Finite-Time Lyapunov Functions and Impulsive Control Design
In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive sy...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/5179752 |
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| _version_ | 1832560154854293504 |
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| author | Huijuan Li Qingxia Ma |
| author_facet | Huijuan Li Qingxia Ma |
| author_sort | Huijuan Li |
| collection | DOAJ |
| description | In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system. |
| format | Article |
| id | doaj-art-08adf4b97f0d475e93c40e5589ccdf37 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-08adf4b97f0d475e93c40e5589ccdf372025-02-03T01:28:14ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/51797525179752Finite-Time Lyapunov Functions and Impulsive Control DesignHuijuan Li0Qingxia Ma1School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, ChinaSchool of Mathematics and Physics, China University of Geosciences, Wuhan 430074, ChinaIn this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.http://dx.doi.org/10.1155/2020/5179752 |
| spellingShingle | Huijuan Li Qingxia Ma Finite-Time Lyapunov Functions and Impulsive Control Design Complexity |
| title | Finite-Time Lyapunov Functions and Impulsive Control Design |
| title_full | Finite-Time Lyapunov Functions and Impulsive Control Design |
| title_fullStr | Finite-Time Lyapunov Functions and Impulsive Control Design |
| title_full_unstemmed | Finite-Time Lyapunov Functions and Impulsive Control Design |
| title_short | Finite-Time Lyapunov Functions and Impulsive Control Design |
| title_sort | finite time lyapunov functions and impulsive control design |
| url | http://dx.doi.org/10.1155/2020/5179752 |
| work_keys_str_mv | AT huijuanli finitetimelyapunovfunctionsandimpulsivecontroldesign AT qingxiama finitetimelyapunovfunctionsandimpulsivecontroldesign |