Reachability of eigenspaces for interval matrices in max-min algebra.

In max-min algebra the standard pair of operations: plus and times is substituted by pair of operations ⊕ and ⊗, where a ⊕ b = max ⁡ { a , b } , a ⊗ b = min ⁡ { a , b }. A square matrix A is X − robust if its eigenspace is reached starting at each vector of a given interval vector X = { x ; x _ ≤ x ≤ x ‾ }. Various versions of the reachability for an interval vector X and an interval matrix A = { A ; A _ ≤ A ≤ A ‾ } depending on the used quantifiers and their order are studied. The universal, possible, tolerance and weak tolerance A -robustness of X and X -robustness of A over max-min algebra are defined and polynomial algorithms for its checking in the case of circulant matrices are described. [ABSTRACT FROM AUTHOR]