Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations

Given a parameterized (by sampling period T ) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally-practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controls is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally-practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.