Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition

Hiroshi Ito, Pierdomenico Pepe, Zhong Ping Jiang

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

Abstract

This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain theorem for the interconnection of these components to assess the stability of the overall time-delay system. Both discrete and distributed delays can be involved in the dynamic and the static components. The result can be considered as a counterpart of the author's previous work which only deals with dynamic components. For the construction of Lyapunov-Krasovskii functionals, this paper introduces a new technique which differs from the one employed in the dynamic case.

Original languageEnglish (US)
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages1310-1316
Number of pages7
DOIs
StatePublished - 2009
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: Dec 15 2009Dec 18 2009

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period12/15/0912/18/09

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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    Ito, H., Pepe, P., & Jiang, Z. P. (2009). Construction of Lyapunov-Krasovskii functionals for interconnection of retarded dynamic and static systems via a small-gain condition. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 1310-1316). [5399840] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5399840