The Model Matching Problem for Max-Plus Linear Systems: A Geometric Approach

Linear systems over the max-plus algebra provide a suitable formalism to model discrete-event systems where synchronization, without competition, is involved. In this article, we consider a formulation of the model matching problem for systems of such class, in which the output of a given system, called the plant, is forced, by a suitable input, to track exactly that of a given model. A necessary and sufficient condition for its solvability is obtained by making a suitable use of geometric methods in the framework of systems over the max-plus algebra.