On the multidimensional generalization of robustness of scattering Hurwitz property of complex polynomials

Recent stability results on the scattering and the immitance description of passive multidimensional systems are used to characterize the robustness of the scattering Hurwitz property of a given multidimensional (complex) polynomial in terms of the scattering Hurwitz property of a finite number of multidimensional (complex) polynomials. The result is a complete proof of a recent conjecture extending V.L. Kharitonov's (Differential Equations, vol.14, p.1483-5, 1979) theorem on the characterization of the interval (strict sense) Hurwitz property of real as well as complex polynomials to multidimensions. The multidimensional versions of the weak and strong forms of Kharitonov's one-dimensional results are presented along with their proofs.>