The class of nonlinear systems described by a discrete-time state-equation containing a repeated scalar nonlinearity as in recurrent neural networks is considered, Given a plant of this form, sufficient conditions are derived for: 1) the parameterization of all controllers of the same farm such that the closed loop is stable In the sense of a diagonally dominant Lyapunov function and 2) the synthesis of a controller of the same form so that the induced norm of the closed loop is under a prescribed level. Several of these conditions can be written into linear matrix inequalities.