New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators

This paper provides new results on a stable discretization of commensurate fractional-order continuous-time LTI systems using the Al-Alaoui and Tustin discretization methods. New, graphical, and analytical stability/instability conditions are given for discrete-time systems obtained by means of the...

Full description

Saved in:
Bibliographic Details
Main Authors: Rafał Stanisławski, Marek Rydel, Krzysztof J. Latawiec
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2018/2036809
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850235438560706560
author Rafał Stanisławski
Marek Rydel
Krzysztof J. Latawiec
author_facet Rafał Stanisławski
Marek Rydel
Krzysztof J. Latawiec
author_sort Rafał Stanisławski
collection DOAJ
description This paper provides new results on a stable discretization of commensurate fractional-order continuous-time LTI systems using the Al-Alaoui and Tustin discretization methods. New, graphical, and analytical stability/instability conditions are given for discrete-time systems obtained by means of the Al-Alaoui discretization scheme. On this basis, an analytically driven stability condition for discrete-time systems using the Tustin-based approach is presented. Finally, the stability of discrete-time systems obtained by finite-length approximation of the Al-Alaoui and Tustin operators are discussed. Simulation experiments confirm the effectiveness of the introduced stability tests.
format Article
id doaj-art-18f7ce8c302a48eeb4c4dc79cbc4c253
institution OA Journals
issn 1076-2787
1099-0526
language English
publishDate 2018-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-18f7ce8c302a48eeb4c4dc79cbc4c2532025-08-20T02:02:15ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/20368092036809New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin OperatorsRafał Stanisławski0Marek Rydel1Krzysztof J. Latawiec2Department of Electrical, Control and Computer Engineering, Opole University of Technology, ul. Prószkowska 76, 45-758 Opole, PolandDepartment of Electrical, Control and Computer Engineering, Opole University of Technology, ul. Prószkowska 76, 45-758 Opole, PolandDepartment of Electrical, Control and Computer Engineering, Opole University of Technology, ul. Prószkowska 76, 45-758 Opole, PolandThis paper provides new results on a stable discretization of commensurate fractional-order continuous-time LTI systems using the Al-Alaoui and Tustin discretization methods. New, graphical, and analytical stability/instability conditions are given for discrete-time systems obtained by means of the Al-Alaoui discretization scheme. On this basis, an analytically driven stability condition for discrete-time systems using the Tustin-based approach is presented. Finally, the stability of discrete-time systems obtained by finite-length approximation of the Al-Alaoui and Tustin operators are discussed. Simulation experiments confirm the effectiveness of the introduced stability tests.http://dx.doi.org/10.1155/2018/2036809
spellingShingle Rafał Stanisławski
Marek Rydel
Krzysztof J. Latawiec
New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators
Complexity
title New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators
title_full New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators
title_fullStr New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators
title_full_unstemmed New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators
title_short New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators
title_sort new stability tests for discretized fractional order systems using the al alaoui and tustin operators
url http://dx.doi.org/10.1155/2018/2036809
work_keys_str_mv AT rafałstanisławski newstabilitytestsfordiscretizedfractionalordersystemsusingthealalaouiandtustinoperators
AT marekrydel newstabilitytestsfordiscretizedfractionalordersystemsusingthealalaouiandtustinoperators
AT krzysztofjlatawiec newstabilitytestsfordiscretizedfractionalordersystemsusingthealalaouiandtustinoperators