THE EXTREME EIGENVALUES AND STABILITY OF HERMITIAN INTERVAL MATRICES

In this paper we present a novel Kharitonov-like algorithm to find the minimal and maximal eigenvalues, i.e., the root clustering interval, of a set of (n x n)-dimensional Hermitian interval matrices. Note that this set contains 2n2 vertex matrices. We prove that the maximal eigenvalue of a given set of Hermitian interval matrices coincides with the maximal eigenvalue of a special set of 2(n2+n-2)/2 Hermitian vertex matrices while its minimal eigenvalue coincides with the minimal eigenvalue of another such special set of the same size. This work is an extension of previous work by this author to find the extreme eigenvalues of real symmetric interval matrices containing 2(n2+n)/2 vertex matrices, where one has to consider two special sets each containing 2n-1 real symmetric vertex matrices. As immediate corollaries of this algorithm we obtain necessary and sufficient conditions for testing Hurwitz and Schur stability of Hermitian interval matrices wherein one has to test stability of 2(n2+n-2)/2 and 2(n2+n)/2 Hermitian vertex matrices, respectively.