A necessary and sufficient `virtual (interior) edge´ solution for checking robust stability of interval matrices

Addresses the issue of developing a finitely computable necessary and sufficient test for checking the robust stability of an interval matrix and provides a complete solution to the problem in the form of a `virtual edge´ (a one dimensional search) result. The result uses the fact that the robust stability problem can be converted to a robust nonsingularity problem involving the original matrix and the associated bialternate sum matrix (which we label as the `tilde´ matrix). The special nature of the `tilde´ matrix is exploited with the introduction of concepts labeled `real axis nonsingularity´,`virtual matrix family´ and `weighted real axis determinant´. The proposed necessary and sufficient condition involves checking if the weighted real axis determinants of the `virtual edge´ matrices are greater than the minimum of the weighted real axis determinants of the vertex matrices. This condition is to be checked in the `tilde´ matrix space. The proposed methodology is illustrated with a variety of examples