Details

Title

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

Journal title

Archives of Control Sciences

Yearbook

2016

Numer

No 4

Publication authors

Divisions of PAS

Nauki Techniczne

Abstract

<jats:title>Abstract</jats:title> <jats:p> The asymptotic stability of discrete-time and continuous-time linear systems described by the equations x<jats:sub>i+1</jats:sub> = Ā<jats:sup>k</jats:sup>x<jats:sub>i</jats:sub> and x(t) = A<jats:sup>k</jats:sup>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 Ā<jats:sup>k</jats:sup> and of the continuous-time systems depends only on phases of the eigenvalues of the matrix A<jats:sup>k</jats:sup>, 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.</jats:p>

Publisher

Committee of Automatic Control and Robotics PAS

Date

2016

Identifier

ISSN 1230-2384

References

KACZOREK (2013), Approximation of fractional positive stable continuous - time linear systems by fractional positive stable discrete - time systems of Applied and, Int J Mathematics Computer Science, 23, 501. ; KACZOREK (2010), Inverse systems of linear systems of, Archives Electrical Engineering, 59, 203, doi.org/10.2478/s10171-010-0016-x ; ŻAK (2003), Systems and Control University Press New York, Oxford. ; KACZOREK (2013), Comparison of approximation methods of positive stable continuous - time linear systems by positive stable discrete - time systems of, Archives Electrical Engineering, 62, 345, doi.org/10.2478/aee-2013-0027 ; KACZOREK (1992), Linear Control Systems vol New York, Research Studies, 1. ; KACZOREK (2014), Influence of the value of discretization step on the stability of positive and fractional systems National Conf on Automation, Proc, 1.

DOI

10.1515/acsc-2016-0030

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