The extreme eigenvalues and stability of Hermitian interval matrices

The author presents a Kharitonov-like algorithm to find the minimal and maximal eigenvalues, i.e. the root clustering interval, of a set of (n×n)-dimensional Hermitian interval matrices. It is proven that the maximal eigenvalue of a given set of Hermitian interval matrices coincides with the maximal eigenvalue of a special set of Hermitian vertex matrices while its minimal eigenvalue coincides with the minimal eigenvalue of another such special set of the same size. As immediate corollaries of this algorithm, necessary and sufficient conditions for testing Hurwitz and Schur stability of Hermitian interval matrices wherein one has to test stability of certain Hermitian vertex matrices are obtained