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 -