In this article, a robust steering control for the last phase of the rolling process in a hot strip mill is proposed. This phase, called tail end phase, may be modelled as a linear switched system. The switchings make the system unstable and the task of the tail end steering control consists in guaranteeing the safety of the industrial plant. The system involves a two time scales dynamics. Hence, the singular perturbation method is used in order to design the control law. The controller has to take into account the physical variations of the rolled products and an uncertainty in the switching time. Results concerning the ArcelorMittal hot strip mill of Eisenhüttenstadt are presented.