Stability of fractional variable order difference systems

Dorota Mozyrska , Piotr Oziabło , Małgorzata Wyrwas

Abstract

AbstractThe problem of stability of the Grünwald-Letnikov-type linear fractional variable order discrete-time systems is discussed. As a definition of the Grünwald-Letnikov difference is a convolution type, the 𝓩-transform is used as an effective tool for the stability analysis. The conditions for asymptotic stability and for instability are presented. In the case of a scalar system we state conditions that guarantee asymptotic stability in inequalities for a coefficient that appears on the right hand side of the equation defined the system}. We describe regions of the stability for systems accordingly to locus of eigenvalues of a matrix associated to the considered system. In the general case of the linear difference systems one can determine the regions of location of eigenvalues of matrices associated to the systems in order to guarantee the asymptotic stability of the considered systems. Some of the frames of these regions are illustrated in the examples.
Author Dorota Mozyrska (FCS / DM)
Dorota Mozyrska,,
- Department of Mathematics
, Piotr Oziabło (FCS)
Piotr Oziabło,,
- Faculty of Computer Science
, Małgorzata Wyrwas (FCS / DM)
Małgorzata Wyrwas,,
- Department of Mathematics
Journal seriesFractional Calculus and Applied Analysis, ISSN 1311-0454, (N/A 100 pkt)
Issue year2019
Vol22
No3
Pages807-824
Publication size in sheets0.85
Keywords in Englishfractional order systems; difference operators; fractional variable orders; stability
ASJC Classification2603 Analysis; 2604 Applied Mathematics
DOIDOI:10.1515/fca-2019-0044
Internal identifierROC 19-20
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 26-03-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2018 = 1.808; WoS Impact Factor: 2018 = 3.514 (2) - 2018=3.524 (5)
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