Generalizations of the Hermite–Biehler theorem: the complex case Original Research Article

The Hermite–Biehler theorem gives necessary and sufficient conditions for the Hurwitz stability of a polynomial in terms of certain interlacing conditions. In this paper, we extend our earlier generalization of the Hermite–Biehler theorem for real, not necessarily Hurwitz polynomials to the domain of polynomials with complex coefficients. This result, which is of interest in its own right, can also be used to analytically solve an important stabilization problem in control theory.