Stable polynomials with complex coefficients

In this paper, the problem of determining whether a given polynomial with complex coefficients is stable or not is considered. A generalized Hurwitz theorem is proved, and then a stable criterion is derived based on the theorem. This criterion is expressed by means of an array, called generalized Routh array. The results are significant because neither division algorithm nor operations of complex numbers are in the generalized Routh array. Finally, an example is given to illustrate this point.