Another simplification in multidimensional stability tests

The main computational burden of checking stability of a multidimensional system is to check whether a multivariable polynomial has zeros on the distinguished boundary of a certain region of analyticity. A transformation is performed yielding an expression which has zeros on the distinguished boundary if and only if the original polynomial has such zeros. In some cases, especially where a linear dependence of certain auxiliary variables defined in the text can be presented in terms of nonnegative integers, the transformed expression is considerably simpler, and its test is easier to perform than the original one. Examples are provided.