Relation between Exponential Stability and Input-to-State Stability of Time-Delay Systems

The main contribution of this paper is to establish a link between the exponential stability of an unforced system and the input-to-state stability (ISS) via the Lyapunov-Krasovskii methodology. A new theorem is provided, which proves that an unforced system whose trivial solution is exponentially stable is input-to-state stable if submitted to a perturbation which can be of an arbitrary size.