Skip to Main content Skip to Navigation
New interface
Preprints, Working Papers, ...

The ISS framework for time-delay systems: a survey

Abstract : At the occasion of Eduardo D. Sontag's 70 th birthday, we provide here an overview of the tools available to study input-to-state stability (ISS) and related notions for time-delay systems. After a hopefully pedagogical presentation of the main differences with respect to the finite-dimensional theory, we review basic stability concepts for input-free time-delay systems, as well as instruments to guarantee them in practice, including the Lyapunov-Krasosvkii, Lyapunov-Razumikhin, and Halanay approaches. We then consider the influence of inputs through the notions of ISS, integral ISS, and input-to-output stability and provide both Lyapunov-like and solutions-based characterizations of these properties. We also show how these notions can be helpful for the stability analysis of interconnected systems, whether in cascade or in feedback form. We finally provide a list of questions which remain open until now.
Document type :
Preprints, Working Papers, ...
Complete list of metadata
Contributor : Antoine Chaillet Connect in order to contact the contributor
Submitted on : Wednesday, June 8, 2022 - 6:29:10 PM
Last modification on : Saturday, June 25, 2022 - 3:26:23 AM


Survey ISS TDS.pdf
Files produced by the author(s)


  • HAL Id : hal-03684326, version 1
  • ARXIV : 2206.06167


Antoine Chaillet, Iasson Karafyllis, Pierdomenico Pepe, Yuan Wang. The ISS framework for time-delay systems: a survey. 2022. ⟨hal-03684326⟩



Record views


Files downloads