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...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/2036809 |
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| 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 |