Continued Fractions and 2D Hurwitz Polynomials

A test based on continued fraction expansion for polynomials with complex coefficients decides whether the polynomial has all its roots in the left half-plane. The test presented here is more effective compared to tests evaluating determinants and allows for generalization to polynomials in two variables. The main result is a new test for polynomials in two variables and new algorithms testing necessary conditions of stability for these polynomials. The results can be used in many further areas of research and can also be further generalized. They also show the strength of the continued fraction techniques and the role of positive functions in many areas of system theory. The algorithms described as procedures in MATHEMATICA© language and examples are also included.