Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay
© 2016 Informa UK Limited, trading as Taylor & Francis Group.This paper investigates the finite-time stability problem of a class of nonlinear fractional-order system with the discrete time delay. Employing the Laplace transform, the Mittag-Leffler function and the generalised Gronwall inequalit...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Taylor and Francis
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/51992 |
| _version_ | 1848758816467845120 |
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| author | Wang, F. Chen, Diyi Zhang, Xinguang Wu, Yong Hong |
| author_facet | Wang, F. Chen, Diyi Zhang, Xinguang Wu, Yong Hong |
| author_sort | Wang, F. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 2016 Informa UK Limited, trading as Taylor & Francis Group.This paper investigates the finite-time stability problem of a class of nonlinear fractional-order system with the discrete time delay. Employing the Laplace transform, the Mittag-Leffler function and the generalised Gronwall inequality, the new criterions are derived to guarantee the finite-time stability of the system with the fractional-order 0 < a < 1. Further, we propose the sufficient conditions for ensuring the finite-time stability of the system with the fractional-order 1 < a < 2. Finally, based on the modified Adams–Bashforth–Moulton algorithm for solving fractional-order differential equations with the time delay, we carry out the numerical simulations to demonstrate the effectiveness of the proposed results, and calculate the estimated time of the finite-time stability. |
| first_indexed | 2025-11-14T09:50:00Z |
| format | Journal Article |
| id | curtin-20.500.11937-51992 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:50:00Z |
| publishDate | 2017 |
| publisher | Taylor and Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-519922017-09-13T15:38:44Z Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay Wang, F. Chen, Diyi Zhang, Xinguang Wu, Yong Hong © 2016 Informa UK Limited, trading as Taylor & Francis Group.This paper investigates the finite-time stability problem of a class of nonlinear fractional-order system with the discrete time delay. Employing the Laplace transform, the Mittag-Leffler function and the generalised Gronwall inequality, the new criterions are derived to guarantee the finite-time stability of the system with the fractional-order 0 < a < 1. Further, we propose the sufficient conditions for ensuring the finite-time stability of the system with the fractional-order 1 < a < 2. Finally, based on the modified Adams–Bashforth–Moulton algorithm for solving fractional-order differential equations with the time delay, we carry out the numerical simulations to demonstrate the effectiveness of the proposed results, and calculate the estimated time of the finite-time stability. 2017 Journal Article http://hdl.handle.net/20.500.11937/51992 10.1080/00207721.2016.1226985 Taylor and Francis restricted |
| spellingShingle | Wang, F. Chen, Diyi Zhang, Xinguang Wu, Yong Hong Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay |
| title | Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay |
| title_full | Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay |
| title_fullStr | Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay |
| title_full_unstemmed | Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay |
| title_short | Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay |
| title_sort | finite-time stability of a class of nonlinear fractional-order system with the discrete time delay |
| url | http://hdl.handle.net/20.500.11937/51992 |