  We propose a simple and computationally efficient approach for designing a
robust Model Predictive Controller (MPC) for constrained uncertain linear
systems. The uncertainty is modeled as an additive disturbance and an additive
error on the system dynamics matrices. Set based bounds for each component of
the model uncertainty are assumed to be known. We separate the constraint
tightening strategy into two parts, depending on the length of the MPC horizon.
For a horizon length of one, the robust MPC problem is solved exactly, whereas
for other horizon lengths, the model uncertainty is over-approximated with a
net-additive component. The resulting MPC controller guarantees robust
satisfaction of state and input constraints in closed-loop with the uncertain
system. With appropriately designed terminal components and an adaptive horizon
strategy, we prove the controller's recursive feasibility and stability of the
origin. With numerical simulations, we demonstrate that our proposed approach
gains up to 15x online computation speedup over a tube MPC strategy, while
stabilizing about 98$\%$ of the latter's region of attraction.
