Generalizations of the Hermite-Biehler theorem

The Hermite-Biehler theorem gives necessary and sufficient conditions for t he Hurwitz stability of a polynomial in terms of certain interlacing condit ions, Im this paper, we generalize the Hermite-Biehler theorem to situation s where the test polynomial is not necessarily Hurwitz. The generalization is given in terms of an analytical expression for the difference between th e numbers of roots of the polynomial in the open left-half and open right-h alf planes. The result can be used to solve important stabilization problem s in control theory and is, therefore, of both academic as well as practica l interest. (C) 1999 Elsevier Science Inc. All rights reserved.