It suffices to check only two special vertex matrices in Kronecker space to analyze the robust stability of an interval matrix

This paper addresses the issue of developing a finitely computable necessary and sufficient test for checking the robust stability of interval matrices and provides a complete solution to the problem in the form of an improved ´extreme point´ result. The novelty of the proposed solution is that for this special case of an ´interval matrix´ with all its vertices being stable, it suffices to check only two vertex matrices in the Kronecker Lyapunov space for assessing the robust stability of the entire matrix family. By exploiting the ´hyper-rectangle´ nature of the interval matrix description, the algorithm achieves this remarkable computational savings by making use of two avenues: in one avenue, we identify only ´two critical vertices´ to be used in the checking, and in the other we avoid all the other unnecessary combinations. These two avenues, when incorporated within the ´extreme point´ algorithm, results eventually in this ´two vertex checking´ algorithm. This checking is done in the higher dimensional ´Kronecker Lyapunov´ space. The proposed methodology is illustrated with a variety of examples. The importance of this result and possible extensions of this result are discussed.