  In this paper, the synchronizability problem of dynamical networks is
addressed, where better synchronizability means that the network synchronizes
faster with lower-overshoot. The L2 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 L2 norm of the error vector e and the H2 norm of the
transfer function G of the linearized network about the equilibrium point.
Consequently, the effect of the network coupling topology on the H2 norm of the
transfer function G is analyzed. Finally, an optimal controller is designed,
according to the so-called LQR problem in modern control theory, which can
drive the whole network to its equilibrium point and meanwhile minimize the L2
norm of the output of the linearized network.
