B. De Schutter and B. De Moor, "Matrix factorization and minimal state space realization in the max-plus algebra," Proceedings of the 1997 American Control Conference, Albuquerque, New Mexico, pp. 3136-3140, June 1997.
The topics of this paper are matrix factorizations and the minimal state space realization problem in the max-plus algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We present a heuristic algorithm to compute a factorization of a matrix in the max-plus algebra. Next we use this algorithm to determine the minimal system order (and to construct a minimal state space realization) of a max-linear time-invariant discrete event system.