Input-to-State Stability of Nonlinear Functional Systems *

The notion of input-to-state stability, given by Sontag in 1989, has had a great impact in the analysis and control of finite dimensional systems described by ordinary differential equations. In the last ten years, the same notion has been investigated for nonlinear functional systems, that is for systems described by retarded functional differential equations, neutral functional differential equations, functional difference equations. In this plenary talk, a summary of the results concerning the Lyapunov-Krasovskii characterization of the input-to-state stability property is reported. New results concerning the Lyapunov-Krasovskii characterization of the input-to-state stability property, for systems described by functional difference equations, are also shown.