Stability Analysis of Retarded Differential Inclusions
Retarded differential inclusions have drawn more and more attention, due to the development of feedback control systems with delays and dynamical systems determined by retarded differential equations with a discontinuous right-hand side. The purpose of this paper is to establish a result on the stab...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/832187 |
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| _version_ | 1849410875599880192 |
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| author | Jiafu Wang Gui Zhang |
| author_facet | Jiafu Wang Gui Zhang |
| author_sort | Jiafu Wang |
| collection | DOAJ |
| description | Retarded differential inclusions have drawn more and more attention, due to the development of feedback control systems with delays and dynamical systems determined by retarded differential equations with a discontinuous right-hand side. The purpose of this paper is to establish a result on the stability and asymptotical stability for retarded differential inclusions. Comparing with the previous results, the main result obtained in this paper allows Lyapunov functions to be nonsmooth. Moreover, to deal with the asymptotical stability, it is not required that Lyapunov functions should have an infinitesimal upper limit, but this condition is needed in most of the previous results. To demonstrate applicability, we use the main result in the analysis of asymptotical stability of a class of neural networks with discontinuous activations and delays. |
| format | Article |
| id | doaj-art-5abcd81e5dd541e0b71f83102b516a84 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5abcd81e5dd541e0b71f83102b516a842025-08-20T03:34:57ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/832187832187Stability Analysis of Retarded Differential InclusionsJiafu Wang0Gui Zhang1Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha, Hunan 410004, ChinaInstitute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha, Hunan 410004, ChinaRetarded differential inclusions have drawn more and more attention, due to the development of feedback control systems with delays and dynamical systems determined by retarded differential equations with a discontinuous right-hand side. The purpose of this paper is to establish a result on the stability and asymptotical stability for retarded differential inclusions. Comparing with the previous results, the main result obtained in this paper allows Lyapunov functions to be nonsmooth. Moreover, to deal with the asymptotical stability, it is not required that Lyapunov functions should have an infinitesimal upper limit, but this condition is needed in most of the previous results. To demonstrate applicability, we use the main result in the analysis of asymptotical stability of a class of neural networks with discontinuous activations and delays.http://dx.doi.org/10.1155/2014/832187 |
| spellingShingle | Jiafu Wang Gui Zhang Stability Analysis of Retarded Differential Inclusions Journal of Applied Mathematics |
| title | Stability Analysis of Retarded Differential Inclusions |
| title_full | Stability Analysis of Retarded Differential Inclusions |
| title_fullStr | Stability Analysis of Retarded Differential Inclusions |
| title_full_unstemmed | Stability Analysis of Retarded Differential Inclusions |
| title_short | Stability Analysis of Retarded Differential Inclusions |
| title_sort | stability analysis of retarded differential inclusions |
| url | http://dx.doi.org/10.1155/2014/832187 |
| work_keys_str_mv | AT jiafuwang stabilityanalysisofretardeddifferentialinclusions AT guizhang stabilityanalysisofretardeddifferentialinclusions |