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

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publicationProceedings of the 2011 American Control Conference, ACC 2011
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1971-1977
Number of pages7
ISBN (Print)9781457700804
DOIs
StatePublished - 2011

Publication series

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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