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State space transformations and state space realization in the max algebra

The topics of this paper are state space transformations and the (partial) state space 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 equations can be transformed into an extended linear complementarity problem to perform state space transformations and 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 matrices. We also give a geometrical description of the set of all equivalent state space realizations.