About the Stabilization of a Nonlinear Perturbed Difference Equation
This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/320302 |
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| _version_ | 1849403852692914176 |
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| author | M. De la Sen |
| author_facet | M. De la Sen |
| author_sort | M. De la Sen |
| collection | DOAJ |
| description | This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions. |
| format | Article |
| id | doaj-art-97a48fd55b6b4dfa93100e7885c55245 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-97a48fd55b6b4dfa93100e7885c552452025-08-20T03:37:09ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/320302320302About the Stabilization of a Nonlinear Perturbed Difference EquationM. De la Sen0Institute of Research and Development of Processes, Campus of Leioa, Bizkaia, 48080 Bilbao, SpainThis paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.http://dx.doi.org/10.1155/2012/320302 |
| spellingShingle | M. De la Sen About the Stabilization of a Nonlinear Perturbed Difference Equation Discrete Dynamics in Nature and Society |
| title | About the Stabilization of a Nonlinear Perturbed Difference Equation |
| title_full | About the Stabilization of a Nonlinear Perturbed Difference Equation |
| title_fullStr | About the Stabilization of a Nonlinear Perturbed Difference Equation |
| title_full_unstemmed | About the Stabilization of a Nonlinear Perturbed Difference Equation |
| title_short | About the Stabilization of a Nonlinear Perturbed Difference Equation |
| title_sort | about the stabilization of a nonlinear perturbed difference equation |
| url | http://dx.doi.org/10.1155/2012/320302 |
| work_keys_str_mv | AT mdelasen aboutthestabilizationofanonlinearperturbeddifferenceequation |