The goal of this paper is to develop a discrete-time multivariable globally linearized control (GLC) algorithm, which provides low computational requirements with constraint handling ability. The control strategy is constructed with four elements: a transformer that accounts for process nonlinearities; an estimator, which observes the required unmeasured states; a variable constraint mapping optimizer that transforms the input constraints of the nonlinear process into constraints on the manipulated inputs of the globally linearized system and a quadratic dynamic matrix controller (QDMC) that provides constraints handling ability. The effectiveness of the designed controller has been tested on a multi-input multi-output (MIMO) nonlinear distillation column through extensive numerical simulations. The control law showed a high quality performance for set point tracking and disturbance rejection in presence of parametric uncertainty. The effect of unmeasured disturbance also has been studied through the simulation experiment. In the comparative study, the proposed GLC-QDMC control technique outperformed the GLC-DMC control law. (C) 2004 Elsevier Ltd. All rights reserved.