Robust stability of interval matrices

Abstract

Sufficient conditions for the Hurwitz and Schur stability of interval matrices are reviewed with some simplifications and some new results. The necessary and sufficient conditions for the Hurwitz and Schur stability of 2*2 matrices are determined. For general m*n interval matrices the pseudodivision method is applied for (2n-4)-dimensional faces for continuous systems and for (2n-2)-dimensional faces for discrete systems as well as for the corresponding lower dimensional faces. The method is applicable to low-dimensional matrices, e.g., n=3 or n=4. For higher dimensions numerical and computational problems arise.