Generalization of strong Kharitonov theorems to the left sector

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 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 orders of the polynomials. The exact number of vertex polynomials to be checked will depend on the damping margins, but it will be independent of the orders of the polynomials. These specially chosen vertex polynomials are independent of the order of the polynomials. The importance of the result lies with the great reduction in computation cost associated with checking the zero locations of interval polynomials