The maximal eigenvalue and stability of a class of real symmetric interval matrices

It is proved that the maximal eigenvalue of a class of (n×n)-dimensional real symmetric interval matrices, say A, coincides with the maximal eigenvalue of a single vertex matrix whose entries are the right endpoint of its intervals. The elements of the interval matrix A are intervals whose right endpoint is not smaller than the absolute value of the left endpoint. As a corollary, a necessary and sufficient condition for A to be Hurwitz-namely, that the above-mentioned vertex matrix is Hurwitz-is obtained. Furthermore, the Hurwitz stability of A implies the Hurwitz stability of the general interval matrix whose entries are allowed to vary in the intervals of A