Stability of nonlinear feedback systems: A new small-gain theorem

Anna L. Chen, Gui Qiang Chen, Randy A. Freeman

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


For the feedback interconnection of general nonlinear systems, the classical small-gain condition is sufficient but not necessary for robust stability. We introduce a weaker notion of gain which yields a small-gain condition that is both necessary and sufficient for robust stability. We also discuss conditions under which the two notions coincide, and we further provide results for dissipation performance measures that are more general than the classical gain measures.

Original languageEnglish (US)
Pages (from-to)1995-2012
Number of pages18
JournalSIAM Journal on Control and Optimization
Issue number6
StatePublished - 2007


  • Conditional gain
  • Dissipativity
  • Feedback connection
  • Nonlinear systems
  • Performance analysis
  • Small-gain theorem

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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