Generalizations of the Hermite-Biehler theorem

Ming Tzu Ho, Aniruddha Datta, S. P. Bhattacharyya

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)135-153
Number of pages19
JournalLinear Algebra and Its Applications
Publication statusPublished - 1999 Dec 1

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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