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

Kentaro Hirata; Yutaka Yamamoto; Allen Tannenbaum

doi:10.1016/S0167-6911(98)00106-6

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

Kentaro Hirata, Yutaka Yamamoto, Allen Tannenbaum

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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
DOIs	https://doi.org/10.1016/S0167-6911(98)00106-6
Publication status	Published - Apr 23 1999
Externally published	Yes

Keywords

Gap metric
Hamiltonian
Skew Toeplitz theory
Toeplitz operator
Two-block problem

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science(all)
Mechanical Engineering
Electrical and Electronic Engineering

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10.1016/S0167-6911(98)00106-6

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title = "Computation of the singular values of Toeplitz operators and the gap metric",

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.",

keywords = "Gap metric, Hamiltonian, Skew Toeplitz theory, Toeplitz operator, Two-block problem",

author = "Kentaro Hirata and Yutaka Yamamoto and Allen Tannenbaum",

note = "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. ",

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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.

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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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VL - 36

SP - 327

EP - 338

JO - Systems and Control Letters

JF - Systems and Control Letters

SN - 0167-6911

IS - 5

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