In this paper, the synchronizability problem of dynamical networks is addressed, where better synchronizability means faster network synchronization with lower vibration. The L-2 norm of the error vector e is taken as a performance index to measure this kind of synchronizability. For the equilibrium synchronization case, it is shown that there is a close relationship between the L-2 norm of the error vector e and the H-2 norm of the transfer function G of the linearized network about the equilibrium point. Consequently, the effect of the network coupling topology on the H-2 norm of the transfer function G is analyzed. Finally, an LQR controller is designed, according to the LQR problem in modern control theory, which can drive the whole network to its equilibrium point and meanwhile minimize the L-2 norm of the output of the linearized network. (C) 2009 Elsevier Ltd. All rights reserved.