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

Date
2011
Advisor
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Source Title
IFAC Proceedings Volumes (IFAC-PapersOnline)
Print ISSN
1474-6670
Electronic ISSN
Publisher
Elsevier
Volume
18
Issue
1
Pages
12532 - 12537
Language
English
Type
Conference Paper
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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.

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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, Root loci, Poles
Citation
Published Version (Please cite this version)