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 nonlinear time-delay systems. The methodology is feasible by the use, for instance, of the M2norm (that is the norm induced by the inner product in the Hilbert space known in literature as M2, 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.