STABILIZATION OF CONDITIONAL UNCERTAIN NEGATIVE-IMAGINARY SYSTEMS USING RICCATI EQUATION APPROACH

Mohamed A. Mabrok; Abhijit G Kallapur; Ian Petersen; Alexander Lanzon

STABILIZATION OF CONDITIONAL UNCERTAIN NEGATIVE-IMAGINARY SYSTEMS USING RICCATI EQUATION APPROACH

Mohamed A. Mabrok
, Abhijit G Kallapur
, Ian Petersen
, Alexander Lanzon

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

Abstract

In this paper, we derive a negative imaginary and a strict negative imaginary lemma based on Riccati equations. The resulting negative imaginary lemma is used to solve a controller synthesis problem. For a given uncertain system, a static controller is constructed to force the system to satisfy the negative imaginary property. As a result, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the proposed results.

Original language	English
Title of host publication	Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012)
Place of Publication	Australia
Publisher	Conference Organising Committee
Pages	1-6
Number of pages	6
Edition	Peer Reviewed
ISBN (Print)	9780646580623
Publication status	Published - 2012
Event	20th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2012 - Melbourne, Australia Duration: 9 Jul 2012 → 13 Jul 2012 http://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=19334

Conference

Conference	20th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2012
Abbreviated title	MTNS 2012
Country/Territory	Australia
City	Melbourne
Period	9/07/12 → 13/07/12
Other	The International Program Committee (IPC) invites contributions to the 20th International Symposium on Mathematical Theory of Networks and Systems 2012 to be held in Melbourne, Victoria, Australia on 9-13 July 2012.
Internet address	http://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=19334

Cite this

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title = "STABILIZATION OF CONDITIONAL UNCERTAIN NEGATIVE-IMAGINARY SYSTEMS USING RICCATI EQUATION APPROACH",

abstract = "In this paper, we derive a negative imaginary and a strict negative imaginary lemma based on Riccati equations. The resulting negative imaginary lemma is used to solve a controller synthesis problem. For a given uncertain system, a static controller is constructed to force the system to satisfy the negative imaginary property. As a result, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the proposed results.",

author = "Mabrok, \{Mohamed A.\} and Kallapur, \{Abhijit G\} and Ian Petersen and Alexander Lanzon",

year = "2012",

language = "English",

isbn = "9780646580623",

pages = "1--6",

booktitle = "Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012)",

publisher = "Conference Organising Committee",

edition = "Peer Reviewed",

note = "20th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2012, MTNS 2012 ; Conference date: 09-07-2012 Through 13-07-2012",

url = "http://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=19334",

}

Mabrok, MA, Kallapur, AG, Petersen, I & Lanzon, A 2012, STABILIZATION OF CONDITIONAL UNCERTAIN NEGATIVE-IMAGINARY SYSTEMS USING RICCATI EQUATION APPROACH. in Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012). Peer Reviewed edn, Conference Organising Committee, Australia, pp. 1-6, 20th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2012, Melbourne, Australia, 9/07/12.

STABILIZATION OF CONDITIONAL UNCERTAIN NEGATIVE-IMAGINARY SYSTEMS USING RICCATI EQUATION APPROACH. / Mabrok, Mohamed A.; Kallapur, Abhijit G; Petersen, Ian et al.
Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012). Peer Reviewed. ed. Australia: Conference Organising Committee, 2012. p. 1-6.

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

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T1 - STABILIZATION OF CONDITIONAL UNCERTAIN NEGATIVE-IMAGINARY SYSTEMS USING RICCATI EQUATION APPROACH

AU - Mabrok, Mohamed A.

AU - Kallapur, Abhijit G

AU - Petersen, Ian

AU - Lanzon, Alexander

PY - 2012

Y1 - 2012

N2 - In this paper, we derive a negative imaginary and a strict negative imaginary lemma based on Riccati equations. The resulting negative imaginary lemma is used to solve a controller synthesis problem. For a given uncertain system, a static controller is constructed to force the system to satisfy the negative imaginary property. As a result, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the proposed results.

AB - In this paper, we derive a negative imaginary and a strict negative imaginary lemma based on Riccati equations. The resulting negative imaginary lemma is used to solve a controller synthesis problem. For a given uncertain system, a static controller is constructed to force the system to satisfy the negative imaginary property. As a result, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the proposed results.

M3 - Conference Paper

SN - 9780646580623

SP - 1

EP - 6

BT - Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012)

PB - Conference Organising Committee

CY - Australia

T2 - 20th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2012

Y2 - 9 July 2012 through 13 July 2012

ER -

STABILIZATION OF CONDITIONAL UNCERTAIN NEGATIVE-IMAGINARY SYSTEMS USING RICCATI EQUATION APPROACH

Abstract

Conference

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