On the existence of strong Kharitonov theorems for interval polynomials

The zero locations of interval polynomials are examined. In particular, it is shown that a family of interval polynomials will have only zeros in a certain class of the left sector if and only if a finite number of specially chosen vertex polynomials have only zeros in the left sector. This finite number of vertex polynomials is dependent on the damping margins of the left sector but is independent of the order of the polynomials