Dynamic Matrix Control (DMC) has proven to be a powerful tool for optimal regulation of chemical processes under constrained condtions. It is based on a linear convolution model derived from step-response measurements. A model predictive control algorithm optimises closed-loop performance for a nominal operating point. However, as the process moves away from this point, control usually becomes sub-optimal due to process non-linearity. As seen in this work, the DMC algorithm can be made adaptive, to establish a new local model, by recursive estimation of the local step response parameters from normal plant variations. However, when used for control of plants containing integrating process units, steady-state offsets occur for sustained changes. Thus, a novel Adaptive Linear Dynamic Matrix Control (ALDMC) algorithm has been developed and used to control a 2-input/2-output system with an integrating behaviour. Comparisons of model control and plant control with and without these features demonstrated the importance of integral compensation for integrating processes, and model adaptation in the case of plant/model mismatch. Some cross-compensation of integration by the adaptive feature was also noted. An holistic technique is demonstrated which simultaneously recognises residual integration disturbances and matrix parameter variations, whereas previous techniques which recognise only one of these will fail in the presence of the other. (C) 2004 Elsevier Ltd. All rights reserved.