  Our goal is to analyze performance of stable linear dynamical networks
subject to external stochastic disturbances. The square of the $\mathcal
H_2$-norm of the network is used as a performance measure to quantify the
expected steady-state dispersion of the outputs of the network. We show that
this performance measure can be tightly bounded from below and above by some
spectral functions of the state-space matrices of the network. This result is
applied to a class of cyclic linear networks and shown that their performance
measure scale quadratically with the network size.
