The integral control is an effective way to track non-zero constant reference. In this paper, to utilize a robust predictive integral control strategy in the output-feedback case, the control requirement and the goals are formulated in a suitable form. Then, by introducing a novel matrix transformation, the controller designing issue is translated into an optimization problem subjected to some constraints. Such constraints are represented in terms of linear matrix inequality (LMI). By solving a minimization problem, the gains of the integral controller are determined and updated at some time instants. Finally, several numerical simulations are given to evaluate the advantages of the suggested robust control method over similar ones. The outcomes confirm the superiority of the proposed idea compared to the existing approach.