A class of weighted complex dynamical network model with heterogeneous delays is introduced, where each
node is a general Lur’e system. Then its synchronization phenomena is investigated by applying feedback injections to a
small fraction of nodes in the whole network. Based on the absolute stability theory, a delay-independent criterion ensuring
the global synchronization of the whole network is derived. A dynamical network composed of identical Chua’s oscillators
is adopted as a numerical example to demonstrate the effectiveness of the proposed results. It is also shown that in some
particular cases, only a single controller can achieve the control objective.