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
Pages1971-1977
Number of pages7
StatePublished - 2011
Event2011 American Control Conference, ACC 2011 - San Francisco, CA, United States
Duration: Jun 29 2011Jul 1 2011

Other

Other2011 American Control Conference, ACC 2011
CountryUnited States
CitySan Francisco, CA
Period6/29/117/1/11

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Lyapunov functions
Stability criteria
Large scale systems

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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). [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.; Ruffer, Björn S.

Proceedings of the 2011 American Control Conference, ACC 2011. 2011. p. 1971-1977 5991069.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ito, H, Jiang, Z-P, 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, pp. 1971-1977, 2011 American Control Conference, ACC 2011, San Francisco, CA, United States, 6/29/11.
Ito H, Jiang Z-P, 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. 2011. p. 1971-1977. 5991069
Ito, Hiroshi ; Jiang, Zhong-Ping ; Dashkovskiy, Sergey N. ; Ruffer, Björn S. / A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems. Proceedings of the 2011 American Control Conference, ACC 2011. 2011. pp. 1971-1977
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