Position-Based Synchronization of Networked Harmonic Oscillators With Asynchronous Sampling and Communication Delays

This paper is concerned with position-based synchronization of networked harmonic oscillators. Note that synchronization cannot be achieved via current-position-based protocols. The objective of this paper is to investigate the positive effects of network-induced delays on the synchronization of networked harmonic oscillators. That is, if taking network-induced delays into account, the motion of harmonic oscillators can be really synchronized via a proper position-based control protocol. In doing so, the harmonic oscillators are connected via a shared digital communication network. Different from some existing results, system measurements from oscillator nodes are sampled in an asynchronous way; and network-induced delays are assumed to be time varying and bounded, and they do not need to be synchronous with those from the other communication channels. At each oscillator node, a buffer is embedded into the controller to store the newest sampled-data packets transmitted from its neighboring nodes through communication channels. Then, based on the store of the buffer, the controller computes its control signal with its own period. As a result, the overall synchronization error system is modeled as a linear system with multiple interval time-varying delays. By employing the discretized Lyapunov-Krasovskii functional method, a sufficient condition on synchronization of networked harmonic oscillators is derived, which can ensure that the synchronization error system is asymptotically stable for network-induced delays falling into a certain closed interval whose lower bound is a positive real number. This condition is thus used to design suitable control protocols in terms of linear matrix inequalities with several tuning parameters. Finally, a multirobot platform is given to demonstrate the effectiveness of the proposed method.