Stabilization of uncertain negative-imaginary systems via state-feedback control

Ian R. Petersen; Alexander Lanzon; Zhuoyue Song

doi:10.23919/ecc.2009.7074636

Stabilization of uncertain negative-imaginary systems via state-feedback control

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

^*Corresponding author for this work

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

9 Citations (SciVal)

Abstract

The controller synthesis problem of uncertain negative-imaginary systems has important engineering applications in, for example, lightly damped flexible structures with colocated position sensors and force actuators. This paper provides a systematic controller synthesis procedure via an LMI approach to construct a state-feedback internally stabilizing controller such that the nominal closed-loop system satisfies negative-imaginary properties and a DC gain condition. As a result of this, the closed-loop system can then be guaranteed to be robustly stable against uncertainties that are stable strictly negative-imaginary (e.g. unmodeled spill-over dynamics in a lightly damped flexible structure). An numerical example is given to show the usefulness of the proposed results.

Original language	English
Title of host publication	2009 European Control Conference, ECC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1605-1609
Number of pages	5
ISBN (Electronic)	9783952417393
DOIs	https://doi.org/10.23919/ecc.2009.7074636
Publication status	Published - 26 Mar 2014
Externally published	Yes
Event	10th European Control Conference: ECC 2009 - Budapest, Hungary Duration: 23 Aug 2009 → 26 Aug 2009 Conference number: 10th http://ieeexplore.ieee.org/document/7074402/ http://ieeexplore.ieee.org/document/7074461/

Publication series

Name	2009 European Control Conference, ECC 2009

Conference

Conference	10th European Control Conference: ECC 2009
Abbreviated title	ECC
Country/Territory	Hungary
City	Budapest
Period	23/08/09 → 26/08/09
Internet address	http://ieeexplore.ieee.org/document/7074402/ http://ieeexplore.ieee.org/document/7074461/

Access to Document

10.23919/ecc.2009.7074636

Cite this

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title = "Stabilization of uncertain negative-imaginary systems via state-feedback control",

abstract = "The controller synthesis problem of uncertain negative-imaginary systems has important engineering applications in, for example, lightly damped flexible structures with colocated position sensors and force actuators. This paper provides a systematic controller synthesis procedure via an LMI approach to construct a state-feedback internally stabilizing controller such that the nominal closed-loop system satisfies negative-imaginary properties and a DC gain condition. As a result of this, the closed-loop system can then be guaranteed to be robustly stable against uncertainties that are stable strictly negative-imaginary (e.g. unmodeled spill-over dynamics in a lightly damped flexible structure). An numerical example is given to show the usefulness of the proposed results.",

keywords = "Bounded real, H control, Lightly damped systems, Negative-imaginary systems, Passivity, Positive real, Small-gain theorem",

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

note = "Publisher Copyright: {\textcopyright} 2009 EUCA.; 10th European Control Conference: ECC 2009, ECC ; Conference date: 23-08-2009 Through 26-08-2009",

year = "2014",

month = mar,

day = "26",

doi = "10.23919/ecc.2009.7074636",

language = "English",

series = "2009 European Control Conference, ECC 2009",

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

pages = "1605--1609",

booktitle = "2009 European Control Conference, ECC 2009",

address = "United States",

url = "http://ieeexplore.ieee.org/document/7074402/, http://ieeexplore.ieee.org/document/7074461/",

}

Petersen, IR, Lanzon, A & Song, Z 2014, Stabilization of uncertain negative-imaginary systems via state-feedback control. in 2009 European Control Conference, ECC 2009., 7074636, 2009 European Control Conference, ECC 2009, Institute of Electrical and Electronics Engineers Inc., pp. 1605-1609, 10th European Control Conference: ECC 2009, Budapest, Hungary, 23/08/09. https://doi.org/10.23919/ecc.2009.7074636

Stabilization of uncertain negative-imaginary systems via state-feedback control. / Petersen, Ian R.; Lanzon, Alexander; Song, Zhuoyue.
2009 European Control Conference, ECC 2009. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1605-1609 7074636 (2009 European Control Conference, ECC 2009).

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

TY - GEN

T1 - Stabilization of uncertain negative-imaginary systems via state-feedback control

AU - Petersen, Ian R.

AU - Lanzon, Alexander

AU - Song, Zhuoyue

N1 - Conference code: 10th

PY - 2014/3/26

Y1 - 2014/3/26

N2 - The controller synthesis problem of uncertain negative-imaginary systems has important engineering applications in, for example, lightly damped flexible structures with colocated position sensors and force actuators. This paper provides a systematic controller synthesis procedure via an LMI approach to construct a state-feedback internally stabilizing controller such that the nominal closed-loop system satisfies negative-imaginary properties and a DC gain condition. As a result of this, the closed-loop system can then be guaranteed to be robustly stable against uncertainties that are stable strictly negative-imaginary (e.g. unmodeled spill-over dynamics in a lightly damped flexible structure). An numerical example is given to show the usefulness of the proposed results.

AB - The controller synthesis problem of uncertain negative-imaginary systems has important engineering applications in, for example, lightly damped flexible structures with colocated position sensors and force actuators. This paper provides a systematic controller synthesis procedure via an LMI approach to construct a state-feedback internally stabilizing controller such that the nominal closed-loop system satisfies negative-imaginary properties and a DC gain condition. As a result of this, the closed-loop system can then be guaranteed to be robustly stable against uncertainties that are stable strictly negative-imaginary (e.g. unmodeled spill-over dynamics in a lightly damped flexible structure). An numerical example is given to show the usefulness of the proposed results.

KW - Bounded real

KW - H control

KW - Lightly damped systems

KW - Negative-imaginary systems

KW - Passivity

KW - Positive real

KW - Small-gain theorem

UR - https://www.scopus.com/pages/publications/84955201516

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DO - 10.23919/ecc.2009.7074636

M3 - Conference Paper

T3 - 2009 European Control Conference, ECC 2009

SP - 1605

EP - 1609

BT - 2009 European Control Conference, ECC 2009

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 10th European Control Conference: ECC 2009

Y2 - 23 August 2009 through 26 August 2009

ER -

Stabilization of uncertain negative-imaginary systems via state-feedback control

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