Small-gain conditions and lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption

Hiroshi Ito; Zhong Ping Jiang

doi:10.1109/ACC.2008.4586834

Small-gain conditions and lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption

Hiroshi Ito, Zhong Ping Jiang

Electrical and Computer Engineering

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

Abstract

This paper addresses the problem of verifying stability of the interconnection of integral input-to-state stable (iISS) systems. This paper strengthens a Lyapunov approach to the problem to the point where the necessity of a small-gain condition holds without technical assumptions such as uniformity and analyticity required by previous work. This paper unifies the treatment of iISS and input-to-state stable (ISS) systems, which has not been achieved by any previous technique of constructing Lyapunov functions. It is shown that iISS systems and ISS systems can share a common form of Lyapunov functions to characterize stability of their interconnection with respect to external signals. Global asymptotic stability is also discussed.

Original language	English (US)
Title of host publication	2008 American Control Conference, ACC
Pages	2297-2303
Number of pages	7
DOIs	https://doi.org/10.1109/ACC.2008.4586834
State	Published - 2008
Event	2008 American Control Conference, ACC - Seattle, WA, United States Duration: Jun 11 2008 → Jun 13 2008

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2008 American Control Conference, ACC
Country/Territory	United States
City	Seattle, WA
Period	6/11/08 → 6/13/08

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/ACC.2008.4586834

Cite this

Ito, H & Jiang, ZP 2008, Small-gain conditions and lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption. in 2008 American Control Conference, ACC., 4586834, Proceedings of the American Control Conference, pp. 2297-2303, 2008 American Control Conference, ACC, Seattle, WA, United States, 6/11/08. https://doi.org/10.1109/ACC.2008.4586834

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abstract = "This paper addresses the problem of verifying stability of the interconnection of integral input-to-state stable (iISS) systems. This paper strengthens a Lyapunov approach to the problem to the point where the necessity of a small-gain condition holds without technical assumptions such as uniformity and analyticity required by previous work. This paper unifies the treatment of iISS and input-to-state stable (ISS) systems, which has not been achieved by any previous technique of constructing Lyapunov functions. It is shown that iISS systems and ISS systems can share a common form of Lyapunov functions to characterize stability of their interconnection with respect to external signals. Global asymptotic stability is also discussed.",

author = "Hiroshi Ito and Jiang, {Zhong Ping}",

year = "2008",

doi = "10.1109/ACC.2008.4586834",

language = "English (US)",

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AB - This paper addresses the problem of verifying stability of the interconnection of integral input-to-state stable (iISS) systems. This paper strengthens a Lyapunov approach to the problem to the point where the necessity of a small-gain condition holds without technical assumptions such as uniformity and analyticity required by previous work. This paper unifies the treatment of iISS and input-to-state stable (ISS) systems, which has not been achieved by any previous technique of constructing Lyapunov functions. It is shown that iISS systems and ISS systems can share a common form of Lyapunov functions to characterize stability of their interconnection with respect to external signals. Global asymptotic stability is also discussed.

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T2 - 2008 American Control Conference, ACC

Y2 - 11 June 2008 through 13 June 2008

ER -

Small-gain conditions and lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption

Abstract

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