Modeling of Time-Varying (max,+) Systems by means of Weighted Timed Event Graphs

The behavior of Timed Event Graphs (TEG) with constant holding times can be described thanks to the (max,+) theory. For time-varying systems, a class of First-In First-Out TEGs with periodic holding times has already been studied in the literature. It is shown here that such systems can be modeled by Weighted TEGs for which an input-output model exists. More precisely one can describe FIFO TEGs with periodic holding times by means of ultimately periodic series in a dioid denoted.