Sine-Based Event-Triggered Control for Synchronizing Kuramoto Networks to a Pacemaker

This article investigates the phase synchronization problem in Kuramoto oscillator networks guided by a pacemaker. A sinusoidal function-based event-triggered strategy is proposed to reduce the dependence on real-time communication in conventional synchronization control. The triggering condition incorporates both the measurement error and an exponentially decaying term, ensuring that control updates and interoscillator communication occur only when necessary. Using the positive invariant set and Lyapunov stability theory, sufficient conditions for exponential synchronization are established, which explicitly relate the convergence rate to the network’s algebraic connectivity and control gain. Furthermore, the exclusion of Zeno behavior is rigorously proven by deriving a strictly positive minimum inter-event time. Numerical examples demonstrate the effectiveness of the proposed approach.