An elementary proof of Kharitonov´s stability theorem with extensions

Gives an elementary proof of Kharitonov´s theorem using simple complex plane geometry without invoking the Hermite-Bieler theorem. Kharitonov´s theorem is a stability result for classes of polynomials defined by letting each coefficient vary independently in an arbitrary interval. The result states that the whole class is Hurwitz if and only if four special, well-defined polynomials are Hurwitz. The paper also gives elementary proofs of two previously known extensions: for polynomials of degree less than six, the requirement is reduced to fewer than four polynomials; and the theorem is generalized to polynomials with complex coefficients