Robust stability of interval polynomials with respect to the left sector

It is known that a family of interval polynomials has all its roots lying within a left sector if and only if a subset of the vertex polynomials has all its roots lying within the left sector. A simple, easy-to-apply, graphical approach to determining the subset of the vertex polynomials is presented. The number of vertex polynomials to be checked depends not only on the damping margins defined by the left sector but also on the degree of interval polynomials. Improvements afforded by the proposed approach over previous methods are also noted