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

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.