Novel stability and passivity analysis for three types of nonlinear LRC circuits
In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of...
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| Format: | Article |
| Language: | English |
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Balikesir University
2021-07-01
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| Series: | An International Journal of Optimization and Control: Theories & Applications |
| Subjects: | |
| Online Access: | http://www.ijocta.org/index.php/files/article/view/1073 |
| _version_ | 1797907147421384704 |
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| author | Muzaffer Ates Nezir Kadah |
| author_facet | Muzaffer Ates Nezir Kadah |
| author_sort | Muzaffer Ates |
| collection | DOAJ |
| description | In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The results are provided within and are of central importance for the analysis of nonlinear electrical, mechanical, and neural systems which based on the system energy perspective. The simulation results given from Matlab successfully verifies the theoretical predictions. |
| first_indexed | 2024-04-10T10:31:58Z |
| format | Article |
| id | doaj.art-54af4a58f499412e9732ea161c395389 |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-04-10T10:31:58Z |
| publishDate | 2021-07-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-54af4a58f499412e9732ea161c3953892023-02-15T16:21:05ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032021-07-0111210.11121/ijocta.01.2021.001073Novel stability and passivity analysis for three types of nonlinear LRC circuitsMuzaffer Ates0Nezir Kadah1Departments of Electrical-Electronics Engineering, University of Van Yuzuncu Yil, TurkeyDepartments of Electrical-Electronics Engineering, Adana Alparslan Turkes Science and Technology University, TurkeyIn this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective. The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The results are provided within and are of central importance for the analysis of nonlinear electrical, mechanical, and neural systems which based on the system energy perspective. The simulation results given from Matlab successfully verifies the theoretical predictions.http://www.ijocta.org/index.php/files/article/view/1073Lyapunov stabilitynonlinear systemspassivityGronwall’s inequality |
| spellingShingle | Muzaffer Ates Nezir Kadah Novel stability and passivity analysis for three types of nonlinear LRC circuits An International Journal of Optimization and Control: Theories & Applications Lyapunov stability nonlinear systems passivity Gronwall’s inequality |
| title | Novel stability and passivity analysis for three types of nonlinear LRC circuits |
| title_full | Novel stability and passivity analysis for three types of nonlinear LRC circuits |
| title_fullStr | Novel stability and passivity analysis for three types of nonlinear LRC circuits |
| title_full_unstemmed | Novel stability and passivity analysis for three types of nonlinear LRC circuits |
| title_short | Novel stability and passivity analysis for three types of nonlinear LRC circuits |
| title_sort | novel stability and passivity analysis for three types of nonlinear lrc circuits |
| topic | Lyapunov stability nonlinear systems passivity Gronwall’s inequality |
| url | http://www.ijocta.org/index.php/files/article/view/1073 |
| work_keys_str_mv | AT muzafferates novelstabilityandpassivityanalysisforthreetypesofnonlinearlrccircuits AT nezirkadah novelstabilityandpassivityanalysisforthreetypesofnonlinearlrccircuits |