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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报

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离散时间观测的非线性随机时滞系统间歇控制

杜  鹏1,   宋公飞1,2,   谢佳杰1   

  1. 1. 南京信息工程大学自动化学院，南京  210044

    2. 江苏省大气环境与装备技术协同创新中心，南京 210044
  • 收稿日期:2022-09-06 接受日期:2023-05-22 出版日期:2025-10-15 发布日期:2025-10-15
  • 基金资助:
    国家自然科学基金 (61973170; 61973168).

Intermittent Control of Stochastic Time-delay Systems with Discrete-time Observation

DU Peng1,   SONG Gongfei1,2,   XIE Jiajie1   

  1. 1. School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044

    2. Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing 210044

  • Received:2022-09-06 Accepted:2023-05-22 Online:2025-10-15 Published:2025-10-15
  • Supported by:
    The National Natural Science Foundation of China (61973170; 61973168).

摘要：

研究了基于离散时间观测的非线性随机时滞系统非周期间歇控制问题。将离散反馈控制策略和间歇性控制策略结合，设计了一个离散时间观测系统状态的非周期间歇反馈控制器，使得受控系统达到均方指数稳定。通过$M$矩阵理论和间歇性控制策略建立了系统稳定的条件，再由Lyapunov函数和伊藤公式证明了非线性随机时滞系统均方指数稳定。最后，给出一个数值例子来说明理论推导的正确性，并给出数值仿真图。

关键词: 非线性, 随机时滞系统, 间歇控制, 离散时间观测, 均方指数稳定

Abstract:

In this paper, the problem of aperiodic intermittent control for nonlinear stochastic time-delay systems based on discrete-time observations is studied. Combining the discrete feedback control strategy with the intermittent control strategy, an aperiodic intermittent feedback controller for observing the state of the system in discrete time is designed, which makes the controlled system reach mean square exponential stability. The conditions for system stability are established through M-matrix theory and intermittent control strategy, and the mean square exponential stability of nonlinear stochastic time-delay systems is proved by Lyapunov function and It\^{o} formula. Finally, a numerical example was provided to demonstrate the correctness of the theoretical derivation.

Key words: nonlinearity, stochastic time-delay system, intermittent control, discrete-time observation, mean square exponential stability

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