Design of an L-2-gain disturbance rejection neural controller for nonlinear systems is presented. The control input is generated from a radial basis network, which is trained offline such that a computed partial derivative of the network output satisfies a Hamilton-Jacobi inequality. Once the network is successfully trained for a given manifold in the state space, the closed-loop system ensures a finite gain between the system disturbance and the system input-output as long as the system states remain within the state manifold. The proposed method may also be applied to obtain an H-infinity controller.