| 引用本文: | 李延波,陈超洋,张晶华,李成群.分布时滞随机偏微分系统的均方指数稳定性[J].控制理论与应用,2022,39(11):2185~2192.[点击复制] |
| LI Yan-bo,CHEN Chao-yang,ZHANG Jing-hua,LI Chen-qun.Mean-square exponential stability of stochastic partial differential systems with distributed time-delay[J].Control Theory and Technology,2022,39(11):2185~2192.[点击复制] |
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| 分布时滞随机偏微分系统的均方指数稳定性 |
| Mean-square exponential stability of stochastic partial differential systems with distributed time-delay |
| 摘要点击 1331 全文点击 328 投稿时间：2021-03-31 修订日期：2022-04-21 |
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| DOI编号 10.7641/CTA.2021.10270 |
| 2022,39(11):2185-2192 |
| 中文关键词 随机偏微分系统 分布时滞 It?o公式 均方指数稳定性 |
| 英文关键词 stochastic partial differential systems (SPDE) distributed time-delay It?o formula mean-square stability |
| 基金项目 国家重点研发计划国际科技创新合作项目(2019YFE0118700), 国家自然科学基金项目(61973110, 71961002), 湖南省杰出青年基金项目(2021JJ1 0030), 湖南省湖湘青年英才科技创新人才项目(2020RC3048), 广西财经学院博士科研启动项目(BS2019002), 统计学广西一流学科建设项目 (2022SXYB03), 广西青年扩展项目(2020KY16018), 数字制造装备与技术国家重点实验室开放基金资助项目(DMETKF2022023)资助. |
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| 中文摘要 |
| 针对一类同时具有分布时滞和维纳过程的随机偏微分系统, 首先基于It?o微分公式, 通过计算弱无穷小算
子, 得到了随机微分导数; 其次利用Green公式和积分不等式及Schur补引理对矩阵不等式进行处理; 然后对微分两
边积分并同时取数学期望处理随机交叉项; 获得了分布时滞随机偏微分系统是均方指数稳定的充分条件. 在此基础
上, 进一步考虑了离散变时滞和分布变时滞在一定约束情形下的分布时滞随机偏微分系统的均方指数稳定性问题.
最后给出仿真实例, 仿真结果表明所获得的线性矩阵不等式条件保证了系统的稳定性, 验证了所得结论的有效性. |
| 英文摘要 |
| The sufficient conditions for mean-square exponential stability of stochastic partial differential system with
distributed delays andWiener processes are given. First of all, the stochastic differential derivative is obtained by calculating
weak infinitesimal operator based on the It?o differential formula. Secondly, the matrix inequality is handled by the Green
formula, the integral inequality and the Schur complement lemma. Then, both sides of the differential are integrated and
mathematical expectation is taken to deal with the random cross term at the same time. On this basis, the mean-square
exponential stability of distributed delay stochastic partial differential systems with discrete and distributed time-varying
delay under certain constraints is further considered. Finally, a simulation example is given. The simulation results show the
obtained linear matrix inequality conditions ensure the stability of the system and verify the effectiveness of the conclusions. |
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