This paper deals with the linear model predictive control (MPC) with infinite prediction horizon (IHMPC) that is nominally stable. The study is focused on the output-tracking problem of systems with stable and integrating modes and unmeasured disturbances. To produce a bounded system response along the infinite prediction horizon, the effect of the integrating modes must be zeroed. The integrating mode zeroing constraint may turn the control problem infeasible, particularly when the system is affected by large disturbances. This work contributes in two ways to the problem of implementing IHMPC. The first contribution refers to the softening of some hard constraints associated with the integrating modes, while nominal stability is preserved. Another contribution is related to the strategy followed to deal with the infinite horizon and the removal of the matrix Lyapunov equation from the controller optimization problem. A real industrial example where the application of the controller has been studied is used to illustrate the advantages of the proposed strategy. (C) 2003 Elsevier Science Ltd. All rights reserved.