turkmath.org

Input-to-state stability (ISS) is a widely used tool to analyze the stability of nonlinear dynamical systems affected by external disturbances. The ISS property imposes that the dynamical system evolves properly in the absence of disturbances and it also preserves this nominal behavior up to a reasonable response to disturbances in the sense that small disturbances generate small steady-state errors. One of its most famous extensions is integral ISS (iISS), which relates the solutions' norm to the input energy, rather than its amplitude. In this talk, we will start reviewing the basics of the ISS framework. We will then present more recent extensions of these results to time-delay systems and underline the key differences with finite-dimensional systems. We will thereafter present our recent results on iISS Lyapunov characterizations of time-delay systems and on growth rate conditions to ensure iISS of time-delay systems in cascade. We will finally list some open questions about the Lyapunov ISS characterization of time-delay systems.