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Generalizations of the Hermite–Biehler theorem

✍ Scribed by Ming-Tzu Ho; Aniruddha Datta; S.P. Bhattacharyya

Book ID
104156633
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
176 KB
Volume
302-303
Category
Article
ISSN
0024-3795

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✦ Synopsis

The Hermite±Biehler theorem gives necessary and sucient 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 dierence 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.

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