TY - JOUR

T1 - Computation of the singular values of Toeplitz operators and the gap metric

AU - Hirata, Kentaro

AU - Yamamoto, Yutaka

AU - Tannenbaum, Allen

N1 - Funding Information:
The first author was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Encouragement of Young Scientists, 10750340, 1998. The second author was supported in part by the Sound Technology Promotion Foundation. The third author was partially supported by the Air Force Office of Scientific Research AF/F49620-94-1-00S8DEF and AF/F49620-949190461, by the Army Research Office DAAL03-92-G-0115, DAAH04-94-G-0054, DAAH04-93-G-0332, and MURI Grant.

PY - 1999/4/23

Y1 - 1999/4/23

N2 - It is widely recognized that the computation of gap metric is equivalent to a certain two-block H∞ problem, i.e., the gap is equal to the norm of a certain two-block operator. However, it can also be characterized as the smallest singular value of a certain Toeplitz operator. This paper derives a simple computational method for finding such singular values and the gap between two plants by using a state space approach.

AB - It is widely recognized that the computation of gap metric is equivalent to a certain two-block H∞ problem, i.e., the gap is equal to the norm of a certain two-block operator. However, it can also be characterized as the smallest singular value of a certain Toeplitz operator. This paper derives a simple computational method for finding such singular values and the gap between two plants by using a state space approach.

KW - Gap metric

KW - Hamiltonian

KW - Skew Toeplitz theory

KW - Toeplitz operator

KW - Two-block problem

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U2 - 10.1016/S0167-6911(98)00106-6

DO - 10.1016/S0167-6911(98)00106-6

M3 - Article

AN - SCOPUS:0345766884

VL - 36

SP - 327

EP - 338

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 5

ER -