A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems

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

doi:10.1109/acc.2011.5991069

A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems

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

Electrical and Computer Engineering

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

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 interconnection of two subsystems. For large-scale systems, stability criteria relying only on gain-type information have been successful only in dealing with input-to-state stable 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 nonlinear sum of individual Lyapunov functions of subsystems given in a dissipation formulation under an appropriate small-gain condition.

Original language	English (US)
Title of host publication	Proceedings of the 2011 American Control Conference, ACC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1971-1977
Number of pages	7
ISBN (Print)	9781457700804
DOIs	https://doi.org/10.1109/acc.2011.5991069
State	Published - 2011

Publication series

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

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/acc.2011.5991069

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Ito, H., Jiang, Z. P., Dashkovskiy, S. N., & Ruffer, B. S. (2011). A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems. In Proceedings of the 2011 American Control Conference, ACC 2011 (pp. 1971-1977). Article 5991069 (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2011.5991069

A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems. / Ito, Hiroshi; Jiang, Zhong Ping; Dashkovskiy, Sergey N. et al.
Proceedings of the 2011 American Control Conference, ACC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 1971-1977 5991069 (Proceedings of the American Control Conference).

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

Ito, H, Jiang, ZP, Dashkovskiy, SN & Ruffer, BS 2011, A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems. in Proceedings of the 2011 American Control Conference, ACC 2011., 5991069, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1971-1977. https://doi.org/10.1109/acc.2011.5991069

Ito H, Jiang ZP, Dashkovskiy SN, Ruffer BS. A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems. In Proceedings of the 2011 American Control Conference, ACC 2011. Institute of Electrical and Electronics Engineers Inc. 2011. p. 1971-1977. 5991069. (Proceedings of the American Control Conference). doi: 10.1109/acc.2011.5991069

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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 interconnection of two subsystems. For large-scale systems, stability criteria relying only on gain-type information have been successful only in dealing with input-to-state stable 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 nonlinear sum of individual Lyapunov functions of subsystems given in a dissipation formulation under an appropriate small-gain condition.

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A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems

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