Classification of units in H∞ and an alternative proof Kharitonov´s theorem

The authors present an alternative proof of Kharitonov´s theorem, using the property of a ratio of odd and even parts of a Hurwitz polynomial and the Nyquist stability criterion. The ratio of Kharitonov´s polynomials in the classification of units in H_∞ , along with its relation to the problem of simultaneous stabilization of one parameter family of plants is discussed. A new theorem on the existence of a Hurwitz polynomial such that its ratio with a Hurwitz interval polynomial family with either the same even or odd part, is a strictly positive real (SPR) function is proved. It is also proved that if the ratio of a polynomial β(s) with four Kharitonov´s polynomials is an SPR function, then the ratio of β(s) with the interval family is an SPR function