Input-to-state stabilization for nonlinear sample-data systems via approximate discrete-time plant models

We provide a framework for the design of L? stabilizing controllers via approximate discrete-time models for sampled-data nonlinear systems with disturbances. In particular, we present sufficient conditions that guarantee that a discrete-time controller that input-to-state stabilizes an approximate discrete-time model of a nonlinear continuous-time plant with disturbances would also input-to-state stabilize (in an appropriate sense) the exact discrete-time plant mode