An improved extreme point solution for checking robust stability of interval matrices with much reduced vertex set and combinatorial effort

This paper addresses a research topic of high interest, namely 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 interval matrices, it is possible to reduce the computational effort significantly in the algorithm for checking the robust stability. By exploiting the hyperrectangle nature of the interval matrix description, the algorithm achieves computational savings in two avenues: in one avenue, we identify the critical vertex set to be used in the checking and in the other we avoid some unnecessary combinations. These two avenues when incorporated within the extreme point algorithm (developed by the author for checking the robust stability of general polytopes of matrices) results eventually in a much reduced number of extreme point (Kronecker nonsingularity matrices) checks in the final 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