Stability of interval matrices using the distance to the set of unstable matrices
J.A. Rojas, Joaquı́n Collado · 2005
We describe sufficient conditions to guarantee stability of interval matrices, based on the distance of the centroid matrix to the set of unstable matrices. We define the centroid matrix as the arithmetic average of the two matrices that define the interval matrix family. First we find the longest distance of the centroid matrix to any of the 2/sup n/spl times/n/ corners of the interval matrix, next, we calculate a lower bound of the distance of the centroid matrix to Q, where Q is the set of the matrices with at least one eigenvalue on the imaginary axis. The result is: If the longest distance from the centroid matrix to any of the 2/sup n/spl times/n/ corners is less than the distance of the centroid matrix to Q, then the interval matrix is stable. The result is the best possible when the uncertainty in every entry is the same. We give numerical examples to illustrate the result.