On the design of a controller based on the discrete-time approximation of the nonlinear plant model

Care should be taken when designing controllers for sampled-data nonlinear systems using approximate discrete-time models, even in the case of fast sampling. Indeed, given a family of approximate discrete-time models for a sampled continuous-time nonlinear plant, where the family is parameterized by the sampling period T, and given a family of discrete-time controllers that globally asymptotically stabilizes the family of plant models for all T sufficiently small, the family of controllers may or may not semi-globally practically asymptotically stabilize the exact discrete-time model of the plant. We provide sufficient conditions that guarantee semi-global practical asymptotic stability for sampled-data nonlinear systems using controllers that asymptotically stabilize approximate discrete-time models.