A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems

Zhong Ping Jiang; Iven M.Y. Mareels; Yuan Wang

doi:10.1016/0005-1098(96)00051-9

A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems

Zhong Ping Jiang, Iven M.Y. Mareels, Yuan Wang

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state-stable (ISS) systems. An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.

Original language	English (US)
Pages (from-to)	1211-1215
Number of pages	5
Journal	Automatica
Volume	32
Issue number	8
DOIs	https://doi.org/10.1016/0005-1098(96)00051-9
State	Published - Aug 1996

Keywords

Interconnected systems
Lyapunov function
Nonlinear gain
Stability

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

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10.1016/0005-1098(96)00051-9

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title = "A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems",

abstract = "The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state-stable (ISS) systems. An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.",

keywords = "Interconnected systems, Lyapunov function, Nonlinear gain, Stability",

author = "Jiang, {Zhong Ping} and Mareels, {Iven M.Y.} and Yuan Wang",

note = "Funding Information: Acknowledgements-Thew ork of Z.-P. Jiang and I. Mareels were supportedi n part by the fundingo f the activitieso f the CRC for Robust and Adaptive Systemsb y the Australian Government under the Cooperative Research Centers program.T he work of Y. Wang was supportedi n part by NSF Grants DMS-9457826a nd DMS-9403924.",

year = "1996",

month = aug,

doi = "10.1016/0005-1098(96)00051-9",

language = "English (US)",

volume = "32",

pages = "1211--1215",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier Ltd",

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TY - JOUR

T1 - A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems

AU - Jiang, Zhong Ping

AU - Mareels, Iven M.Y.

AU - Wang, Yuan

N1 - Funding Information: Acknowledgements-Thew ork of Z.-P. Jiang and I. Mareels were supportedi n part by the fundingo f the activitieso f the CRC for Robust and Adaptive Systemsb y the Australian Government under the Cooperative Research Centers program.T he work of Y. Wang was supportedi n part by NSF Grants DMS-9457826a nd DMS-9403924.

PY - 1996/8

Y1 - 1996/8

N2 - The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state-stable (ISS) systems. An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.

AB - The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear small-gain theorem for interconnected input/state-stable (ISS) systems. An ISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.

KW - Interconnected systems

KW - Lyapunov function

KW - Nonlinear gain

KW - Stability

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DO - 10.1016/0005-1098(96)00051-9

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SN - 0005-1098

VL - 32

SP - 1211

EP - 1215

JO - Automatica

JF - Automatica

IS - 8

ER -

A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems

Abstract

Keywords

ASJC Scopus subject areas

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