A lyapunov function for interconnected ISS systems derived from dissipation inequalities

Hiroshi Ito; Zhong Ping Jiang

doi:10.1109/CDC.2007.4434199

A lyapunov function for interconnected ISS systems derived from dissipation inequalities

Hiroshi Ito, Zhong Ping Jiang

Electrical and Computer Engineering

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

Abstract

This paper addresses the problem of establishing stability of interconnected nonlinear systems consisting of individually input-to-state stable (ISS) subsystems. This paper aims to extend the capability of the ISS small-gain technique with emphasis on Lyapunov functions and necessity. This paper derives an explicit formula for constructing Lyapunov functions characterizing ISS property of interconnected systems from dissipation inequalities of subsystems. This paper focuses on the case where nonlinear loop gain approaches unity asymptotically as magnitude of signals tends to zero and infinity. The new formula of Lyapunov functions deals with the non-uniform contraction of loop gain and covers one of authors' previous developments as a special case. The Lyapunov functions obtained here are differentiable. The formulation based on dissipation inequalities also allows us to prove the necessity of the small-gain condition without making a technical assumption of uniformity.

Original language	English (US)
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4465-4470
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434199
State	Published - 2007
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: Dec 12 2007 → Dec 14 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 12/14/07

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/CDC.2007.4434199

Cite this

Ito, H., & Jiang, Z. P. (2007). A lyapunov function for interconnected ISS systems derived from dissipation inequalities. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 4465-4470). Article 4434199 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434199

A lyapunov function for interconnected ISS systems derived from dissipation inequalities. / Ito, Hiroshi; Jiang, Zhong Ping.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 4465-4470 4434199 (Proceedings of the IEEE Conference on Decision and Control).

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

Ito, H & Jiang, ZP 2007, A lyapunov function for interconnected ISS systems derived from dissipation inequalities. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434199, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4465-4470, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434199

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A lyapunov function for interconnected ISS systems derived from dissipation inequalities

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