Browsing by Subject "Simple substitution"

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Open Access
A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems
(Elsevier, 2012-08-14) Fioravanti, A.R.; Bonnet, C.; Özbay, Hitay; Niculescu, S. I.
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.
Open Access
Stability windows and unstable root-loci for linear fractional time-delay systems
(Elsevier, 2011) Fioravanti, A.R.; Bonnet, C.; Özbay, Hitay; Niculescu, S.-I.
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.