Nonlinear small-gain theorems for discrete-time large-scale systems

Zhongping Jiang, Yuandan Lin, Yuan Wang

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


In this work, we present generalizations of the nonlinear ISS small-gain theorem for discrete-time large-scale systems consisting of multiple subsystems, in a general setting of input-to-output stability. In other words, these discrete-time, large-scale small-gain theorems are established in terms of several types of gain functions, such as asymptotic gains, gains in decay estimations of the output functions, and Lyapunov gains. As a result, the set of cyclic small-gain conditions recovers the case of previously developed small-gain theorems either for an interconnected system comprised of two subsystems, or a network of ISS systems.

Original languageEnglish (US)
Title of host publicationProceedings of the 27th Chinese Control Conference, CCC
Number of pages5
StatePublished - 2008
Event27th Chinese Control Conference, CCC - Kunming, Yunnan, China
Duration: Jul 16 2008Jul 18 2008

Publication series

NameProceedings of the 27th Chinese Control Conference, CCC


Other27th Chinese Control Conference, CCC
CityKunming, Yunnan


  • Discrete-time systems
  • IOS
  • ISS ("input-to-state stability")
  • Large-scale systems
  • Nonlinear small-gain

ASJC Scopus subject areas

  • Control and Systems Engineering


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