Three decades have passed encompassing a flurry of research and commercial activities in model predictive control (MPC). However, the massive strides made by the academic community in guaranteeing stability through a state- space framework have not always been directly applicable in an industrial setting. This paper is concerned with a priori and/or a posteriori certification of persistent feasibility, boundedness of industrial MPC controllers (i) based on input-output formu- lation (ii) using shorter control than prediction horizon (iii) and without terminal conditions.