H-infinity pinning synchronization of directed networks with aperiodic sampled-data communications

This paper addresses the global pinning synchronization problem for a class of directed networks with aperiodic sampled-data communications. Important yet challenging issues of how many and which nodes should be pinned for realizing global synchronization in a fixed directed network without external disturbances are first discussed. By using a combined tool from the input-delay approach and free-weighting matrices technique, some sufficient synchronizability conditions are then derived for such networks. Furthermore, a multi-step algorithm is designed to estimate the upper bound of the maximum allowable sampling intervals for achieving synchronization. Theoretical results are then extended to global pinning synchronization in fixed and switched directed networks with external disturbances, showing that a finite performance index can be guaranteed under some suitable conditions. Finally, numerical simulations are performed to demonstrate the effectiveness of the analytical results.