This article discusses the existing linear model predictive control concepts in a unified theoretical framework based on a stabilizing, infinite horizon, linear quadratic regulator. In order to represent unstable as well as stable multivariable systems, the standard state-space formulation is used for the plant model. The incorporation of a nominally stabilizing constrained regulator eliminates the current requirement of tuning for nominal stability. Output feedback is addressed in the well-established framework of the linear quadratic state-estimation problem. This framework allows the flexibility to handle nonsquare systems, noisy inputs and outputs, and nonzero input, output, and state disturbances. This formulation subsumes the integral control schemes designed to remove steady-state offset currently in industrial use. The online implementation of the controller requires the solution of a standard quadratic program that is no more computationally intensive than existing algorithms.