A new small-gain theorem with an application to the stabilization of the chemostat

Iasson Karafyllis, Zhong Ping Jiang

Research output: Contribution to journalArticlepeer-review


New small-gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous small-gain results usually utilize to prove stability properties. The results allow the application of the small-gain perspective to various systems that satisfy less-demanding stability notions than the input-to-output stability property. The robust global feedback stabilization problem of an uncertain time-delayed chemostat model is solved by means of the new small-gain results.

Original languageEnglish (US)
Pages (from-to)1602-1630
Number of pages29
JournalInternational Journal of Robust and Nonlinear Control
Issue number14
StatePublished - Sep 25 2012


  • chemostat models
  • feedback systems
  • input-to-output stability
  • small-gain theorem

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Chemical Engineering
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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