The exponential input-to-state stability property: characterisations and feedback connections

Chris Guiver, Hartmut Logemann

Research output: Contribution to journalArticlepeer-review


The exponential input-to-state stability (ISS) property is considered for systems of controlled nonlinear ordinary differential equations. A characterisation of this property is provided, including in terms of a so-called exponential ISS Lyapunov function and a natural concept of linear state/input-to-state L2-gain. Further, the feedback connection of two exponentially ISS systems is shown to be exponentially ISS provided a suitable small-gain condition is satisfied.

Original languageEnglish
JournalMathematics of Control, Signals, and Systems
Early online date31 Jan 2023
Publication statusE-pub ahead of print - 31 Jan 2023


  • Differential equation
  • Exponential input-to-state stability
  • Feedback connection
  • Global exponential stability
  • Robust stability
  • Small-gain condition

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Control and Optimization
  • Applied Mathematics


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