Finite-time synchronization control of complex dynamical networks with time delay

► The finite-time synchronization between two complex networks with non-delayed and delayed coupling is studied. ► An impulsive controller and a periodically intermittent controller to guarantee the finite-time synchronization are obtained. ► Numerical simulations are given to show the effectiveness of theoretical results. In this paper, the finite-time synchronization between two complex networks with non-delayed and delayed coupling is proposed by using the impulsive control and the periodically intermittent control. Some novel and useful finite-time synchronization criteria are derived based on finite-time stability theory. Especially, the traditional synchronization criteria are improved by using the impulsive control and the periodically intermittent control in the convergence time, the results of this paper are important. Finally, numerical examples are given to verify the effectiveness and correctness of the synchronization criteria.