Synchronization of Coupled Harmonic Oscillators With Asynchronous Intermittent Communication

This paper adopts two different approaches, the small-gain technique and the integral quadratic constraints (IQCs), to investigate the synchronization problem of coupled harmonic oscillators (CHOs) via an event-triggered control strategy in a directed graph. First, a novel control protocol is proposed such that every state signal of the CHO decides when to exchange information with its neighbors asynchronously. Then, the resulting closed-loop system based on the designed control protocol is converted into a feedback interconnection of a linear system and a bounded operator, and the stable condition of the feedback interconnection is presented by employing the small-gain technique. In order to better describe the relationship between the input and output, the IQCs theorem is applied to derive the stable condition on the basis of the Kalman–Yakubovich–Popov lemma. Finally, a simulation example is provided to verify the proposed new algorithms.