Robust multivariate scattering Hurwitz interval polynomials

Abstract The relationship between multivariate scattering Hurwitz polynomials and multivariate complex reactance functions is exploited to prove that a specified set of bivariate interval polynomials is characterizable by the scattering Hurwitz property from tests on a finite set of extreme bivariate polynomials. Specifically, it is shown that the cardinality of this finite set when the coefficients are restricted to the field of real numbers is 8. This bivariate result is expected to be generalizable to the n-variate case, for both the real and the complex coefficient cases, if one proceeds with adequate caution.