Discrete-time models with state-dependent parameters are derived for non-linear sampled-data systems. Velocity-based linearization of the continuous-time system followed by integration over the sampling interval is used to represent the sampled-data system by a discrete-time state-space model with state-dependent parameters. By reconstructing the state a quasi-ARX model is obtained, the parameters of which are functions of past inputs and outputs. As the velocity-based linearization procedure does not involve suppression of higher-order terms, the state-dependent state-space model and the quasi-ARX description give exact representations of the non-linear system.