TY - GEN

T1 - An extension of the generalized hermite-biehler theorem

T2 - 1998 American Control Conference, ACC 1998

AU - Ho, Ming Tzu

AU - Datta, Aniruddha

AU - Bhattacharyya, S. P.

PY - 1998/12/1

Y1 - 1998/12/1

N2 - Recently in [1, 3], a generalization of the classical Hermite-Biehler Theorem was derived and shown to be useful for solving a number of fixed order and structure stabilization problems. This generalization, though adequate for solving these stabilization problems, required the assumption that the polynomial in question have no roots on the imaginary axis except for possibly a simple root at the origin. In this note, the result of [1] is extended to also allow roots on the imaginary axis: the main conclusion is that the roots, if any, at the origin modify the earlier Theorem statement only very slightly while the other imaginary axis roots leave it unchanged. The extension presented here permits a clearer exposition of the stabilization results in [1, 3].

AB - Recently in [1, 3], a generalization of the classical Hermite-Biehler Theorem was derived and shown to be useful for solving a number of fixed order and structure stabilization problems. This generalization, though adequate for solving these stabilization problems, required the assumption that the polynomial in question have no roots on the imaginary axis except for possibly a simple root at the origin. In this note, the result of [1] is extended to also allow roots on the imaginary axis: the main conclusion is that the roots, if any, at the origin modify the earlier Theorem statement only very slightly while the other imaginary axis roots leave it unchanged. The extension presented here permits a clearer exposition of the stabilization results in [1, 3].

UR - http://www.scopus.com/inward/record.url?scp=33645417614&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645417614&partnerID=8YFLogxK

U2 - 10.1109/ACC.1998.688454

DO - 10.1109/ACC.1998.688454

M3 - Conference contribution

AN - SCOPUS:33645417614

SN - 0780345304

SN - 9780780345300

T3 - Proceedings of the American Control Conference

SP - 3206

EP - 3209

BT - Proceedings of the 1998 American Control Conference, ACC 1998

Y2 - 24 June 1998 through 26 June 1998

ER -