Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models
This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robu...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/8833768 |
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| author | Zeineb Rayouf Chekib Ghorbel Naceur Benhadj Braiek |
| author_facet | Zeineb Rayouf Chekib Ghorbel Naceur Benhadj Braiek |
| author_sort | Zeineb Rayouf |
| collection | DOAJ |
| description | This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness. |
| format | Article |
| id | doaj-art-ae809226fddf4780acec94ea280404ae |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-ae809226fddf4780acec94ea280404ae2025-02-03T01:04:12ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/88337688833768Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein ModelsZeineb Rayouf0Chekib Ghorbel1Naceur Benhadj Braiek2Laboratory of Advanced Systems, Polytechnic High School of Tunisia, University of Carthage, BP 743, 2078, La Marsa, TunisiaLaboratory of Advanced Systems, Polytechnic High School of Tunisia, University of Carthage, BP 743, 2078, La Marsa, TunisiaLaboratory of Advanced Systems, Polytechnic High School of Tunisia, University of Carthage, BP 743, 2078, La Marsa, TunisiaThis paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness.http://dx.doi.org/10.1155/2021/8833768 |
| spellingShingle | Zeineb Rayouf Chekib Ghorbel Naceur Benhadj Braiek Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models Complexity |
| title | Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models |
| title_full | Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models |
| title_fullStr | Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models |
| title_full_unstemmed | Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models |
| title_short | Nonfragile H∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models |
| title_sort | nonfragile h∞ stabilizing nonlinear systems described by multivariable hammerstein models |
| url | http://dx.doi.org/10.1155/2021/8833768 |
| work_keys_str_mv | AT zeinebrayouf nonfragilehstabilizingnonlinearsystemsdescribedbymultivariablehammersteinmodels AT chekibghorbel nonfragilehstabilizingnonlinearsystemsdescribedbymultivariablehammersteinmodels AT naceurbenhadjbraiek nonfragilehstabilizingnonlinearsystemsdescribedbymultivariablehammersteinmodels |