Edge-event- and self-triggered synchronization of coupled harmonic oscillators with quantization and time delays

This paper considers the synchronization problem of coupled harmonic oscillators via event- and self-triggered control. In the presence of periodic event detection, an event-detecting algorithm is provided to determine the update times of each controller. Then, two self-triggered synchronization algorithms are designed to further decrease resource consumption. In the considered system, time-invariant delays appear in all edge information channels, and the design of control protocol and triggering conditions is only based on quantized relative state information, termed edge information. Numerical simulations are provided to validate the theoretical results.