Invariant sets for a class of linear systems with variable time-delay

This paper focuses on the control of a class of linear systems with polytopic uncertainty to model the presence of variable delay affecting the input. It is shown that the embedding problem can be casted as a polytopic containment problem and a new approach to construct a simplex enclosure is proposed. The stability of the closed-loop system is guaranteed by forcing the state trajectories to attain a robust positively invariant set in a given prediction window. Illustrative examples complete the paper.