P_(max)1 and S_(max) properties and asymptotic stability in the max algebra

摘要

In this work, we introduce the class of P_(max)~1- matrices for the max algebra and derive some properties of these that echo similar results for P-matrices in the conventional algebra. In analogy with [1], we define the row- P_(max)~1-property and the S _(max)-property of a finite set of nonnegative matrices. Moreover, we relate these concepts to stability questions for sets of matrices and difference inclusions in the max algebra.