Distributed Pinning Synchronization of Lur’e Dynamical Networks

In the past two decades, collective behaviors of complex networks and systems, such as consensus
and synchronization, have drawn increasingly attention from different fields of researchers. In this
regard, synchronization [8] is undoubtedly one of the most significant collective behaviors of a
dynamic system because of its potential applications in practical society, such as regulation of power
grid, parallel image processing, the operation of no-man air vehicle, the realization of chain
detonation, and etc., see [92,105] and references therein. The main purpose of synchronization is to
achieve the coordination of events in order to force systems into unification. Until now, various types
of synchronization phenomena have been investigated, such as complete synchronization [90],
cluster synchronization [91], lag synchronization [102], phase synchronization [103] and impulsive
synchronization [104]. While cluster synchronization requires the coupled oscillators split into
subgroups called cluster, such that the oscillators synchronized with one another in the same cluster,
but there is no synchronization among different clusters. For instance, Wu, Zhou and Chen [80]
discussed the issue of the cluster synchronization for general networks by means of a pinning control
strategy.