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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 ›› 2026, Vol. 43 ›› Issue (2): 301-315.doi: 10.3969/j.issn.1005-3085.2026.02.007cstr: 32411.14.cjem.CN61-1269/O1.2026.02.007

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一类带有多重时滞的非线性混合随机微分系统的动态事件触发控制

唐  俊,  吴爱龙   

  1. 湖北师范大学数学与统计学院，黄石 435000
  • 收稿日期:2023-07-09 接受日期:2024-04-30 出版日期:2026-04-15 发布日期:2026-06-15
  • 通讯作者: 吴爱龙 E-mail: hbnuwu@yeah.net
  • 基金资助:
    国家自然科学基金 (62476082)；湖北省杰出青年基金 (2021CFA080).

Dynamic Event-triggered Control for a Class of Nonlinear Hybrid Stochastic Differential  Systems with Multiple Time-delays

TANG Jun,  WU Ailong   

  1. College of Mathematics and Statistics, Hubei Normal University, Huangshi 435000
  • Received:2023-07-09 Accepted:2024-04-30 Online:2026-04-15 Published:2026-06-15
  • Contact: A. Wu. E-mail address: hbnuwu@yeah.net
  • Supported by:
    The National Natural Science Foundation of China (62476082); the Outstanding Youth Fund of Hubei Province (2021CFA080).

摘要：

混合随机系统是用于描述复杂系统动态行为的一种有效工具，针对具有外部干扰和不确定性的非线性混合随机系统的镇定问题，因受到多个时滞的干扰，其稳定性分析面临巨大挑战。基于动态事件触发机制，为降低反馈控制信号的传输频率，同时排除Zeno行为，采用非周期间歇事件触发控制策略。应用实际输入到状态稳定性来描述事件触发方案下控制目标的动态性能。此外，凭借动态事件触发反馈控制，使用李亚普诺夫函数和线性矩阵不等式的方法，获得具有多重时滞的非线性混合随机系统镇定准则。最后，通过几个算例和仿真实验验证了结论的有效性。

关键词: 事件触发控制, 实际输入到状态稳定, 多重时滞, 混合随机系统

Abstract:

Hybrid stochastic system serve as an effective tool for describing the dynamic behavior of complex systems.
For the stabilization problem of nonlinear stochastic systems with external disturbances and uncertainties, their stability analysis faces tremendous challenges due to the interference from multiple time delays. Based on the dynamic event-triggered mechanisms, in order to reduce the transmission frequency of feedback control signal and avoid Zeno behavior, the aperiodic intermittent event-triggered control strategy is adopted. The practically input-to-state stability is used to describe the dynamic performance of control target in the event-triggered schemes. Besides, by means of dynamic event-triggered feedback control, the stabilization criteria for nonlinear hybrid stochastic  systems with multiple time-delays are obtained by using Lyapunov function and linear matrix inequality method.  Finally, the effectiveness of the conclusions is verified by several examples and simulations.

Key words: event-trigger control, practically input-to-state stability, multiple time-delays, hybrid stochastic systems

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