CLASSIFICATION OF UNITS IN H-INFINITY AND AN ALTERNATIVE PROOF KHARITONOVS THEOREM

This brief presents an alternative proof of Kharitonov's theorem, usin g the property of a ratio of odd and even parts of a Hurwitz polynomia l and the Nyquist stability criterion, The ratio of Kharitonov's polyn omials in the classification of units in H-infinity, along with its re lation to the problem of simultaneous stabilization of one parameter f amily of plants is discussed, A new theorem on the existence of a Hurw itz polynomial such that its ratio with a Hurwitz interval polynomial family with either the same even or odd part, is a strictly positive r eal (SPR) function is proved. It is also proved that if the ratio of a polynomial beta(s) with four Kharitonov's polynomials is an SPR funct ion, then the ratio of beta(s) with the interval family is an SPR func tion.