This report focuses on the synchronization of discrete-time complex networks with two aspects:

(1) Exponential synchronization of discrete-time complex networks with both time-varying delays and stochastic disturbances. Based on the discrete-time delayed impulsive system theory and linear matrix inequality (LMI) technique, an iterative Lyapunov function is constructed, a new synchronization criterion with topology matrices and impulsive conditions is developed. (2) Pinning synchronization of discrete-time complex networks with different time-varying delays. An important lemma and detailed analysis is given to yield some synchronization criteria for this kind of networks. The results provide an effective way to synchronize discrete-time complex networks by reducing control cost. Furthermore, they are illustrated by a complex network via two kinds of pinning schemes. Finally, some numerical simulations are provided to verify the above theoretical results respectively.