H∞ model order reduction of uncertain linear systems using generalized KYP Lemma

Gustavo S. Mazzoccante; Gijs Hilhorst; Goele Pipeleers; Ricardo C.L.F. Oliveira

doi:10.23919/ECC.2018.8550355

H∞ model order reduction of uncertain linear systems using generalized KYP Lemma

Gustavo S. Mazzoccante, Gijs Hilhorst, Goele Pipeleers, Ricardo C.L.F. Oliveira

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

This article presents a new LMI-based approach for the \mathcal{H-{\infty}} model order reduction problem of continuous-time uncertain linear systems over frequency ranges. Differently from the previous methods in the literature, the approach is specially developed to treat uncertain systems, being able not only to reduce the order of the system, but to remove uncertain parameters. By means ofthe generalized Kalman-Yakubovich-Popov (gKYP) Lemma design conditions are provided in terms of LMIs relaxations associated to scalar searches and iterative procedures to assess low-frequency specifications. Numerical examples from the literature are used to illustrate the potentialities of the proposed approach when compared to existing methods.

Original language	English
Title of host publication	2018 European Control Conference, ECC 2018
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	2616-2622
Number of pages	7
ISBN (Electronic)	9783952426982
DOIs	https://doi.org/10.23919/ECC.2018.8550355
Publication status	Published - 27 Nov 2018
Event	16th European Control Conference, ECC 2018 - Limassol, Cyprus, Limassol, Cyprus Duration: 12 Jun 2018 → 15 Jun 2018 Conference number: 16

Conference

Conference	16th European Control Conference, ECC 2018
Abbreviated title	ECC 2018
Country/Territory	Cyprus
City	Limassol
Period	12/06/18 → 15/06/18

Keywords

finite frequency
H∞ norm
KYP
LMI relaxations
Model reduction
uncertain linear systems

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10.23919/ECC.2018.8550355

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title = "H∞ model order reduction of uncertain linear systems using generalized KYP Lemma",

abstract = "This article presents a new LMI-based approach for the \mathcal{H-{\infty}} model order reduction problem of continuous-time uncertain linear systems over frequency ranges. Differently from the previous methods in the literature, the approach is specially developed to treat uncertain systems, being able not only to reduce the order of the system, but to remove uncertain parameters. By means ofthe generalized Kalman-Yakubovich-Popov (gKYP) Lemma design conditions are provided in terms of LMIs relaxations associated to scalar searches and iterative procedures to assess low-frequency specifications. Numerical examples from the literature are used to illustrate the potentialities of the proposed approach when compared to existing methods.",

keywords = "finite frequency, H∞ norm, KYP, LMI relaxations, Model reduction, uncertain linear systems",

author = "Mazzoccante, {Gustavo S.} and Gijs Hilhorst and Goele Pipeleers and Oliveira, {Ricardo C.L.F.}",

year = "2018",

month = nov,

day = "27",

doi = "10.23919/ECC.2018.8550355",

language = "English",

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booktitle = "2018 European Control Conference, ECC 2018",

publisher = "Institute of Electrical and Electronics Engineers",

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note = "16th European Control Conference, ECC 2018, ECC 2018 ; Conference date: 12-06-2018 Through 15-06-2018",

}

Mazzoccante, GS, Hilhorst, G, Pipeleers, G & Oliveira, RCLF 2018, H∞ model order reduction of uncertain linear systems using generalized KYP Lemma. in 2018 European Control Conference, ECC 2018., 8550355, Institute of Electrical and Electronics Engineers, Piscataway, pp. 2616-2622, 16th European Control Conference, ECC 2018, Limassol, Cyprus, 12/06/18. https://doi.org/10.23919/ECC.2018.8550355

H∞ model order reduction of uncertain linear systems using generalized KYP Lemma. / Mazzoccante, Gustavo S.; Hilhorst, Gijs; Pipeleers, Goele et al.
2018 European Control Conference, ECC 2018. Piscataway: Institute of Electrical and Electronics Engineers, 2018. p. 2616-2622 8550355.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - H∞ model order reduction of uncertain linear systems using generalized KYP Lemma

AU - Mazzoccante, Gustavo S.

AU - Hilhorst, Gijs

AU - Pipeleers, Goele

AU - Oliveira, Ricardo C.L.F.

N1 - Conference code: 16

PY - 2018/11/27

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N2 - This article presents a new LMI-based approach for the \mathcal{H-{\infty}} model order reduction problem of continuous-time uncertain linear systems over frequency ranges. Differently from the previous methods in the literature, the approach is specially developed to treat uncertain systems, being able not only to reduce the order of the system, but to remove uncertain parameters. By means ofthe generalized Kalman-Yakubovich-Popov (gKYP) Lemma design conditions are provided in terms of LMIs relaxations associated to scalar searches and iterative procedures to assess low-frequency specifications. Numerical examples from the literature are used to illustrate the potentialities of the proposed approach when compared to existing methods.

AB - This article presents a new LMI-based approach for the \mathcal{H-{\infty}} model order reduction problem of continuous-time uncertain linear systems over frequency ranges. Differently from the previous methods in the literature, the approach is specially developed to treat uncertain systems, being able not only to reduce the order of the system, but to remove uncertain parameters. By means ofthe generalized Kalman-Yakubovich-Popov (gKYP) Lemma design conditions are provided in terms of LMIs relaxations associated to scalar searches and iterative procedures to assess low-frequency specifications. Numerical examples from the literature are used to illustrate the potentialities of the proposed approach when compared to existing methods.

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KW - H∞ norm

KW - KYP

KW - LMI relaxations

KW - Model reduction

KW - uncertain linear systems

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M3 - Conference contribution

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BT - 2018 European Control Conference, ECC 2018

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T2 - 16th European Control Conference, ECC 2018

Y2 - 12 June 2018 through 15 June 2018

ER -

H∞ model order reduction of uncertain linear systems using generalized KYP Lemma

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