B. De Schutter and B. De Moor, "Minimal state space realization of MIMO systems in the max algebra," Proceedings of the 3rd European Control Conference (ECC'95), Rome, Italy, pp. 411-416, Sept. 1995.
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 multivariate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to find 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.