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A discrete-time time-varying smooth state feedback controller is presented for the set point control of non-holonomic chained systems. The control law drives the system state to zero with an exponential convergent rate without any assumption on the initial state and the sampling rate. Specifically, the discretised model is broken up into two subsystems, and the first control input is explicitly designed such that the second subsystem is transformed into a perturbed linear time-varying system by introducing a novel state transformation, for which classical linear control techniques can be easily adopted to drive the state to the origin. Simulation results are provided to validate the presented approach.