A simple synchronization criterion for a complex network based on the feedback

Based on the Lyapunov stability theory, some simple generic criterions are derived for local and global synchronization of a complex network using the method of linear state feedback. The criterions are expressed by some algebraic inequalities instead of matrix inequalities which means that the original computational effort required is greatly decreased and no matter whether the coupling configuration matrix or the inner coupling matrix is symmetric. A network with typical topology structure is chosen to illustrate the effectiveness of the criterion.