The ISS framework for time-delay systems: a survey

At the occasion of Eduardo D. Sontag’s 70th birthday, we provide here an overview tools available to study input-to-state stability (ISS) and related notions for time-delay systems. After a hopefully pedagogical presentation main differences with respect finite-dimensional theory, review basic concepts input-free systems, as well instruments guarantee them in practice, including Lyapunov–Krasovskii, Lyapunov–Razumikhin, Halanay approaches. We then consider influence inputs through ISS, integral input-to-output both Lyapunov-like solutions-based characterizations these properties. also show how can be helpful analysis interconnected whether cascade or feedback form. finally list questions which remain open until now.