  In this paper, we consider the robust closed-loop model predictive control
(MPC) of a linear time-variant (LTV) system with norm bounded disturbances and
LTV model uncertainty, wherein a series of constrained optimal control problems
(OCPs) are solved. Guaranteeing robust feasibility of these OCPs is challenging
due to disturbances perturbing the predicted states, and model uncertainty,
both of which can render the closed-loop system unstable. As such, a trade-off
between the numerical tractability and conservativeness of the solutions is
often required. We use the System Level Synthesis (SLS) framework to
reformulate these constrained OCPs over closed-loop system responses, and show
that this allows us to transparently account for norm bounded additive
disturbances and LTV model uncertainty by computing robust state feedback
policies. We further show that by exploiting the underlying linear fractional
structure of the resulting robust OCPs, we can significantly reduce the
conservativeness of existing SLS-based and tube-MPC-based robust control
methods while also improving computational efficiency. We conclude with
numerical examples demonstrating the effectiveness of our methods.
