Tuning Model Predictive Control (MPC) laws often requires trial and error, as many classical linear control design techniques are not directly applicable. In this paper we overcome this issue by adopting the controller matching approach suggested in [1]-[3]... We assume that a baseline linear controller has been already designed to control the system in the absence of constraints, and that we want to tune a MPC to satisfy them while delivering the same linear feedback whenever they are not active. We prove that a positive-definite stage cost matrix yielding this matching property can be computed for all stabilizing linear controllers. Additionally, we prove that the constrained estimation problem can also solved similarly, by matching a linear observer with a Moving Horizon Estimator (MHE). Finally, we discuss in some examples various aspects regarding the practical implementation of the proposed technique. (read more)