  This paper is concerned with a dissipativity theory for dynamical systems
governed by linear Ito stochastic differential equations driven by random noise
with an uncertain drift. The deviation of the noise from a standard Wiener
process in the nominal model is quantified by relative entropy. We discuss a
dissipation inequality for the noise relative entropy supply. The problem of
minimizing the supply required to drive the system between given Gaussian state
distributions over a specified time horizon is considered. This problem, known
in the literature as the Schroedinger bridge, was treated previously in the
context of reciprocal processes. A closed-form smooth solution is obtained for
a Hamilton-Jacobi equation for the minimum required relative entropy supply by
using nonlinear algebraic techniques.
