On finite gain /spl Lscr//sub p/ stability of nonlinear sampled-data systems

Abstract

It is shown that uniform global exponential stability of the input-free discrete-time model of a globally Lipschitz sampled-data time-varying nonlinear system with inputs implies finite gain /spl Lscr//sub p/ stability of the sampled-data system for all p /spl isin/ [1, /spl infin/]. This result generalizes results on /spl Lscr//sub p/ stability of sampled-data linear systems and it is an important tool for analysis of robustness of sampled-data nonlinear systems with inputs.