On finite gain ℒp stability of nonlinear sampled-data systems

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 L_p stability of the sampled-data system for all p ∈ [1, ∞]. This result generalizes results on L_p stability of sampled-data linear systems and it is an important tool for analysis of robustness of sampled-data nonlinear systems with inputs.