On the computation of the gap metric

Tryphon T. Georgiou

doi:10.1016/0167-6911(88)90067-9

On the computation of the gap metric

Tryphon T. Georgiou

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

159 Scopus citations

Abstract

This paper deals with the computation of the gap metric introduced by Zames and El-Sakkary [17]. It is shown that the gap between two systems (P₁, P₂) is precisely the maximum of the two expressions inf Qε{lunate}H∞ D_i N_i - D_j N_jQ _∞ for (i, j) equal to (1, 2) and (2, 1), and (N_i, D_i) being normalized right coprine factorizations of P_i, i = 1, 2, in the sense of Vidyasagar [12]. This expression is computable using well-known techniques from interpolation theory.

Original language	English (US)
Pages (from-to)	253-257
Number of pages	5
Journal	Systems and Control Letters
Volume	11
Issue number	4
DOIs	https://doi.org/10.1016/0167-6911(88)90067-9
State	Published - Oct 1988
Externally published	Yes

Bibliographical note

Funding Information:
* This research was supported in part by NSF under Grant No. ECS-8705291 and MIP-8708811.

Keywords

Gap metric
Graph metric
Topology of unstable systems

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10.1016/0167-6911(88)90067-9

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title = "On the computation of the gap metric",

abstract = "This paper deals with the computation of the gap metric introduced by Zames and El-Sakkary [17]. It is shown that the gap between two systems (P1, P2) is precisely the maximum of the two expressions inf Qε\{lunate\}H∞ Di Ni - Dj NjQ ∞ for (i, j) equal to (1, 2) and (2, 1), and (Ni, Di) being normalized right coprine factorizations of Pi, i = 1, 2, in the sense of Vidyasagar [12]. This expression is computable using well-known techniques from interpolation theory.",

keywords = "Gap metric, Graph metric, Topology of unstable systems",

author = "Georgiou, \{Tryphon T.\}",

note = "Funding Information: * This research was supported in part by NSF under Grant No. ECS-8705291 and MIP-8708811.",

year = "1988",

month = oct,

doi = "10.1016/0167-6911(88)90067-9",

language = "English (US)",

volume = "11",

pages = "253--257",

journal = "Systems and Control Letters",

issn = "0167-6911",

publisher = "Elsevier B.V.",

number = "4",

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T1 - On the computation of the gap metric

AU - Georgiou, Tryphon T.

N1 - Funding Information: * This research was supported in part by NSF under Grant No. ECS-8705291 and MIP-8708811.

PY - 1988/10

Y1 - 1988/10

N2 - This paper deals with the computation of the gap metric introduced by Zames and El-Sakkary [17]. It is shown that the gap between two systems (P1, P2) is precisely the maximum of the two expressions inf Qε{lunate}H∞ Di Ni - Dj NjQ ∞ for (i, j) equal to (1, 2) and (2, 1), and (Ni, Di) being normalized right coprine factorizations of Pi, i = 1, 2, in the sense of Vidyasagar [12]. This expression is computable using well-known techniques from interpolation theory.

AB - This paper deals with the computation of the gap metric introduced by Zames and El-Sakkary [17]. It is shown that the gap between two systems (P1, P2) is precisely the maximum of the two expressions inf Qε{lunate}H∞ Di Ni - Dj NjQ ∞ for (i, j) equal to (1, 2) and (2, 1), and (Ni, Di) being normalized right coprine factorizations of Pi, i = 1, 2, in the sense of Vidyasagar [12]. This expression is computable using well-known techniques from interpolation theory.

KW - Gap metric

KW - Graph metric

KW - Topology of unstable systems

UR - https://www.scopus.com/pages/publications/0024088669

UR - https://www.scopus.com/pages/publications/0024088669#tab=citedBy

U2 - 10.1016/0167-6911(88)90067-9

DO - 10.1016/0167-6911(88)90067-9

M3 - Article

AN - SCOPUS:0024088669

SN - 0167-6911

VL - 11

SP - 253

EP - 257

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 4

ER -

On the computation of the gap metric

Abstract

Bibliographical note

Keywords

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