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

Hiroshi Ito, Zhong-Ping Jiang

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publication2008 American Control Conference, ACC
Pages2297-2303
Number of pages7
DOIs
StatePublished - 2008
Event2008 American Control Conference, ACC - Seattle, WA, United States
Duration: Jun 11 2008Jun 13 2008

Other

Other2008 American Control Conference, ACC
CountryUnited States
CitySeattle, WA
Period6/11/086/13/08

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Lyapunov functions
Asymptotic stability

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Small-gain conditions and lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption. / Ito, Hiroshi; Jiang, Zhong-Ping.

2008 American Control Conference, ACC. 2008. p. 2297-2303 4586834.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ito, H & Jiang, Z-P 2008, Small-gain conditions and lyapunov functions applicable equally to iISS and ISS systems without uniformity assumption. in 2008 American Control Conference, ACC., 4586834, 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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