On state-space characterization for strict negative-imaginariness of LTI systems

Zhuoyue Song; Sourav Patra; Alexander Lanzon; Ian R. Petersen

doi:10.1109/CDC.2011.6160638

On state-space characterization for strict negative-imaginariness of LTI systems

Zhuoyue Song^*, Sourav Patra, Alexander Lanzon, Ian R. Petersen

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

Negative-imaginary systems appear quite often in engineering applications, for example, in flexible structures with collocated position sensors and force actuators, in electrical circuits, in system biology, etc. In this paper, a strongly strict negative-imaginary lemma is proposed to ensure the strict negative-imaginary property of an LTI system. This result will facilitate both robustness analysis and controller synthesis for interconnected negative-imaginary systems. In the proposed characterization, numerical advantages are achieved by avoiding a minimality assumption, a non-convex rank constraint and a non-strict inequality condition present in previous literature. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

Original language	English
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	453-458
Number of pages	6
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6160638
Publication status	Published - 2011
Externally published	Yes
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: 12 Dec 2011 → 15 Dec 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 15/12/11

Access to Document

10.1109/CDC.2011.6160638

Cite this

Song, Z., Patra, S., Lanzon, A., & Petersen, I. R. (2011). On state-space characterization for strict negative-imaginariness of LTI systems. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 453-458). Article 6160638 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2011.6160638

Song, Zhuoyue ; Patra, Sourav ; Lanzon, Alexander et al. / On state-space characterization for strict negative-imaginariness of LTI systems. 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. pp. 453-458 (Proceedings of the IEEE Conference on Decision and Control).

@inproceedings{80a5ceae7439404ab03277f479e5e2ab,

title = "On state-space characterization for strict negative-imaginariness of LTI systems",

abstract = "Negative-imaginary systems appear quite often in engineering applications, for example, in flexible structures with collocated position sensors and force actuators, in electrical circuits, in system biology, etc. In this paper, a strongly strict negative-imaginary lemma is proposed to ensure the strict negative-imaginary property of an LTI system. This result will facilitate both robustness analysis and controller synthesis for interconnected negative-imaginary systems. In the proposed characterization, numerical advantages are achieved by avoiding a minimality assumption, a non-convex rank constraint and a non-strict inequality condition present in previous literature. Two numerical examples are provided to illustrate the effectiveness of the proposed results.",

author = "Zhuoyue Song and Sourav Patra and Alexander Lanzon and Petersen, {Ian R.}",

year = "2011",

doi = "10.1109/CDC.2011.6160638",

language = "English",

isbn = "9781612848006",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "453--458",

booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

address = "United States",

note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

}

Song, Z, Patra, S, Lanzon, A & Petersen, IR 2011, On state-space characterization for strict negative-imaginariness of LTI systems. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6160638, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 453-458, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160638

On state-space characterization for strict negative-imaginariness of LTI systems. / Song, Zhuoyue; Patra, Sourav; Lanzon, Alexander et al.
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 453-458 6160638 (Proceedings of the IEEE Conference on Decision and Control).

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

TY - GEN

T1 - On state-space characterization for strict negative-imaginariness of LTI systems

AU - Song, Zhuoyue

AU - Patra, Sourav

AU - Lanzon, Alexander

AU - Petersen, Ian R.

PY - 2011

Y1 - 2011

N2 - Negative-imaginary systems appear quite often in engineering applications, for example, in flexible structures with collocated position sensors and force actuators, in electrical circuits, in system biology, etc. In this paper, a strongly strict negative-imaginary lemma is proposed to ensure the strict negative-imaginary property of an LTI system. This result will facilitate both robustness analysis and controller synthesis for interconnected negative-imaginary systems. In the proposed characterization, numerical advantages are achieved by avoiding a minimality assumption, a non-convex rank constraint and a non-strict inequality condition present in previous literature. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

AB - Negative-imaginary systems appear quite often in engineering applications, for example, in flexible structures with collocated position sensors and force actuators, in electrical circuits, in system biology, etc. In this paper, a strongly strict negative-imaginary lemma is proposed to ensure the strict negative-imaginary property of an LTI system. This result will facilitate both robustness analysis and controller synthesis for interconnected negative-imaginary systems. In the proposed characterization, numerical advantages are achieved by avoiding a minimality assumption, a non-convex rank constraint and a non-strict inequality condition present in previous literature. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

UR - http://www.scopus.com/inward/record.url?scp=84860650224&partnerID=8YFLogxK

U2 - 10.1109/CDC.2011.6160638

DO - 10.1109/CDC.2011.6160638

M3 - Conference contribution

SN - 9781612848006

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 453

EP - 458

BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

Y2 - 12 December 2011 through 15 December 2011

ER -

Song Z, Patra S, Lanzon A, Petersen IR. On state-space characterization for strict negative-imaginariness of LTI systems. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc. 2011. p. 453-458. 6160638. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2011.6160638

On state-space characterization for strict negative-imaginariness of LTI systems

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this