Industrial framework needs methods to take into account complex and non-differentiable requirements given by customers directly in control design for disturbed systems. The aim of this paper is to take into account any evaluable requirements in the design of control laws for systems subject to additive disturbances. To achieve this goal, Barrier Model Predictive Control and invariant set theory are used. It allows considering state and input constraints and also to improve robustness with regard to disturbances.