Robust feedback stability of negative imaginary systems: An integral quadratic constraint approach

Sei Zhen Khong; Ian R. Petersen; Anders Rantzer

doi:10.1109/ECC.2015.7330832

Robust feedback stability of negative imaginary systems: An integral quadratic constraint approach

Sei Zhen Khong, Ian R. Petersen, Anders Rantzer

Institute for Mathematics and its Applications

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 Scopus citations

Abstract

Sufficient conditions for stability of feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. These extend existing results in the literature by exploiting the flexibility present at the static and infinite frequencies to reduce conservatism. Negative imaginary transfer functions with poles on the imaginary axis are accommodated using a recently generalised IQC-based robustness result. In particular, the negative imaginary property of systems is shown to give rise to IQCs on positive frequencies that are bounded away from zero and infinity. Additional quadratic conditions are introduced to take care of the IQCs near the DC and instantaneous gains of the systems.

Original language	English (US)
Title of host publication	2015 European Control Conference, ECC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1998-2002
Number of pages	5
ISBN (Electronic)	9783952426937
DOIs	https://doi.org/10.1109/ECC.2015.7330832
State	Published - Nov 16 2015
Event	European Control Conference, ECC 2015 - Linz, Austria Duration: Jul 15 2015 → Jul 17 2015

Publication series

Name	2015 European Control Conference, ECC 2015

Other

Other	European Control Conference, ECC 2015
Country/Territory	Austria
City	Linz
Period	7/15/15 → 7/17/15

Bibliographical note

Publisher Copyright:
© 2015 EUCA.

Keywords

Negative imaginary systems
feedback stability
integral quadratic constraints

Publisher link

10.1109/ECC.2015.7330832

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Khong, S. Z., Petersen, I. R., & Rantzer, A. (2015). Robust feedback stability of negative imaginary systems: An integral quadratic constraint approach. In 2015 European Control Conference, ECC 2015 (pp. 1998-2002). Article 7330832 (2015 European Control Conference, ECC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ECC.2015.7330832

Robust feedback stability of negative imaginary systems: An integral quadratic constraint approach. / Khong, Sei Zhen; Petersen, Ian R.; Rantzer, Anders.
2015 European Control Conference, ECC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1998-2002 7330832 (2015 European Control Conference, ECC 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Khong, SZ, Petersen, IR & Rantzer, A 2015, Robust feedback stability of negative imaginary systems: An integral quadratic constraint approach. in 2015 European Control Conference, ECC 2015., 7330832, 2015 European Control Conference, ECC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 1998-2002, European Control Conference, ECC 2015, Linz, Austria, 7/15/15. https://doi.org/10.1109/ECC.2015.7330832

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abstract = "Sufficient conditions for stability of feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. These extend existing results in the literature by exploiting the flexibility present at the static and infinite frequencies to reduce conservatism. Negative imaginary transfer functions with poles on the imaginary axis are accommodated using a recently generalised IQC-based robustness result. In particular, the negative imaginary property of systems is shown to give rise to IQCs on positive frequencies that are bounded away from zero and infinity. Additional quadratic conditions are introduced to take care of the IQCs near the DC and instantaneous gains of the systems.",

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N2 - Sufficient conditions for stability of feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. These extend existing results in the literature by exploiting the flexibility present at the static and infinite frequencies to reduce conservatism. Negative imaginary transfer functions with poles on the imaginary axis are accommodated using a recently generalised IQC-based robustness result. In particular, the negative imaginary property of systems is shown to give rise to IQCs on positive frequencies that are bounded away from zero and infinity. Additional quadratic conditions are introduced to take care of the IQCs near the DC and instantaneous gains of the systems.

AB - Sufficient conditions for stability of feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. These extend existing results in the literature by exploiting the flexibility present at the static and infinite frequencies to reduce conservatism. Negative imaginary transfer functions with poles on the imaginary axis are accommodated using a recently generalised IQC-based robustness result. In particular, the negative imaginary property of systems is shown to give rise to IQCs on positive frequencies that are bounded away from zero and infinity. Additional quadratic conditions are introduced to take care of the IQCs near the DC and instantaneous gains of the systems.

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KW - feedback stability

KW - integral quadratic constraints

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SP - 1998

EP - 2002

BT - 2015 European Control Conference, ECC 2015

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 15 July 2015 through 17 July 2015

ER -

Robust feedback stability of negative imaginary systems: An integral quadratic constraint approach

Abstract

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