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Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients

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  • You, Surong
  • Mao, Wei
  • Mao, Xuerong
  • Hu, Liangjian

Abstract

This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations (PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Based on the second criterion, robust stability of a perturbed hybrid PSDE is also investigated. The theory shows how much an exponentially stable hybrid PSDE can tolerate to remain stable.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:263:y:2015:i:c:p:73-83
    DOI: 10.1016/j.amc.2015.04.022
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    References listed on IDEAS

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    1. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    Cited by:

    1. Zhan, Weijun & Gao, Yan & Guo, Qian & Yao, Xiaofeng, 2019. "The partially truncated Euler–Maruyama method for nonlinear pantograph stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 109-126.
    2. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
    3. Xu, Yan & He, Zhimin & Wang, Peiguang, 2015. "pth moment asymptotic stability for neutral stochastic functional differential equations with Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 594-605.
    4. 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.
    5. Jiang, Yan & Zhai, Junyong, 2019. "Observer-based stabilization of sector-bounded nonlinear stochastic systems in the presence of intermittent measurements," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 740-752.
    6. Yu, Peilin & Deng, Feiqi & Sun, Yuanyuan & Wan, Fangzhe, 2022. "Stability analysis of impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    7. 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.

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