Synchronization of sampled-data networked harmonic oscillators with controller failure and communication time delays

This paper is concerned with the synchronization problem of networked harmonic oscillators in undirected networks with communication delays and controller failures. It is assumed that each oscillator updates its state based on the sampled velocity information relative to its neighbors at discrete moments. A distributed algorithm is proposed in virtue of time driven digital samplers and controllers and event driven zero-order holders. Some simple yet generic sufficient conditions on exponential convergence for such algorithm over, respectively, fixed and switching network topologies are presented by analyzing the analytic solution of the dynamical error system. Finally, numerical simulations are given to demonstrate the effectiveness and advantages of the proposed algorithm.