Generalizations of the Hermite-Biehler theorem Conference Paper

abstract

• 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 generalize the Hermite-Biehler theorem to situations where the test polynomial is not necessarily Hurwitz. The generalization is given in terms of an analytical expression for the difference between the numbers of roots of the polynomial in the open left-half and open right-half planes. The result can be used to solve important stabilization problems in control theory and is, therefore, of both academic as well as practical interest. 1999 Elsevier Science Inc. All rights reserved.

authors

• Datta, Aniruddha

published proceedings

• LINEAR ALGEBRA AND ITS APPLICATIONS

author list (cited authors)

• Ho, M. T., Datta, A., & Bhattacharyya, S. P.

citation count

• 44

complete list of authors

• Ho, MT||Datta, A||Bhattacharyya, SP

publication date

• December 1999

publisher

• Elsevier  Publisher

published in

• Linear Algebra and Its Applications  Journal

keywords

• Generalized Interlacing
• Hermite-biehler Theorem
• Root Distribution
• STABILITY

Digital Object Identifier (DOI)

• 10.1016/s0024-3795(99)00069-5

start page

• 135

end page

• 153

volume

• 303

URL

• http://dx.doi.org/10.1016/s0024-3795(99)00069-5