In this work we present a rigorous methodology for the simultaneous design of moving horizon estimation (MHE) and robust model predictive control based on multi-parametric programming. First, an explicit/multi-parametric solution of the MHE is derived. Then, a novel method is presented that allows for the derivation of the estimation error dynamics, the bounding set of the estimation error, and the state estimate dynamic equations of constrained MHE. A framework is then presented for the design of robust explicit/multi-parametric model predictive control (MPC) controllers, based on tube-based MPC methods, which ensures that no constraints are violated due to the estimation error and the process noise in the system. This framework is first shown for the Kalman filter and unconstrained MHE and is then extended to the constrained MHE. (C) 2013 Elsevier Ltd. All rights reserved.