  We consider linear time invariant systems with exogenous stochastic
disturbances, and in feedback with structured stochastic uncertainties. This
setting encompasses linear systems with both additive and multiplicative noise.
Our concern is to characterize second-order properties such as mean-square
stability and performance. A purely input-output treatment of these systems is
given without recourse to state space models, and thus the results are
applicable to certain classes of distributed systems. We derive necessary and
sufficient conditions for mean-square stability in terms of the spectral radius
of a linear matrix operator whose dimension is that of the number of
uncertainties, rather than the dimension of any underlying state space models.
Our condition is applicable to the case of correlated uncertainties, and
reproduces earlier results for uncorrelated uncertainties. For cases where
state space realizations are given, Linear Matrix Inequality (LMI) equivalents
of the input-output conditions are given.
