Analysis and comparison of the stability of discrete-time and continuous-time linear systems

Tadeusz Kaczorek

Abstract

The asymptotic stability of discrete-time and continuous-time linear systems described by the equations x(i+1) = (A) over bar (k)x(i) and (x)over dot (t) = A(k)x(t) for k being integers and rational numbers is addressed. Necessary and sufficient conditions for the asymptotic stability of the systems are established. It is shown that: 1) the asymptotic stability of discrete-time systems depends only on the modules of the eigenvalues of matrix (A) over bar (k) and of the continuous-time systems depends only on phases of the eigenvalues of the matrix A(k), 2) the discrete-time systems are asymptotically stable for all admissible values of the discretization step if and only if the continuous-time systems are asymptotically stable, 3) the upper bound of the discretization step depends on the eigenvalues of the matrix A.
Author Tadeusz Kaczorek (FoEE / ICIE) - [Bialystok University of Technology (PB)]
Tadeusz Kaczorek,,
- The Institute of Control and Industrial Electronics
- Politechnika Białostocka
Journal seriesArchives of Control Sciences, ISSN 2300-2611
Issue year2016
Vol26
No4
Pages551-563
Publication size in sheets0.6
Keywords in Englishanalysis; comparison; stability; discrete-time; continuous-time; linear system
DOIDOI:10.1515/acsc-2016-0030
LanguageEnglish
Score (nominal)0
Score sourcejournalList
ScoreMinisterial score = 0.0, 11-07-2020, ArticleFromJournal
Ministerial score (2013-2016) = 0.0, 11-07-2020, ArticleFromJournal
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