A lyapunov function for interconnected ISS systems derived from dissipation inequalities

Hiroshi Ito, Zhong-Ping Jiang

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages4465-4470
Number of pages6
DOIs
StatePublished - 2007
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Other

Other46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

Fingerprint

Lyapunov functions
Large scale systems
Nonlinear systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety

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). [4434199] 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. 2007. p. 4465-4470 4434199.

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

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., 4434199, 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
Ito H, Jiang Z-P. A lyapunov function for interconnected ISS systems derived from dissipation inequalities. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. 2007. p. 4465-4470. 4434199 https://doi.org/10.1109/CDC.2007.4434199
Ito, Hiroshi ; Jiang, Zhong-Ping. / A lyapunov function for interconnected ISS systems derived from dissipation inequalities. Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. 2007. pp. 4465-4470
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