A Lyapunov-Krasovskii methodology. for ISS of time-delay systems

This paper presents a Lyapunov-Krasovskii methodology for studying the input-to-state stability of non-linear time-delay systems. The methodology is feasible by the use, for instance, of the M-2 norm (that is the norm induced by the inner product in the Hilbert space known in literature as M-2, or Z) in the space of continuous functions, and by the use of functionals which have a suitable (simple) integral term with strictly increasing kernel. The proposed results can be seen as a preliminary step towards extending some existing stability criteria to nonlinear time-delay systems with disturbance inputs.