Minimal realization in the max algebra is an extended linear complementarity problem

Reference:
B. De Schutter and B. De Moor, "Minimal realization in the max algebra is an extended linear complementarity problem," Systems & Control Letters, vol. 25, no. 2, pp. 103-111, May 1995.

Abstract:
We demonstrate that the minimal state space realization problem in the max algebra can be transformed into an Extended Linear Complementarity Problem (ELCP). We use an algorithm that finds all solutions of an ELCP to find all equivalent minimal state space realizations of a single input single output (SISO) discrete event system. We also give a geometrical description of the set of all minimal realizations of a SISO max-linear discrete event system.