Interpreting the iISS small-gain theorem as transient plus ISS small-gain regulation

Hiroshi Ito; Randy A. Freeman; Antoine Chaillet

doi:10.1109/CDC.2010.5717732

Interpreting the iISS small-gain theorem as transient plus ISS small-gain regulation

Hiroshi Ito^*, Randy A. Freeman, Antoine Chaillet

^*Corresponding author for this work

Electrical and Computer Engineering

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

5 Scopus citations

Abstract

This paper addresses the problem of establishing stability of interconnections of integral input-to-state stable (iISS) systems. Recently, the small-gain theorem for input-to-state stable (ISS) systems has been extended to the class of iISS systems. It has been also proved that at least one of the two iISS subsystems comprising a feedback interconnection needs to be ISS with respect to the state of the other subsystem for guaranteeing the iISS of the overall system. This paper shows that making use of this necessary condition enables to provide more insight on the iISS small gain theorem by giving an alternative proof of this result from the perspective of transient plus ISS small-gain regulation.

Original language	English (US)
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages	2432-2437
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2010.5717732
State	Published - 2010
Event	2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States Duration: Dec 15 2010 → Dec 17 2010

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	2010 49th IEEE Conference on Decision and Control, CDC 2010
Country	United States
City	Atlanta, GA
Period	12/15/10 → 12/17/10

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2010.5717732

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Cite this

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title = "Interpreting the iISS small-gain theorem as transient plus ISS small-gain regulation",

abstract = "This paper addresses the problem of establishing stability of interconnections of integral input-to-state stable (iISS) systems. Recently, the small-gain theorem for input-to-state stable (ISS) systems has been extended to the class of iISS systems. It has been also proved that at least one of the two iISS subsystems comprising a feedback interconnection needs to be ISS with respect to the state of the other subsystem for guaranteeing the iISS of the overall system. This paper shows that making use of this necessary condition enables to provide more insight on the iISS small gain theorem by giving an alternative proof of this result from the perspective of transient plus ISS small-gain regulation.",

author = "Hiroshi Ito and Freeman, {Randy A.} and Antoine Chaillet",

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doi = "10.1109/CDC.2010.5717732",

language = "English (US)",

isbn = "9781424477456",

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

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Ito, H, Freeman, RA & Chaillet, A 2010, Interpreting the iISS small-gain theorem as transient plus ISS small-gain regulation. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717732, Proceedings of the IEEE Conference on Decision and Control, pp. 2432-2437, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717732

Interpreting the iISS small-gain theorem as transient plus ISS small-gain regulation. / Ito, Hiroshi; Freeman, Randy A.; Chaillet, Antoine.

2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 2432-2437 5717732 (Proceedings of the IEEE Conference on Decision and Control).

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

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AB - This paper addresses the problem of establishing stability of interconnections of integral input-to-state stable (iISS) systems. Recently, the small-gain theorem for input-to-state stable (ISS) systems has been extended to the class of iISS systems. It has been also proved that at least one of the two iISS subsystems comprising a feedback interconnection needs to be ISS with respect to the state of the other subsystem for guaranteeing the iISS of the overall system. This paper shows that making use of this necessary condition enables to provide more insight on the iISS small gain theorem by giving an alternative proof of this result from the perspective of transient plus ISS small-gain regulation.

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