Stability of a set of multivariate complex polynomials with coefficients varying in diamond domain

Recently, attention has been focused on the (open left half plane) stability of a family of polynomials with complex coefficients with their real and imaginary parts each varying in a diamond. It has been concluded that the stability of a diamond family of polynomials is equivalent to the stability of the specific 16-edge polynomials of the diamond. This result is extended to the n-variate case. It is proved that the scattering Hurwitz property of the certain 16n diamond edge polynomials can guarantee the scattering Hurwitz property of the whole diamond family of n-variate complex polynomials.<
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