Root locations of interval plants

The authors consider the determination of robust stability of interval polynomials with respect to an arbitrary closed convex contour in the left half complex plane. 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 margins 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