Nonlinear small-gain theorems for discrete-time large-scale systems

Zhongping Jiang; Yuandan Lin; Yuan Wang

doi:10.1109/CHICC.2008.4605053

Nonlinear small-gain theorems for discrete-time large-scale systems

Zhongping Jiang, Yuandan Lin, Yuan Wang

Electrical and Computer Engineering

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

Abstract

In this work, we present generalizations of the nonlinear ISS small-gain theorem for discrete-time large-scale systems consisting of multiple subsystems, in a general setting of input-to-output stability. In other words, these discrete-time, large-scale small-gain theorems are established in terms of several types of gain functions, such as asymptotic gains, gains in decay estimations of the output functions, and Lyapunov gains. As a result, the set of cyclic small-gain conditions recovers the case of previously developed small-gain theorems either for an interconnected system comprised of two subsystems, or a network of ISS systems.

Original language	English (US)
Title of host publication	Proceedings of the 27th Chinese Control Conference, CCC
Pages	704-708
Number of pages	5
DOIs	https://doi.org/10.1109/CHICC.2008.4605053
State	Published - 2008
Event	27th Chinese Control Conference, CCC - Kunming, Yunnan, China Duration: Jul 16 2008 → Jul 18 2008

Publication series

Name	Proceedings of the 27th Chinese Control Conference, CCC

Other

Other	27th Chinese Control Conference, CCC
Country	China
City	Kunming, Yunnan
Period	7/16/08 → 7/18/08

Keywords

Discrete-time systems
IOS
ISS ("input-to-state stability")
Large-scale systems
Nonlinear small-gain

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.1109/CHICC.2008.4605053

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Cite this

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title = "Nonlinear small-gain theorems for discrete-time large-scale systems",

abstract = "In this work, we present generalizations of the nonlinear ISS small-gain theorem for discrete-time large-scale systems consisting of multiple subsystems, in a general setting of input-to-output stability. In other words, these discrete-time, large-scale small-gain theorems are established in terms of several types of gain functions, such as asymptotic gains, gains in decay estimations of the output functions, and Lyapunov gains. As a result, the set of cyclic small-gain conditions recovers the case of previously developed small-gain theorems either for an interconnected system comprised of two subsystems, or a network of ISS systems.",

keywords = "Discrete-time systems, IOS, ISS ({"}input-to-state stability{"}), Large-scale systems, Nonlinear small-gain",

author = "Zhongping Jiang and Yuandan Lin and Yuan Wang",

year = "2008",

doi = "10.1109/CHICC.2008.4605053",

language = "English (US)",

isbn = "9787900719706",

series = "Proceedings of the 27th Chinese Control Conference, CCC",

pages = "704--708",

booktitle = "Proceedings of the 27th Chinese Control Conference, CCC",

note = "27th Chinese Control Conference, CCC ; Conference date: 16-07-2008 Through 18-07-2008",

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TY - GEN

T1 - Nonlinear small-gain theorems for discrete-time large-scale systems

AU - Jiang, Zhongping

AU - Lin, Yuandan

AU - Wang, Yuan

PY - 2008

Y1 - 2008

N2 - In this work, we present generalizations of the nonlinear ISS small-gain theorem for discrete-time large-scale systems consisting of multiple subsystems, in a general setting of input-to-output stability. In other words, these discrete-time, large-scale small-gain theorems are established in terms of several types of gain functions, such as asymptotic gains, gains in decay estimations of the output functions, and Lyapunov gains. As a result, the set of cyclic small-gain conditions recovers the case of previously developed small-gain theorems either for an interconnected system comprised of two subsystems, or a network of ISS systems.

AB - In this work, we present generalizations of the nonlinear ISS small-gain theorem for discrete-time large-scale systems consisting of multiple subsystems, in a general setting of input-to-output stability. In other words, these discrete-time, large-scale small-gain theorems are established in terms of several types of gain functions, such as asymptotic gains, gains in decay estimations of the output functions, and Lyapunov gains. As a result, the set of cyclic small-gain conditions recovers the case of previously developed small-gain theorems either for an interconnected system comprised of two subsystems, or a network of ISS systems.

KW - Discrete-time systems

KW - IOS

KW - ISS ("input-to-state stability")

KW - Large-scale systems

KW - Nonlinear small-gain

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DO - 10.1109/CHICC.2008.4605053

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T3 - Proceedings of the 27th Chinese Control Conference, CCC

SP - 704

EP - 708

BT - Proceedings of the 27th Chinese Control Conference, CCC

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