Eigenvectors of interval matrices over max-plus algebra

The behaviour of a discrete event dynamic system is often conveniently described using a matrix algebra with operations max and plus Such a system moves forward in regular steps of length equal to the eigenvalue of the system matrix if it is set to operation at time instants corresponding to one of its eigenvectors However due to imprecise measurements it is often unappropriate to use exact matrices One possibility to model im precision is to use interval matrices We show that the problem to decide whether a given vector is an eigenvector of one of the matrices in the given matrix interval is polynomial while the complexity of the existence prob lem of a universal eigenvector remains open As an aside we propose an alternative combinatorial method for solving two sided systems of linear equations over the max plus algebra