The Model Matching Problem for Periodic Max-Plus Systems

Max-plus linear systems are suitable to model discrete event systems with synchronization phenomena, but not competition. In specific situations, competition can be introduced by considering event-varying periodic parameters, which allow us to model shared resources allocated in accordance to a periodic schedule, thus obtaining a periodic max-plus linear system. In this paper, we propose an extension of the geometric approach to systems of such class. The new results can be used to solve the model matching problem, so as to force a given plant to match the output of a given model exactly. A geometric, structural, necessary and sufficient condition for the solvability of such problem is presented.