A new extension to Kharitonov´s theorem

An extension to a well-known theorem due to Kharitonov is presented, Kharitonov´s theorem gives a necessary and sufficient condition for all polynomials in a given family to be Hurwitz stable. In Kharitonov´s theorem, the family of polynomials considered is obtained by allowing each of the polynomial coefficients to vary independently within an interval. Kharitonov´s theorem shows that stability of this family of polynomials can be determined by looking at the stability of four specially constructed vertex polynomials. Kharitonov´s theorem is extended to allow for more general families of polynomials and to allow a given margin of stability to be guaranteed for the family of polynomials