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

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      Author(s)
      Fioravanti, A.R.
      Bonnet, C.
      Özbay, Hitay
      Niculescu, S.-I.
      Date
      2011
      Source Title
      IFAC Proceedings Volumes (IFAC-PapersOnline)
      Print ISSN
      1474-6670
      Publisher
      Elsevier
      Volume
      18
      Issue
      1
      Pages
      12532 - 12537
      Language
      English
      Type
      Conference Paper
      Item Usage Stats
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      117
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      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. © 2011 IFAC.
      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
      Root loci
      Poles
      Permalink
      http://hdl.handle.net/11693/28276
      Published Version (Please cite this version)
      https://doi.org/10.3182/20110828-6-IT-1002.03086
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      • Department of Electrical and Electronics Engineering 3702
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