Stability analysis of stochastic delay differential equations with Lévy noise
This paper is concerned with pth moment exponential stability problem for a class of stochastic delay differential equations driven by Lévy processes. Several new stability theorems are obtained by developing a method—proof by contradiction. Moreover, the results are applied to investigate the pth m...
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| Published in | Systems & control letters Vol. 118; pp. 62 - 68 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.08.2018
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-6911 |
| DOI | 10.1016/j.sysconle.2018.05.015 |
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| Abstract | This paper is concerned with pth moment exponential stability problem for a class of stochastic delay differential equations driven by Lévy processes. Several new stability theorems are obtained by developing a method—proof by contradiction. Moreover, the results are applied to investigate the pth moment exponential stability of stochastic neural networks with Lévy noise. In particular, the time-varying delay in our results is not required to be differentiable, even not continuous. The obtained results improve greatly some previous works given in the literature. In particular, our method can easily correct the incorrect proofs appeared in two recent papers. Finally, two examples are provided to show the effectiveness of the theoretical results. |
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| AbstractList | This paper is concerned with pth moment exponential stability problem for a class of stochastic delay differential equations driven by Lévy processes. Several new stability theorems are obtained by developing a method—proof by contradiction. Moreover, the results are applied to investigate the pth moment exponential stability of stochastic neural networks with Lévy noise. In particular, the time-varying delay in our results is not required to be differentiable, even not continuous. The obtained results improve greatly some previous works given in the literature. In particular, our method can easily correct the incorrect proofs appeared in two recent papers. Finally, two examples are provided to show the effectiveness of the theoretical results. |
| Author | Zhu, Quanxin |
| Author_xml | – sequence: 1 givenname: Quanxin orcidid: 0000-0003-3130-4923 surname: Zhu fullname: Zhu, Quanxin email: zqx22@126.com organization: Key Laboratory of HPC-SIP (MOE), College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, Hunan, China |
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| SubjectTerms | [formula omitted]th moment exponential stability Lévy noise Neural network Stochastic delay differential equation Time-varying delay |
| Title | Stability analysis of stochastic delay differential equations with Lévy noise |
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