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

An approach from 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 16 one-dimensional edges of the diamond for the type of stability characterized by the strict Hurwitz property of polynomials. The approach is straightforward, and the corresponding recent result (N.K. Bose and Y.Q. Shi, ibid., vol.CAS-34, no.10, p.1233-7, 1987; J. Garloff and N.K. Bose, in Reliability in Computing: The Role of Interval Methods in Scientific Computing, p.391-402, 1988) advanced for the case of polynomials with real coefficients falls out as a special case. The procedure also applies to a far wider class of regions in parameter space than those represented by either a boxed domain or its set dual-a diamond