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This work investigates a stabilizing control law for a plant with not necessarily known nonlinearities under the assumption that the dynamics of the system are slow relative to the sample period. Here we treat the coefficients of an affine model of the dynamics as unknown parameters. It is shown that it is feasible to construct an adaptive control law provided that the plant is pointwise stabilizable. We investigate the general applicability of this technique by quantifying the restrictions required for closed loop stability of the adaptive system.