The robust controlled invariance describes the ability to maintain, using suitable control actions, the state of a system in a set for any value of the disturbances. By considering a class of monotone systems and a multidimensional interval as target set, we obtain a simple characterization of the robust controlled invariance. We then give a method to stabilize the state into a robust controlled invariant interval when it is initialized outside of the target set. These results are applied to a model for the temperature control in an intelligent building equipped with automated underfloor air distribution (UFAD) and implemented in a small-scale experimental UFAD flat. (C) 2016 Elsevier Ltd. All rights reserved.