On possibilities of the extension of Kharitonov's stability test for interval polynomials to the discrete-time case

It is shown that the Kharitonov test for Hurwitz stability of an interval polynomial does not extend in general to the discrete-time case, unless the degree n of the polynomial is not greater than two. For
n \leq 3
a given monic interval polynomial has all roots inside the unit disk if all
2^{3} = 8
extreme polynomials have that property (instead of only four polynomials in Kharitonov's test). For
n = 4
it is shown by a counterexample that discrete-time stability of all extreme polynomials does not guarantee the stability of the interval polynomial.