### 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 |

### Fingerprint

### 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

*Systems and Control Letters*,

*36*(5), 327-338.

**Computation of the singular values of Toeplitz operators and the gap metric.** / Hirata, Kentaro; Yamamoto, Yutaka; Tannenbaum, Allen.

Research output: Contribution to journal › Article

*Systems and Control Letters*, vol. 36, no. 5, pp. 327-338.

}

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 -