AE and EA robustness of interval circulant matrices in max-product algebra

Abstract

Max-product algebra is defined as a linearly ordered set with two binary operations. Classical addition and multiplication are replaced by maximum and multiplication, respectively. A square matrix A is robust, if for each starting vector x, the orbit stabilizes. If this property holds only for starting vectors from an interval vector X, we say that A is X-robust. We shall deal with the matrices of special type: circulant and the corresponding interval version, so-called interval circulant matrices. The interval approach in this paper is applied in combination with for-all–exists quantification of the values – not all of the considered interval matrix entries have the same importance: whereby, for some more important data, all values of the interval must be taken into account and for some less important data it is sufficient to be considered for at least one value of the interval. In this manner, we define the EA and AE robustness and X-robustness of interval circulant matrices over max-product algebra. Polynomial algorithms for checking these types of robustness and X-robustness are presented.