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

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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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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.",

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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",

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

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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

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SP - 253

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JO - Systems and Control Letters

JF - Systems and Control Letters

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On the computation of the gap metric

Abstract

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Keywords

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