Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control
In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/4706491 |
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| author | J. Humberto Pérez-Cruz Pedro A. Tamayo-Meza Maricela Figueroa Ramón Silva-Ortigoza Mario Ponce-Silva R. Rivera-Blas Mario Aldape-Pérez |
| author_facet | J. Humberto Pérez-Cruz Pedro A. Tamayo-Meza Maricela Figueroa Ramón Silva-Ortigoza Mario Ponce-Silva R. Rivera-Blas Mario Aldape-Pérez |
| author_sort | J. Humberto Pérez-Cruz |
| collection | DOAJ |
| description | In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach. |
| format | Article |
| id | doaj-art-f5d75b4987c248b7b251b1a6c612f205 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f5d75b4987c248b7b251b1a6c612f2052025-02-03T01:27:42ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/47064914706491Exponential Synchronization of Chaotic Xian System Using Linear Feedback ControlJ. Humberto Pérez-Cruz0Pedro A. Tamayo-Meza1Maricela Figueroa2Ramón Silva-Ortigoza3Mario Ponce-Silva4R. Rivera-Blas5Mario Aldape-Pérez6Sección de Estudios de Posgrado e Investigación, Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSección de Estudios de Posgrado e Investigación, Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoSección de Estudios de Posgrado e Investigación, Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Azcapotzalco, Instituto Politécnico Nacional, Ciudad de México 02250, MexicoÁrea de Mecatrónica, Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional, Ciudad de México 07700, MexicoDepartamento de Ingeniería Electrónica, Tecnológico Nacional de México, CENIDET, Cuernavaca 62490, MexicoÁrea de Mecatrónica, Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional, Ciudad de México 07700, MexicoÁrea de Mecatrónica, Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional, Ciudad de México 07700, MexicoIn this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.http://dx.doi.org/10.1155/2019/4706491 |
| spellingShingle | J. Humberto Pérez-Cruz Pedro A. Tamayo-Meza Maricela Figueroa Ramón Silva-Ortigoza Mario Ponce-Silva R. Rivera-Blas Mario Aldape-Pérez Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control Complexity |
| title | Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control |
| title_full | Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control |
| title_fullStr | Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control |
| title_full_unstemmed | Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control |
| title_short | Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control |
| title_sort | exponential synchronization of chaotic xian system using linear feedback control |
| url | http://dx.doi.org/10.1155/2019/4706491 |
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