MINIMAL STATE SPACE REALIZATION OF MIMO SYSTEMS INTHE MAX ALGEBRA Bart

The topic of this paper is the (partial) minimal realization problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multi-variate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to nd all equivalent minimal state space realizations of a multiple input multiple output (MIMO) max-linear discrete event system starting from its impulse response matrices. We also give a geometrical description of the set of all minimal state space realizations.