Abstract
In this paper, the problems on the exponential stability in p-th (p ≥ 2)-moment and the almost sure exponential stability for neutral stochastic differential delay equation with Markovian switching and impulses are analyzed. By establishing an impulsive delay integral inequality, the Lyapunov theorem on the exponential stability in p-th (p ≥ 2)-moment is given. Then, by using the Borel-Cantelli lemma, the almost sure exponential stability theorem is also proved. Two major advantages of these two results are that the differentiability or continuity of the delay function is not required, and that while considering the concerned problem, the difficulty coming from the simultaneous presence of the neutral item, the impulsive disturbance and the stochastic perturbations is overcome. An example is provided to examine the effectiveness and potential of the theoretic results obtained.
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This work is supported by the Natural Science Foundation of China under Grant No. 62163027, the Natural Science Foundation of Jiangxi Province of China under Grants No. 20171BAB201007, 20171BCB23001, and the Foundation of Jiangxi Provincial Educations of China under Grant No. GJJ14155.
Yuntao Qiu is a undergraduate student with the Department of Mathematics, Nanchang University, China. He is currently interested in mathematics financial and stochastic differential equations.
Huabin Chen received his Ph.D. degree in mathematics from Huazhong University of Science and Technology, Wuhan, China, in 2009. He is a professor in the Department of Mathematics, Nanchang University, China. His current research interest includes systems and control theory and stochastic differential equations.
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Qiu, Y., Chen, H. Exponential Stability for Neutral Stochastic Differential Delay Equations with Markovian Switching and Nonlinear Impulsive Effects. Int. J. Control Autom. Syst. 21, 367–375 (2023). https://doi.org/10.1007/s12555-021-0283-x
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DOI: https://doi.org/10.1007/s12555-021-0283-x