A Gramian-based approach to model reduction for uncertain systems

Li Li; Ian R. Petersen

doi:10.1109/CDC.2007.4434211

A Gramian-based approach to model reduction for uncertain systems

Li Li^*
, Ian R. Petersen

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

The paper considers the problem of model reduction for a class of uncertain systems with structured norm bounded uncertainty. The paper introduces controllability and observability Gramians in terms of certain parameterized algebraic Riccati inequalities. This enables a balanced trun-cation model reduction procedure for uncertain systems to be presented. Error bounds for this model reduction procedure are derived. The paper also investigates H ^∞ model reduction for uncertain systems. The solution to this problem is shown to involve constructing the underlying Gramians satisfying a certain rank constraint.

Original language	English
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4373-4378
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434211
Publication status	Published - 2007
Externally published	Yes
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: 12 Dec 2007 → 14 Dec 2007

Publication series

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

Conference

Conference	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 14/12/07

Access to Document

10.1109/CDC.2007.4434211

Cite this

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title = "A Gramian-based approach to model reduction for uncertain systems",

abstract = "The paper considers the problem of model reduction for a class of uncertain systems with structured norm bounded uncertainty. The paper introduces controllability and observability Gramians in terms of certain parameterized algebraic Riccati inequalities. This enables a balanced trun-cation model reduction procedure for uncertain systems to be presented. Error bounds for this model reduction procedure are derived. The paper also investigates H ∞ model reduction for uncertain systems. The solution to this problem is shown to involve constructing the underlying Gramians satisfying a certain rank constraint.",

author = "Li Li and Petersen, \{Ian R.\}",

year = "2007",

doi = "10.1109/CDC.2007.4434211",

language = "English",

isbn = "1424414989",

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

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

pages = "4373--4378",

booktitle = "Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC",

address = "United States",

note = "46th IEEE Conference on Decision and Control 2007, CDC ; Conference date: 12-12-2007 Through 14-12-2007",

}

Li, L & Petersen, IR 2007, A Gramian-based approach to model reduction for uncertain systems. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434211, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4373-4378, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434211

A Gramian-based approach to model reduction for uncertain systems. / Li, Li; Petersen, Ian R.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 4373-4378 4434211 (Proceedings of the IEEE Conference on Decision and Control).

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

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DO - 10.1109/CDC.2007.4434211

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T2 - 46th IEEE Conference on Decision and Control 2007, CDC

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ER -

A Gramian-based approach to model reduction for uncertain systems

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