A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems
Date
2012-08-14Source Title
Automatica
Print ISSN
0005-1098
Publisher
Elsevier
Volume
48
Issue
11
Pages
2824 - 2830
Language
English
Type
ArticleItem Usage Stats
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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 effectsFractional 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/11693/21277Published Version (Please cite this version)
http://dx.doi.org/10.1016/j.automatica.2012.04.009Collections
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