Existence criterion for nonessential singularities of the second kind

The stability of a single-input single-output multivariable system is governed by the zeros of the numerator as well as the denominator of its multivariable transfer function. Where the relatively prime numerator and denominator polynomials share a common zero, the transfer function is said to have a nonessential singularity of the second kind. Such a singularity on the stability region boundary mandates more complicated stability tests than would otherwise be needed. Thus, their existence must be known. A criterion for their existence is described in this short paper.