Stability of Fuzzy Dynamical Systems via Lyapunov Functions
The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterizati...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2020/6218424 |
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| _version_ | 1850177205615722496 |
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| author | Abdelati El Allaoui Said Melliani Lalla Saadia Chadli |
| author_facet | Abdelati El Allaoui Said Melliani Lalla Saadia Chadli |
| author_sort | Abdelati El Allaoui |
| collection | DOAJ |
| description | The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stability. Some examples are given to illustrate the obtained results. |
| format | Article |
| id | doaj-art-c23d9764868841b2a19de2ca0d9a0084 |
| institution | OA Journals |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-c23d9764868841b2a19de2ca0d9a00842025-08-20T02:19:03ZengWileyInternational Journal of Differential Equations1687-96431687-96512020-01-01202010.1155/2020/62184246218424Stability of Fuzzy Dynamical Systems via Lyapunov FunctionsAbdelati El Allaoui0Said Melliani1Lalla Saadia Chadli2Sultan Moulay Slimane University, Department of Mathematics, Laboratory of Applied Mathematics & Scientific Calculus, Beni Mellal, P.O. Box 523, MoroccoSultan Moulay Slimane University, Department of Mathematics, Laboratory of Applied Mathematics & Scientific Calculus, Beni Mellal, P.O. Box 523, MoroccoSultan Moulay Slimane University, Department of Mathematics, Laboratory of Applied Mathematics & Scientific Calculus, Beni Mellal, P.O. Box 523, MoroccoThe purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stability. Some examples are given to illustrate the obtained results.http://dx.doi.org/10.1155/2020/6218424 |
| spellingShingle | Abdelati El Allaoui Said Melliani Lalla Saadia Chadli Stability of Fuzzy Dynamical Systems via Lyapunov Functions International Journal of Differential Equations |
| title | Stability of Fuzzy Dynamical Systems via Lyapunov Functions |
| title_full | Stability of Fuzzy Dynamical Systems via Lyapunov Functions |
| title_fullStr | Stability of Fuzzy Dynamical Systems via Lyapunov Functions |
| title_full_unstemmed | Stability of Fuzzy Dynamical Systems via Lyapunov Functions |
| title_short | Stability of Fuzzy Dynamical Systems via Lyapunov Functions |
| title_sort | stability of fuzzy dynamical systems via lyapunov functions |
| url | http://dx.doi.org/10.1155/2020/6218424 |
| work_keys_str_mv | AT abdelatielallaoui stabilityoffuzzydynamicalsystemsvialyapunovfunctions AT saidmelliani stabilityoffuzzydynamicalsystemsvialyapunovfunctions AT lallasaadiachadli stabilityoffuzzydynamicalsystemsvialyapunovfunctions |