An approach is presented for the robust stabilization of non-linear systems. The proposed strategy can be adopted whenever it is possible to compute a control law that steers the state in finite time from any initial condition to a point closer to the desired equilibrium. Under suitable assumptions, such control law can be applied in an iterative fashion, obtaining uniform asymptotic stability of the equilibrium point, with exponential rate of convergence. Small non-persistent perturbations are rejected, while persistent perturbations induce limited errors. In order to show the usefulness of the presented theoretical developments, the approach is applied to chained-form systems and, for illustration, simulations results are given for the robust stabilization of a unicycle.