  Contraction properties of the Riccati operator are studied within the context
of non-stationary linear-quadratic optimal control. A lifting approach is used
to obtain a bound on the rate of strict contraction, with respect to the
Riemannian metric, across a sufficient number of iterations. This number of
iterations is related to an assumed uniform controllability and observability
property of the dynamics and stage-cost in the original formulation of the
problem.
