  We present a robust model predictive control method (MPC) for discrete-time
linear time-delayed systems with state and control input constraints. The
system is subject to both polytopic model uncertainty and additive
disturbances. In the proposed method, a time-varying feedback control policy is
optimized such that the robust satisfaction of all constraints for the
closed-loop system is guaranteed. By encoding the effects of the delayed states
and inputs into the feedback policy, we solve the robust optimal control
problem in MPC using System Level Synthesis which results in a convex quadratic
program that jointly conducts uncertainty over-approximation and robust
controller synthesis. Notably, the number of variables in the quadratic program
is independent of the delay horizon. The effectiveness and scalability of our
proposed method are demonstrated numerically.
