In this paper, a discontinuous dynamic state feedback that robustly stabilizes affine in control uncertain non-linear systems is proposed. The formulation is based on Hamilton-Jacobi-Isaacs partial differential equations with two boundary conditions. The resulting dynamic state feedback is then expressed in terms of the solution of the related PDEs. An interesting feature is that the internal state of the resulting dynamic state feedback may have discontinuous behaviour as a function of time. The proposed scheme is illustrated through the example of the stabilization of the angular velocities of a rigid body under two actuators.