On state space realizations of impulse responses of max-linear systems

The topic of this paper is state space realization of impulse responses in the max-plus 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 and inequalities can be transformed into an Extended Linear Complementarity Problem to find all equivalent fixed order state space realizations of a multiple-input multiple-output max-linear discrete event system starting from its impulse response. This paper presents research results of the Belgian programme on interuniversity attraction poles (IUAP50) initiated by the Belgian State, Prime Minister’s Office for Science, Technology and Culture. The scientific responsibility is assumed by its authors. Research Assistant with the N.F.W.O. (Belgian National Fund for Scientific Research). Senior Research Associate with the N.F.W.O.