Robust stability of networks of iISS systems: Construction of sum-type Lyapunov functions

Hiroshi Ito; Zhong Ping Jiang; Sergey N. Dashkovskiy; Björn S. R̈uffer

doi:10.1109/TAC.2012.2231552

Robust stability of networks of iISS systems: Construction of sum-type Lyapunov functions

Hiroshi Ito, Zhong Ping Jiang, Sergey N. Dashkovskiy, Björn S. R̈uffer

Electrical and Computer Engineering

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

Abstract

This paper gives a solution to the problem of verifying stability of networks consisting of integral input-to-state stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnections of two subsystems. For large-scale systems, stability criteria relying only on gain-type information that were previously developed address only input-to-state stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of a sum of nonlinearly rescaled individual Lyapunov functions of subsystems under an appropriate small-gain condition.

Original language	English (US)
Pages (from-to)	1192-1207
Number of pages	16
Journal	IEEE Transactions on Automatic Control
Volume	58
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2012.2231552
State	Published - May 2013

Keywords

Integral input-to-state stability (iISS)
Large-scale systems
Lyapunov functions
Nonlinear systems
Robust stability criteria

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2012.2231552

Cite this

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title = "Robust stability of networks of iISS systems: Construction of sum-type Lyapunov functions",

abstract = "This paper gives a solution to the problem of verifying stability of networks consisting of integral input-to-state stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnections of two subsystems. For large-scale systems, stability criteria relying only on gain-type information that were previously developed address only input-to-state stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of a sum of nonlinearly rescaled individual Lyapunov functions of subsystems under an appropriate small-gain condition.",

keywords = "Integral input-to-state stability (iISS), Large-scale systems, Lyapunov functions, Nonlinear systems, Robust stability criteria",

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T2 - Construction of sum-type Lyapunov functions

AU - Ito, Hiroshi

AU - Jiang, Zhong Ping

AU - Dashkovskiy, Sergey N.

AU - R̈uffer, Björn S.

PY - 2013/5

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AB - This paper gives a solution to the problem of verifying stability of networks consisting of integral input-to-state stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnections of two subsystems. For large-scale systems, stability criteria relying only on gain-type information that were previously developed address only input-to-state stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of a sum of nonlinearly rescaled individual Lyapunov functions of subsystems under an appropriate small-gain condition.

KW - Integral input-to-state stability (iISS)

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KW - Lyapunov functions

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Robust stability of networks of iISS systems: Construction of sum-type Lyapunov functions

Abstract

Keywords

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