In the context of gene regulatory networks, a negative feedback loop is modelled by N-coupled ordinary differential equations, highly non-linear due to Hill functions. This classic dynamical system properly captures the two main biological behaviours arising from this type of recurrent network motif: homeostasis under global stability of the unique fixed point, and biochemical oscillations otherwise. Various diseases may appear in case of homeostasis disruption. In this context, a quantized control strategy is designed in order to remove the undesirable oscillations emerging from such a disorder. For this purpose, the expression of one gene is either amplified or reduced in the controlled system [1]. The piecewise constant nature of the control law is adapted to control techniques commonly used in biotechnology [3] and biological constraints such as qualitative nature of the measurements. Under appropriate conditions on the control law, global convergence towards the fixed point is achieved through successive repulsive regions of the state space and a final sliding mode. In case of uncertain and more realistic measurements, the control strategy is slightly modified in order to highlight an adjustable zone of convergence around the fixed point. These two results are illustrated with a specific synthetic biological oscillator: the Repressilator [2].