  We consider inhomogeneous matrix products over max-plus algebra, where the
matrices in the product satisfy certain assumptions under which the matrix
products of sufficient length be rank-one, as it was shown in [6][L. Shue,
B.D.O. Anderson, S. Dey: On steady state properties of certain max-plus
products. Proceedings of the American Control Conference, Philadelphia,
Pensylvania, (June 1998), 1909 1913.]. We establish a bound on the transient
after which this starts to happen for any product of matrices whose length
exceeds that bound.
