A sliding horizon control strategy proposed for discrete time-varying systems is examined in terms of its stability and robustness properties. It is found that, under the given conditions, the controller renders a discrete time-varying system exponentially stable in the large and the additive effect of a sector-type non-linearity can be tolerated to an extent depending on the design parameters. An easy-to-test stabilizability condition is presented. Dual results for a corresponding estimator are also given.