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We consider inhomogeneous matrix products over max-plus algebra, where thematrices in the product satisfy certain assumptions under which the matrixproducts 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-plusproducts. Proceedings of the American Control Conference, Philadelphia,Pensylvania, (June 1998), 1909 1913.]. We establish a bound on the transientafter which this starts to happen for any product of matrices whose lengthexceeds that bound.

A Bound for the Rank-One Transient of Inhomogeneous Matrix Products in Special Case