Prescribed-time stabilization for nonlinear systems via hybrid continuous and dynamic event-triggered impulsive control

Yanmei Yang; Xiaoying Zhu; Lichao Feng; Liping Du; Yanmei Yang; Xiaoying Zhu; Lichao Feng; Liping Du

doi:10.3934/nhm.2025054

Networks and Heterogeneous Media

2025, Volume 20, Issue 4: 1251-1268. doi: 10.3934/nhm.2025054

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Research article

Prescribed-time stabilization for nonlinear systems via hybrid continuous and dynamic event-triggered impulsive control

1.
College of Science, North China University of Science and Technology, Tangshan 063210, China
2.
Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China

Received: 12 October 2025 Revised: 11 November 2025 Accepted: 18 November 2025 Published: 24 November 2025

Here, by integrating continuous control and dynamic event-triggered impulsive control (DETIC) based on a piecewise function ratio framework, a hybrid control strategy is developed to solve prescribed-time stabilization (PTS) for nonlinear systems. Different from the traditional methods, the designed hybrid control strategy is rooted in DETIC, and the designed triggering mechanism allows the impulsive triggering instants to be dynamically adjusted, with the Zeno behavior being eliminated. The dynamic event-triggered mechanism (DETM) is utilized to determine the instants of impulses, thereby reducing unnecessary control execution and enhancing control efficiency. Moreover, the proposed approach is utilized for the master-slave synchronization of the Lorenz system, and numerical experiments are conducted to demonstrate the practicality and efficiency of the developed hybrid control scheme.
- dynamic event-triggered impulsive control,
- hybrid control,
- prescribed-time stability,
- prescribed-time synchronization
Citation: Yanmei Yang, Xiaoying Zhu, Lichao Feng, Liping Du. Prescribed-time stabilization for nonlinear systems via hybrid continuous and dynamic event-triggered impulsive control[J]. Networks and Heterogeneous Media, 2025, 20(4): 1251-1268. doi: 10.3934/nhm.2025054

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Abstract

Here, by integrating continuous control and dynamic event-triggered impulsive control (DETIC) based on a piecewise function ratio framework, a hybrid control strategy is developed to solve prescribed-time stabilization (PTS) for nonlinear systems. Different from the traditional methods, the designed hybrid control strategy is rooted in DETIC, and the designed triggering mechanism allows the impulsive triggering instants to be dynamically adjusted, with the Zeno behavior being eliminated. The dynamic event-triggered mechanism (DETM) is utilized to determine the instants of impulses, thereby reducing unnecessary control execution and enhancing control efficiency. Moreover, the proposed approach is utilized for the master-slave synchronization of the Lorenz system, and numerical experiments are conducted to demonstrate the practicality and efficiency of the developed hybrid control scheme.

References

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