Synchronization of Singular Perturbation Complex Networks with an Event-Triggered Delayed Impulsive Control

Kun Liang, Kaiwen Zheng, Mengshen Chen and Xin Wang ()
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Kun Liang: School of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090, China
Kaiwen Zheng: School of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090, China
Mengshen Chen: Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Xin Wang: School of Cyber Science and Engineering, Sichuan University, Chengdu 610065, China

Mathematics, 2025, vol. 13, issue 18, 1-21

Abstract: This paper investigates the synchronization problem of singularly perturbed complex networks with time delays, in which a novel event-triggered delayed impulsive control strategy is developed. To conserve limited communication bandwidth, a dynamic event-triggered mechanism is proposed based on a Lyapunov function construction, while incorporating both delay and singular perturbation parameter ε information to avoid ill conditioning. Unlike conventional triggering approaches, the proposed mechanism only requires the Lyapunov function to decrease at impulsive instants, thereby relaxing the constraint on the energy function. Moreover, an impulse-assisted variable θ is introduced to adjust the event-triggered threshold according to the intensity of impulsive control, which reduces the triggering frequency while ensuring synchronization. By employing stability theory and the singular perturbation method, a singular perturbation parameter ε -dependent Lyapunov function is constructed to derive sufficient synchronization conditions and provide the design of the impulsive gain matrix. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed approach.

Keywords: singularly perturbed complex networks; delay impulsive control; Lyapunov-based event-triggered mechanism; coupling delay; exponential synchronization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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