  We propose a novel approach to design a robust Model Predictive Controller
(MPC) for constrained uncertain linear systems. The uncertain system is modeled
as linear parameter varying with additive disturbance. Set bounds for the
system matrices and the additive uncertainty are assumed to be known. We
formulate a novel optimization-based constraint tightening strategy around a
predicted nominal trajectory which utilizes these bounds. With an appropriately
designed terminal cost function and constraint set, we prove robust
satisfaction of the imposed constraints by the resulting MPC in closed-loop
with the uncertain system, and Input to State Stability of the origin. We
highlight the efficacy of our proposed approach via a numerical example.
