Discretization of a non-linear, exponentially stabilizing control law using an Lp-gain approach

Considers the input-output stability of exponentially stable, non-linear systems with sampled-data output. Results for linear systems are generalized showing that the Lp-gain with respect to the sampled-data output exists and converges to the Lp-gain associated with the continuous-time output when the sampling period approaches +0. The results are applied to a non-linear control configuration and compared to a Lyapunov function analysis based approach previously developed for a non-linear sliding-mode like control. In contrast to the Lyapunov function technique, the sampling-time constraint vanishes for a stable plant if no control is used.