Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality
The concept of the exponentially stable limit cycle (ESLC) is introduced, and the ESLC phenomenon for a class of nonlinear systems is explored. Based on time-domain approach with differential inequality, the existence and uniqueness of the ESLC for such nonlinear systems can be guaranteed. Besides,...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/712932 |
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| _version_ | 1832554570696359936 |
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| author | Yeong-Jeu Sun Yu-Biaw Wu Ching-Cheng Wang |
| author_facet | Yeong-Jeu Sun Yu-Biaw Wu Ching-Cheng Wang |
| author_sort | Yeong-Jeu Sun |
| collection | DOAJ |
| description | The concept of the exponentially stable limit cycle (ESLC) is introduced, and the ESLC phenomenon for a class of nonlinear systems is explored. Based on time-domain approach with differential inequality, the existence and uniqueness of the ESLC for such nonlinear systems can be guaranteed. Besides, the period of oscillation, the amplitude of oscillation, and guaranteed convergence rate can be accurately estimated. Finally, two numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result. |
| format | Article |
| id | doaj-art-6dfe3b526b3840149fd2c5c8072ebb6a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6dfe3b526b3840149fd2c5c8072ebb6a2025-02-03T05:51:04ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/712932712932Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential InequalityYeong-Jeu Sun0Yu-Biaw Wu1Ching-Cheng Wang2Department of Electrical Engineering, I-Shou University, No.1, Sec. 1, Syuecheng Road, Dashu District, Kaohsiung City 84001, TaiwanInstitute of Manufacturing Information and Systems, National Cheng Kung University, Tainan, TaiwanInstitute of Manufacturing Information and Systems, National Cheng Kung University, Tainan, TaiwanThe concept of the exponentially stable limit cycle (ESLC) is introduced, and the ESLC phenomenon for a class of nonlinear systems is explored. Based on time-domain approach with differential inequality, the existence and uniqueness of the ESLC for such nonlinear systems can be guaranteed. Besides, the period of oscillation, the amplitude of oscillation, and guaranteed convergence rate can be accurately estimated. Finally, two numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result.http://dx.doi.org/10.1155/2013/712932 |
| spellingShingle | Yeong-Jeu Sun Yu-Biaw Wu Ching-Cheng Wang Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality Journal of Applied Mathematics |
| title | Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality |
| title_full | Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality |
| title_fullStr | Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality |
| title_full_unstemmed | Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality |
| title_short | Existence and Uniqueness of the Exponentially Stable Limit Cycle for a Class of Nonlinear Systems via Time-Domain Approach with Differential Inequality |
| title_sort | existence and uniqueness of the exponentially stable limit cycle for a class of nonlinear systems via time domain approach with differential inequality |
| url | http://dx.doi.org/10.1155/2013/712932 |
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