LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation
In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality...
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MDPI AG
2021-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/10/1128 |
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| author | Hamede Karami Saleh Mobayen Marzieh Lashkari Farhad Bayat Arthur Chang |
| author_facet | Hamede Karami Saleh Mobayen Marzieh Lashkari Farhad Bayat Arthur Chang |
| author_sort | Hamede Karami |
| collection | DOAJ |
| description | In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches. |
| first_indexed | 2024-03-10T11:21:57Z |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T11:21:57Z |
| publishDate | 2021-05-01 |
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| spelling | doaj.art-6b8ec4e2aa57407cbac43df5823c45032023-11-21T19:58:56ZengMDPI AGMathematics2227-73902021-05-01910112810.3390/math9101128LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and PerturbationHamede Karami0Saleh Mobayen1Marzieh Lashkari2Farhad Bayat3Arthur Chang4Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, IranDepartment of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, IranDepartment of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, IranDepartment of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, IranBachelor Program in Interdisciplinary Studies, National Yunlin University of Science and Technology, Yunlin 64002, TaiwanIn this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches.https://www.mdpi.com/2227-7390/9/10/1128chaos controloutput feedbackstabilizationLipchitz systemobserver-based control |
| spellingShingle | Hamede Karami Saleh Mobayen Marzieh Lashkari Farhad Bayat Arthur Chang LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation Mathematics chaos control output feedback stabilization Lipchitz system observer-based control |
| title | LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation |
| title_full | LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation |
| title_fullStr | LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation |
| title_full_unstemmed | LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation |
| title_short | LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation |
| title_sort | lmi observer based stabilizer for chaotic systems in the existence of a nonlinear function and perturbation |
| topic | chaos control output feedback stabilization Lipchitz system observer-based control |
| url | https://www.mdpi.com/2227-7390/9/10/1128 |
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