Sampled-data Group Synchronization of Coupled Harmonic Oscillators Subject to Controller Failure

This paper is concerned with the sampled-data group synchronization issue of coupled harmonic oscillators subject to controller failure. A group synchronization algorithm in directed networks of multiple groups consisting of coupled harmonic oscillators is proposed based on the sampled-data velocity measurement with controller failures. Some simple and general criteria for such algorithm are proposed by using tools from matrix analysis theory and algebraic graph theory. It is shown that, for the case of directed acyclic topology, the group synchronization can always be guaranteed by the structure of acyclic partition, and thereby it is convenient in practical applications. Finally, the performance of the proposed control scheme is shown by numerical simulation results.