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

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      Author(s)
      Fioravanti, A.R.
      Bonnet, C.
      Özbay, Hitay
      Niculescu, S. I.
      Date
      2012-08-14
      Source Title
      Automatica
      Print ISSN
      0005-1098
      Publisher
      Elsevier
      Volume
      48
      Issue
      11
      Pages
      2824 - 2830
      Language
      English
      Type
      Article
      Item Usage Stats
      236
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      296
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      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
      Asymptotic position
      Commensurate delays
      Delay effects
      Fractional systems
      Imaginary axis
      Neutral systems
      Numerical algorithms
      Simple substitution
      Time-delay systems
      Algorithms
      Delay control systems
      Poles
      Root loci
      Stability
      Permalink
      http://hdl.handle.net/11693/21277
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.automatica.2012.04.009
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      • Department of Electrical and Electronics Engineering 3868
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