A small-gain theorem for a wide class of feedback systems with control applications

Iasson Karafyllis, Zhong Ping Jiang

Research output: Contribution to journalArticle


A small-gain theorem, which can be applied to a wide class of systems that includes systems satisfying the weak semigroup property, is presented in the present work. The result generalizes all existing results in the literature and exploits notions of weighted, uniform, and nonuniform input-to-output stability properties. Applications to partial state feedback stabilization problems with sampled-data feedback applied with zero order hold and positive sampling rate are also presented.

Original languageEnglish (US)
Pages (from-to)1483-1517
Number of pages35
JournalSIAM Journal on Control and Optimization
Issue number4
StatePublished - Dec 1 2007



  • Control systems
  • Input-to-output stability
  • Small-gain theorem

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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