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

Chris Guiver, Hartmut Logemann

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)


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
Pages (from-to)375-398
Number of pages24
JournalMathematics of Control, Signals, and Systems
Issue number2
Early online date31 Jan 2023
Publication statusPublished - 30 Jun 2023

Bibliographical note

Funding Information:
We are grateful to three anonymous reviewers, and Prof. Matthew Turner, whose constructive and insightful comments have helped to improve the work. Chris Guiver’s contribution to this work has been partially supported by a Personal Research Fellowship from the Royal Society of Edinburgh (RSE). Chris Guiver expresses gratitude to the RSE for their support.


  • 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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