This paper deals with the finite-time synchronization issue of time-varying delayed neural networks (DNNs) with discontinuous activations. Based on master-slave concept, several sufficient conditions are given to guarantee the finite-time synchronization of discontinuous DNNs. In order to control the synchronization error to converge zero in a finite time, we design three classes of novel switching state-feedback controllers which involve time-delays and discontinuous factors. The analysis in this paper employs the extended differential inclusi...