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A note on stability of hybrid stochastic differential equations

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  • Li, Bing

Abstract

In this paper, the pth moment stability of hybrid stochastic differential equations is investigated. Several new sufficient conditions are derived by constructing an auxiliary delayed differential equation and using the comparison principle. The proposed criteria remove some harsh restrictions imposed on the diffusion operators and improve some previous related works. Numerical examples and simulations are given to illustrate the effectiveness of theoretical results.

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  • Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
    • Handle: RePEc:eee:apmaco:v:299:y:2017:i:c:p:45-57
    DOI: 10.1016/j.amc.2016.11.034
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    References listed on IDEAS

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    1. Xie, Jing & Kao, Yonggui & Wang, Changhong & Gao, Cunchen, 2015. "Delay-dependent robust stability of uncertain neutral-type Itoˆ stochastic systems with Markovian jumping parameters," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 576-585.
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    5. You, Surong & Mao, Wei & Mao, Xuerong & Hu, Liangjian, 2015. "Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 73-83.
    6. Shen, Mouquan & Yan, Shen & Zhang, Guangming & Park, Ju H., 2016. "Finite-time H∞ static output control of Markov jump systems with an auxiliary approach," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 553-561.
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    Cited by:

    1. Fu, Xiaozheng & Zhu, Quanxin & Guo, Yingxin, 2019. "Stabilization of stochastic functional differential systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 776-789.
    2. Li, Yuyuan & Lu, Jianqiu & Kou, Chunhai & Mao, Xuerong & Pan, Jiafeng, 2018. "Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 152-161.
    3. Zhang, Tian & Chen, Huabin, 2019. "The stability with a general decay of stochastic delay differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 294-307.
    4. Ruan, Dehao & Xu, Liping & Luo, Jiaowan, 2019. "Stability of hybrid stochastic functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 832-841.
    5. Feng, Lichao & Liu, Qiumei & Cao, Jinde & Zhang, Chunyan & Alsaadi, Fawaz, 2022. "Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 417(C).

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