比较原理与一类具有时滞和马尔科夫切换的随机抛物方程组的稳定性分析

李钊,李树勇

系统科学与数学 ›› 2019, Vol. 39 ›› Issue (4) : 648-658.

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PDF(201 KB)
系统科学与数学 ›› 2019, Vol. 39 ›› Issue (4) : 648-658. DOI: 10.12341/jssms13621
论文

比较原理与一类具有时滞和马尔科夫切换的随机抛物方程组的稳定性分析

    李钊1,李树勇1,2
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Comparison Principle and Stability Analysis of a Class of Stochastic Parabolic Equations with Delay and Markovian Switching

    LI Zhao1 ,LI Shuyong 1,2
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摘要

研究一类具有时滞和马尔科夫切换的随机抛物方程组的均方稳定性. 通过建立比较原理, 运用时滞微分不等式和随机分析技巧, 获得了该系统的均方稳定、均方 一致稳定、均方渐近稳定和均方指数稳定. 最后, 给出了主要定理的一个应用实例.

Abstract

This paper investigates the mean square stability for stochastic parabolic equations with delay and Markovian switching. By establishing the comparison principle, using delay differential inequality and stochastic analysis techniques, the mean square stability, mean square uniform stability, mean square asymptotic stability and mean square exponential stability for the system are obtained. Finally, an example is given to illustrate the main theoretical result.

关键词

比较原理 / 均方稳定 / 均方渐近稳定 / 均方指数稳定 / 具有时滞和马尔科夫切换的随机抛物方程组.

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李钊 , 李树勇. 比较原理与一类具有时滞和马尔科夫切换的随机抛物方程组的稳定性分析. 系统科学与数学, 2019, 39(4): 648-658. https://doi.org/10.12341/jssms13621
LI Zhao , LI Shuyong. Comparison Principle and Stability Analysis of a Class of Stochastic Parabolic Equations with Delay and Markovian Switching. Journal of Systems Science and Mathematical Sciences, 2019, 39(4): 648-658 https://doi.org/10.12341/jssms13621
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