  We propose a robust model predictive control (MPC) method for discrete-time
linear systems with polytopic model uncertainty and additive disturbances.
Optimizing over linear time-varying (LTV) state feedback controllers has been
successfully used for robust MPC when only additive disturbances are present.
However, it is challenging to design LTV state feedback controllers in the face
of model uncertainty whose effects are difficult to bound. To address this
issue, we propose a novel approach to over-approximate the effects of both
model uncertainty and additive disturbances by a filtered additive disturbance
signal. Using the System Level Synthesis framework, we jointly search for
robust LTV state feedback controllers and the bounds on the effects of
uncertainty online, which allows us to reduce the conservatism and minimize an
upper bound on the worst-case cost in robust MPC. We provide a comprehensive
numerical comparison of our method and representative robust MPC methods from
the literature. Numerical examples demonstrate that our proposed method can
significantly reduce the conservatism over a wide range of uncertainty
parameters with comparable computational effort as the baseline methods.
