Exponential stability of impulsive nonlinear stochastic differential equations with mixed delays |
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Authors: | Quanxin Zhu Bing Song |
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Affiliation: | 1. Department of Mathematics, Ningbo University, Ningbo 315211, Zhejiang, China;2. Jiangsu Institute of Economic Trade Technology, Nanjing 211168, Jiangsu, China |
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Abstract: | This paper is concerned with the problem of exponential stability for a class of impulsive nonlinear stochastic differential equations with mixed time delays. By applying the Lyapunov–Krasovskii functional, Dynkin formula and Razumikhin technique with a stochastic version as well as the linear matrix inequalities (LMIs) technique, some novel sufficient conditions are derived to ensure the exponential stability of the trivial solution in the mean square. The obtained results generalize and improve some recent results. In particular, our results are expressed in terms of LMIs, and thus they are more easily verified and applied in practice. Finally, a numerical example and its simulation are given to illustrate the theoretical results. |
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