Interval robustness of (interval) max-plus matrices

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A max-plus matrix A (operations max and plus are denoted by ⊕ and ⊗, respectively) is called X–robust if the orbit x,A⊗x,A2⊗x,… of any initial vector x belonging to the interval X={x:x̲≤x≤x¯} ends up with a max-plus algebraic eigenvector of A. The X–robustness of a max-plus matrix is extended to interval vectors X using forall–exists quantification of their interval entries (so-called XAE–robustness and XEA–robustness). A complete characterization of XAE–robustness and XEA–robustness of matrices and possible (universal) XAE (XEA)–robustness of interval circulant matrices is presented.