THE MAXIMAL EIGENVALUE AND STABILITY OF A CLASS OF REAL SYMMETRICAL INTERVAL MATRICES

In this correspondence we prove that the maximal eigenvalue of a class of (n x n)-dimensional real symmetric interval matrices, say A, coinc ides with the maximal eigenvalue of a single vertex matrix whose entri es are the right endpoint of its intervals. The elements of the interv al matrix A are intervals whose right endpoint is not smaller than the absolute value of the left endpoint. As a corollary we obtain a neces sary and sufficient condition for A to be Hurwitz; namely, that the ab ove mentioned vertex matrix is Hurwitz. Furthermore, the Hurwitz stabi lity of A implies the Hurwitz stability of the general interval matrix whose entries are allowed to vary in the intervals of A.