基于边界采样控制的随机反应扩散系统稳定性

王云竹

doi:10.21656/1000-0887.450309

基于边界采样控制的随机反应扩散系统稳定性

doi: 10.21656/1000-0887.450309

王云竹^,

浙大城市学院理学基础教育中心，杭州 310015

详细信息

作者简介:
王云竹（1992—），女，博士(E-mail: hzcu_wyz@163.com).

通讯作者:
王云竹（1992—），女，博士(E-mail: hzcu_wyz@163.com).

中图分类号: O231.3
计量
- 文章访问数: 14
- HTML全文浏览量: 4
- PDF下载量: 1
- 被引次数: 0
出版历程
- 收稿日期: 2024-11-18
- 修回日期: 2025-12-15
- 网络出版日期: 2026-04-30

Stability of Stochastic Reaction-Diffusion Systems via Boundary Sampled-Data Control

WANG Yunzhu^,

Foundation Science Education Center, Hangzhou City University, Hangzhou 310015, P.R.China

摘要

摘要: 利用边界采样控制讨论了随机反应扩散系统(stochastic reactiondiffusion system， SRDS)稳定性问题.当系统状态可以全部获取时，设计了一个边界采样控制器(boundary sampling controller，BSC)，构建了与采样间隔相关的分段不连续Lyapunov函数.对于SRDS，利用空间积分型Wirtinger不等式和同构离散变换，得到了矩阵不等式形式的均方指数稳定和鲁棒均方指数稳定的充分条件.当系统状态无法完全获得时，提出了一种基于观测器的边界采样控制策略，分别得到了系统均方指数稳定和鲁棒均方指数稳定的研究结果.最后，通过三个数值例子验证了所提方法的可行性.
- 边界采样控制 /
- 稳定性 /
- 随机反应扩散系统 /
- 观测器
Abstract: The stability of stochastic reaction-diffusion systems under boundary sampling control was discussed. With the fully accessible system state, a boundary sampled-data controller was proposed, and a piecewise discontinuous Lyapunov function related to the sampling interval was constructed. For stochastic reaction-diffusion systems, sufficient conditions for mean-square exponential stability, both in nominal and robust settings, were obtained with the Wirtinger inequality for spatial integrals and isomorphic discrete transformations, in the form of matrix inequalities. With the not fully accessible system state, an observer-based boundary sampled-data control strategy was proposed, and results for the mean-square exponential stability and the robust mean-square exponential stability of the system were obtained, respectively. Finally, the feasibility of the proposed methods was demonstrated through 3 numerical examples.
- boundary sampled-data control /
- stability /
- stochastic reaction-diffusion system /
- observer

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