Stability of a complex polynomial set with coefficients in a diamond and generalizations

An approach originating in system theory is used to prove that the strict Hurwitz property of a family of polynomials having complex coefficients with their real and imaginary parts each varying in a diamond requires the checking of sixteen one-dimensional edges of the diamond for the type of stability that is characterized by the strict Hurwitz property of polynomials. The approach is straightforward and the corresponding recent result advanced for the case of polynomials with real coefficients falls out as a special case. The procedure advanced also applies to a far wider class of regions in parameter space than those represented either by a boxed domain or its set dual-a diamond