Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Sev...
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| Format: | Article |
| Language: | English |
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Sciendo
2012-09-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.2478/v10006-012-0040-7 |
| _version_ | 1818583659934908416 |
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| author | Ostalczyk Piotr |
| author_facet | Ostalczyk Piotr |
| author_sort | Ostalczyk Piotr |
| collection | DOAJ |
| description | Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented. |
| first_indexed | 2024-12-16T08:08:48Z |
| format | Article |
| id | doaj.art-5565c9f560794c62be1fbb6718031735 |
| institution | Directory Open Access Journal |
| issn | 2083-8492 |
| language | English |
| last_indexed | 2024-12-16T08:08:48Z |
| publishDate | 2012-09-01 |
| publisher | Sciendo |
| record_format | Article |
| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj.art-5565c9f560794c62be1fbb67180317352022-12-21T22:38:24ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922012-09-0122353353810.2478/v10006-012-0040-7Equivalent descriptions of a discrete-time fractional-order linear system and its stability domainsOstalczyk Piotr0Institute of Applied Computer Science Łódź University of Technology, ul. Stefanowskiego 18/22, 90-924 Łódź, PolandTwo description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.https://doi.org/10.2478/v10006-012-0040-7fractional calculuslinear discrete-time systemstability domain |
| spellingShingle | Ostalczyk Piotr Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains International Journal of Applied Mathematics and Computer Science fractional calculus linear discrete-time system stability domain |
| title | Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains |
| title_full | Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains |
| title_fullStr | Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains |
| title_full_unstemmed | Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains |
| title_short | Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains |
| title_sort | equivalent descriptions of a discrete time fractional order linear system and its stability domains |
| topic | fractional calculus linear discrete-time system stability domain |
| url | https://doi.org/10.2478/v10006-012-0040-7 |
| work_keys_str_mv | AT ostalczykpiotr equivalentdescriptionsofadiscretetimefractionalorderlinearsystemanditsstabilitydomains |