On the robust stability of a family of disk polynomials

In his well-known theorem, V.L. Kharitonov (1978) established that Hurwitz stability of a set F_I of interval polynomials with complex coefficients is equivalent to the Hurwitz stability of only eight polynomials in this set. In this study the authors consider an alternative but equally meaningful model of uncertainty by introducing a set F_D of disk polynomials, characterized by the fact that each coefficient of a typical element P(s) in F_D can be any complex number in an arbitrary but fixed disk of the complex plane. The result shows that the entire set is Hurwitz stable if and only if the `center´ polynomial is stable and the H_∞-norms of two specific stable rational functions are less than one. Unlike Kharitonov´s theorem, the present result can be readily applied to the Schur stability problem, and the resulting condition is equally simple