线性随机系统的周期性间歇控制
Periodic Intermittent Control for Linear Stochastic Systems
DOI: 10.12677/aam.2025.145267, PDF,   
作者: 李 乔：东华大学物理学院，上海；胡良剑：东华大学数学与统计学院，上海；姜雅赧*：上海立信会计金融学院信息管理学院，上海
关键词: 随机系统；伊藤公式；间歇控制；均方指数稳定；Stochastic System； Itô Formula； Intermittent Control； Mean-Square Stability
摘要: 本文针对不稳定线性随机系统，研究了周期性间歇控制策略，能够有效地抑制随机干扰，使得受控系统满足稳定性要求。运用Lyapunov函数和伊藤公式，给出了间歇控制作用下闭环系统均方指数稳定的两类充分性条件。这些条件用线性矩阵不等式(LMI)表达，以方便地进行控制器设计。最后，通过一个数值例子说明了本文理论的有效性。
Abstract: This paper focuses on unstable linear stochastic systems and studies the periodic intermittent control strategy, which can effectively suppress random disturbances and ensure that the controlled system meets the stability requirements. By using Lyapunov function and Itô formula, two types of sufficiency conditions for the mean-square exponential stability of the closed-loop system under intermittent control are presented. These conditions are expressed in terms of linear matrix inequalities (LMIs) to facilitate controller design. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results in this paper.
文章引用：李乔, 胡良剑, 姜雅赧. 线性随机系统的周期性间歇控制[J]. 应用数学进展, 2025, 14(5): 377-386. https://doi.org/10.12677/aam.2025.145267

参考文献

[1] Basak, G.K., Bisi, A. and Ghosh, M.K. (1996) Stability of a Random Diffusion with Linear Drift. Journal of Mathematical Analysis and Applications, 202, 604-622. [Google Scholar] [CrossRef] 
[2] Mao, X. (2006) Stochastic Differential Equations and Applications. 2nd Edition, Academic Press.
[3] El Ghaoui, L. (1995) State-Feedback Control of Systems with Multiplicative Noise via Linear Matrix Inequalities. Systems & Control Letters, 24, 223-228. [Google Scholar] [CrossRef] 
[4] Hu, L. and Mao, X. (2008) Almost Sure Exponential Stabilisation of Stochastic Systems by State-Feedback Control. Automatica, 44, 465-471. [Google Scholar] [CrossRef] 
[5] Jiang, Y., Hu, L., Lu, J., Mao, W. and Mao, X. (2021) Stabilization of Hybrid Systems by Intermittent Feedback Controls Based on Discrete‐time Observations with a Time Delay. IET Control Theory & Applications, 15, 2039-2052. [Google Scholar] [CrossRef] 
[6] 宋公飞, 张子梦, 李涛. 强非线性中立型随机时滞系统的间歇性反馈控制[J]. 控制理论与应用, 2023, 40(9): 1657-1664.
[7] Liu, Y., Liu, J. and Li, W. (2021) Stabilization of Highly Nonlinear Stochastic Coupled Systems via Periodically Intermittent Control. IEEE Transactions on Automatic Control, 66, 4799-4806. [Google Scholar] [CrossRef] 
[8] 王丽丽, 徐瑞. 一类具有Leakage时滞的反应扩散神经网络在间歇控制下的指数同步[J]. 应用数学进展, 2016, 5(2): 298-309.
[9] Mao, W., You, S., Jiang, Y. and Mao, X. (2023) Stochastic Stabilization of Hybrid Neural Networks by Periodically Intermittent Control Based on Discrete-Time State Observations. Nonlinear Analysis: Hybrid Systems, 48, Article ID: 101331. [Google Scholar] [CrossRef] 
[10] Wan, F., Zhao, X., Deng, F. and Huang, Y. (2025) Periodically Intermittent Control of Hybrid Stochastic Delay Systems with Asynchronous Switching by Sampled-Data Feedback. IEEE Transactions on Automatic Control, 70, 174-189. [Google Scholar] [CrossRef] 
[11] Zhao, Y. and Zhu, Q. (2022) Stabilization of Highly Nonlinear Neutral Stochastic Systems with Markovian Switching by Periodically Intermittent Feedback Control. International Journal of Robust and Nonlinear Control, 32, 10201-10214. [Google Scholar] [CrossRef] 
[12] Wang, X., Liu, S., Lv, G. and Zou, G. (2024) Stabilization by the Discrete Observations Feedback Control and Intermittent Control. Filomat, 38, 6371-6383. [Google Scholar] [CrossRef] 
[13] 俞立. 鲁棒控制: 线性矩阵不等式处理方法[M]. 北京: 清华大学出版社, 2002.

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