Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 327-338 |
| Number of pages | 12 |
| Journal | Systems and Control Letters |
| Volume | 36 |
| Issue number | 5 |
| Publication status | Published - Apr 23 1999 |
| Externally published | Yes |
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Keywords
- Gap metric
- Hamiltonian
- Skew Toeplitz theory
- Toeplitz operator
- Two-block problem
ASJC Scopus subject areas
- Control and Systems Engineering
- Electrical and Electronic Engineering
Cite this
Computation of the singular values of Toeplitz operators and the gap metric. / Hirata, Kentaro; Yamamoto, Yutaka; Tannenbaum, Allen.
In: Systems and Control Letters, Vol. 36, No. 5, 23.04.1999, p. 327-338.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Computation of the singular values of Toeplitz operators and the gap metric
AU - Hirata, Kentaro
AU - Yamamoto, Yutaka
AU - Tannenbaum, Allen
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
UR - http://www.scopus.com/inward/record.url?scp=0345766884&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0345766884&partnerID=8YFLogxK
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 -