Robust stability of an interval plant with respect to a convex region in the complex plane

The determination of robust stability of interval polynomials with respect to an arbitrary closed convex contour in the left-half complex plane is considered. It is shown that the problem can be solved by checking only the root locations of a subset of the exposed edges of the family. The number of exposed edges to be checked depends on the damping margin defined by the contour and the degree of interval polynomials, but does not depend on the exact shape of the contour. A simple, easy-to-apply, graphical approach determines the subset of the exposed edges. An example illustrates the merit of the approach