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Stability of second-order stochastic neutral partial functional differential equations driven by impulsive noises

脉冲噪声驱动的二阶随机中立型偏泛函方程的稳定性

Abstract

This paper investigates the stability of second-order stochastic neutral partial functional differential equations driven by impulsive noises. Some sufficient conditions ensuring pth moment exponential stability of the second-order stochastic neutral partial functional differential equations driven by impulsive noises are obtained by establishing a new impulsive-integral inequality. These existing results are generalized and improved by the present study. Finally, an example is given to show the effectiveness of our results.

创新点

本文主要讨论的是脉冲驱动的二阶随机中立型偏泛函方程的指数稳定性。首先建立了一个新的脉冲积分不等式, 这个新的脉冲积分不等式能够很好的处理中立项及脉冲噪声所带来的困难, 并且在参数取不同值时也适用于非脉冲影响的系统和非中立型的情形, 然后通过这个新建立的脉冲积分不等式给出了脉冲驱动的二阶随机中立型偏泛函方程的指数稳定性的代数判据, 有效地避免了将二阶随机方程转化为一阶随机方程的研究方法, 具有更好的适应性。

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61304067, 11271146), Natural Science Foundation of Hubei Province of China (Grant No. 2013CFB443), Key Program of National Natural Science Foundation of China (Grant No. 61134012), and Prior Developing Field for the Doctoral Program of Higher Education of China (Grant No. 20130142130012).

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Correspondence to Feng Jiang.

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Jiang, F., Yang, H. & Shen, Y. Stability of second-order stochastic neutral partial functional differential equations driven by impulsive noises. Sci. China Inf. Sci. 59, 112208 (2016). https://doi.org/10.1007/s11432-015-0818-1

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Keywords

  • second-order stochastic neutral partial functional differential equations
  • exponential stability
  • impulsive noises
  • sine family
  • cosine family

关键词

  • 二阶随机中立型偏泛函方程
  • 指数稳定
  • 脉冲噪声
  • 正弦族
  • 余弦族