The full information output regulation problem
for linear stochastic systems is addressed. A general class of
linear systems is considered, namely systems in which the
state, control variable and exogenous variable may appear
simultaneously in the drift term and in the diffusion term
of the differential equation. Similarly, we consider a stochas-
tic signal generator, thus allowing tracking and/or rejecting
Brownian motions in addition to deterministic trajectories. In
the paper we first characterize the steady-state response of the
interconnection of the system with the signal generator and then
we solve the full information output regulation problem. The
results of the paper are illustrated by means of two examples.
Finally a short discussion of the error feedback regulator
problem concludes the paper.