Comments on `Boundary implications of stability and positivity properties of multidimensional systems´ by S. Basu

In the above-mentioned work by S. Basu (see ibid., vol.78, p.614-626, 1990), one of the main focal points is the robustness of positive property for a k-variate interval rational function having complex coefficients (hereafter the property is referred to as the PC property). It is concluded that the PC property of the specific 16(2^k)² extreme members of the set can imply the PC property of the set. In this comment, it is proven that the PC property of a k-variate complex interval rational function can be assured by the PC property of its certain 16(2^k) extreme members, which are a proper subset of those 16(2^k)² extreme members defined in the above-mentioned work