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

Date
2012-08-14
Authors
Fioravanti, A.R.
Bonnet, C.
Özbay, Hitay
Niculescu, S. I.
Advisor
Instructor
Source Title
Automatica
Print ISSN
0005-1098
Electronic ISSN
Publisher
Elsevier
Volume
48
Issue
11
Pages
2824 - 2830
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
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.

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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
Citation
Published Version (Please cite this version)