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 operate 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 imprecision 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 problem of a universal eigenvector remains open. As an aside, we propose a combinatorial method for solving two-sided systems of linear equations over the max-plus algebra.