The extreme eigenvalues and stability of real symmetric interval matrices

A novel Khoritonov-like algorithm for computing the minimal and maximal eigenvalues of n*n dimensional symmetric interval matrices is presented and it is proved that the maximal and minimal eigenvalue of a given set of intervals matrices coincide with the maximal of a special set of 2/sup n-1/ symmetric vertex matrices.

Abstract

A novel Khoritonov-like algorithm for computing the minimal and maximal eigenvalues of n*n dimensional symmetric interval matrices is presented. It is proved that the maximal eigenvalue of a given set of interval matrices coincides with the maximal eigenvalue of a special set of 2/sup n-1/ symmetric vertex matrices, whereas its minimal eigenvalue coincides with the minimal of another special set of 2/sup n-1/ symmetric vertex matrices. As immediate corollaries of this algorithm, weak necessary and sufficient conditions for testing the Hurwitz and Schur stability of symmetric interval matrices, where one has to test the stability of 2/sup n-1/ and 2/sup n/ symmetric vertex matrices, respectively, are obtained.>