We consider (max,+)-linear systems (i.e., discrete event systems ruled by conditions of the form: “for all k ≥ l, occurrence k of event e2 is at least t units of time after occurrence k−l of event e1” with t , l ∈ N0) with the additional restriction that certain events can only occur at time instants in predefined ultimately periodic sets of integers. Such phenomena frequently occur in transportation networks (e.g., traffic lights).
In this paper, we extend transfer function matrix models and model reference control developed for (max,+)-linear systems to the above class of systems, which is more general than (max,+)-linear systems. To illustrate these results, we consider a road traffic example with traffic lights.