On the margin stability of interval matrices.

Abstract

In the first part of this thesis, some necessary and sufficient conditions for h-stability of a class of interval matrices are developed. It is proved that the problem of determining the h-stability of an interval matrix is related to that of existence and positiveness of the inverse of a point matrix constructed from the given interval matrix. In the second part some results on positive definiteness and stability of interval matrices are extended to h-positive definiteness and h-stability. In the third part some verifiable necessary and sufficient conditions for regularity of interval matrices are established. Based on these conditions an algorithm for determining the regularity of interval matrices is developed which lead to several algorithms for checking the stability and positive definiteness of interval matrices.