Quasi-Synchronization of Coupled Nonlinear Hyperbolic Systems by Hybrid-Trigger-Based Impulsive Pinning Control

In this note, the quasi-synchronization problem for coupled nonlinear hyperbolic systems with delays and different external inputs is addressed through a hybrid-trigger-based impulsive pinning control framework. First, a unified control architecture that synergistically integrates event-triggered impulsive control, time-triggered impulsive control, and pinning control is proposed. This hybrid strategy significantly reduces control costs while ensuring bounded synchronization errors and rigorously excluding Zeno behavior. Second, a less conservative sufficient criterion for quasi-synchronization is derived via Lyapunov stability analysis and average dwell-time techniques. The event-triggered mechanism employs an exponentially decaying threshold function, which rigorously excludes Zeno phenomena and allows for analytical quantification of the minimum interevent interval. Finally, numerical simulations validate the effectiveness and superiority of the proposed method in balancing convergence rate, steady-state error, and resource efficiency.