherine Bonnet, Hitay Ozbay, Silviu-Iulian Niculescu. Stability windows and unstable root-loci for linear fractionnal time-delay systems. IFAC'11 : The 18 th World Congress of the International Federation of Automatic Control, Aug 2011, Milan, Italy. pp.1-6, ⟨10.3182/20110828-6-IT-1002.03086⟩. ⟨hal-00664439⟩

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