A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties

Wynita M. Griggs; Brian D.O. Anderson; Alexander Lanzon; Michael C. Rotkowitz

doi:10.1109/CDC.2007.4434398

A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties

Wynita M. Griggs^*, Brian D.O. Anderson, Alexander Lanzon, Michael C. Rotkowitz

^*Corresponding author for this work

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

8 Citations (Scopus)

Abstract

A feedback interconnection consisting of two nonlinear systems is shown to be input-output stable when a "mixed" small gain and passivity assumption is placed on each of the systems. The "mixed" small gain and passivity property captures the well-known notions of passivity and small gain associated with systems: the property can be appropriately reduced to an input and output strictly passive system description; or alternatively can be reduced to a description of a system with small, finite gain. More importantly, the property captures a concept of "blending" of the small gain and passivity ideas. This concept of "blending" can be visualized, for example, by considering linear time-invariant systems that exhibit passivetype properties at, say low frequencies; and lose these passivetype properties but have small gain at high frequencies.

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	4489-4494
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434398
Publication status	Published - 2007
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.2007.4434398

Cite this

Griggs, W. M., Anderson, B. D. O., Lanzon, A., & Rotkowitz, M. C. (2007). A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 4489-4494). Article 4434398 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434398

Griggs, Wynita M. ; Anderson, Brian D.O. ; Lanzon, Alexander et al. / A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties. Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. pp. 4489-4494 (Proceedings of the IEEE Conference on Decision and Control).

@inproceedings{4a39ab24530d46b795177f2ecc98ed2b,

title = "A stability result for interconnections of nonlinear systems with {"}mixed{"} small gain and passivity properties",

abstract = "A feedback interconnection consisting of two nonlinear systems is shown to be input-output stable when a {"}mixed{"} small gain and passivity assumption is placed on each of the systems. The {"}mixed{"} small gain and passivity property captures the well-known notions of passivity and small gain associated with systems: the property can be appropriately reduced to an input and output strictly passive system description; or alternatively can be reduced to a description of a system with small, finite gain. More importantly, the property captures a concept of {"}blending{"} of the small gain and passivity ideas. This concept of {"}blending{"} can be visualized, for example, by considering linear time-invariant systems that exhibit passivetype properties at, say low frequencies; and lose these passivetype properties but have small gain at high frequencies.",

author = "Griggs, {Wynita M.} and Anderson, {Brian D.O.} and Alexander Lanzon and Rotkowitz, {Michael C.}",

year = "2007",

doi = "10.1109/CDC.2007.4434398",

language = "English",

isbn = "1424414989",

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

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

pages = "4489--4494",

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",

}

Griggs, WM, Anderson, BDO, Lanzon, A & Rotkowitz, MC 2007, A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434398, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4489-4494, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434398

A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties. / Griggs, Wynita M.; Anderson, Brian D.O.; Lanzon, Alexander et al.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 4489-4494 4434398 (Proceedings of the IEEE Conference on Decision and Control).

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

TY - GEN

T1 - A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties

AU - Griggs, Wynita M.

AU - Anderson, Brian D.O.

AU - Lanzon, Alexander

AU - Rotkowitz, Michael C.

PY - 2007

Y1 - 2007

N2 - A feedback interconnection consisting of two nonlinear systems is shown to be input-output stable when a "mixed" small gain and passivity assumption is placed on each of the systems. The "mixed" small gain and passivity property captures the well-known notions of passivity and small gain associated with systems: the property can be appropriately reduced to an input and output strictly passive system description; or alternatively can be reduced to a description of a system with small, finite gain. More importantly, the property captures a concept of "blending" of the small gain and passivity ideas. This concept of "blending" can be visualized, for example, by considering linear time-invariant systems that exhibit passivetype properties at, say low frequencies; and lose these passivetype properties but have small gain at high frequencies.

AB - A feedback interconnection consisting of two nonlinear systems is shown to be input-output stable when a "mixed" small gain and passivity assumption is placed on each of the systems. The "mixed" small gain and passivity property captures the well-known notions of passivity and small gain associated with systems: the property can be appropriately reduced to an input and output strictly passive system description; or alternatively can be reduced to a description of a system with small, finite gain. More importantly, the property captures a concept of "blending" of the small gain and passivity ideas. This concept of "blending" can be visualized, for example, by considering linear time-invariant systems that exhibit passivetype properties at, say low frequencies; and lose these passivetype properties but have small gain at high frequencies.

UR - http://www.scopus.com/inward/record.url?scp=62749100528&partnerID=8YFLogxK

U2 - 10.1109/CDC.2007.4434398

DO - 10.1109/CDC.2007.4434398

M3 - Conference contribution

SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4489

EP - 4494

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

PB - Institute of Electrical and Electronics Engineers Inc.

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

Y2 - 12 December 2007 through 14 December 2007

ER -

Griggs WM, Anderson BDO, Lanzon A, Rotkowitz MC. A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc. 2007. p. 4489-4494. 4434398. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2007.4434398

A stability result for interconnections of nonlinear systems with "mixed" small gain and passivity properties

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this