TY - JOUR

T1 - Generalizations of the Hermite-Biehler theorem

AU - Ho, Ming Tzu

AU - Datta, Aniruddha

AU - Bhattacharyya, S. P.

N1 - Funding Information:
This work was supported in part by the National Science Foundation under Grant ECS-9417004 and in part by the Texas Advanced Technology Program under Grant No. 999903-002.

PY - 1999/12/1

Y1 - 1999/12/1

N2 - 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.

AB - 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.

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U2 - 10.1016/S0024-3795(99)00069-5

DO - 10.1016/S0024-3795(99)00069-5

M3 - Article

AN - SCOPUS:4243407297

VL - 302-303

SP - 135

EP - 153

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -