Impulsive sampled-data synchronization of directed coupled harmonic oscillators

In this paper we propose a distributed protocol for synchronization of directed coupled harmonic oscillators with local instantaneous interaction. We provide convergence analysis for such protocol over fixed and switching directed network topologies, respectively. It is shown that directed coupled harmonic oscillators can synchronize when coupling strengthen is less than a given threshold value and impulsive intervals belong to certain interval. Furthermore, if the impulsive intervals are constant, those conditions are sufficient and necessary. Subsequently, numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results.