  In uncertainty quantification, a stochastic modelling is often applied, where
parameters are substituted by random variables. We investigate linear dynamical
systems of ordinary differential equations with a quantity of interest as
output. Our objective is to analyse the sensitivity of the output with respect
to the random variables. A variance-based approach generates partial variances
and sensitivity indices. We expand the random output using the generalised
polynomial chaos. The stochastic Galerkin method yields a larger system of
ordinary differential equations. The partial variances represent quadratic
outputs of this system. We examine system norms of the stochastic Galerkin
formulation to obtain sensitivity measures. Furthermore, we apply model order
reduction by balanced truncation, which allows for an efficient computation of
the system norms with guaranteed error bounds. Numerical results are shown for
a test example.
