This paper presents a control algorithm that combines three valuable features in robust and non-linear control, namely modelling using neural networks, input-output feedback linearization and LMI-based robust controller design. In the first step of the algorithm an affine description of a feedforward neural network model is derived. By performing an input-output feedback (IOF) linearization an uncertainty description of the IOF linearized system is derived based on the parametric uncertainties of the affine model. Then the LMI-based robust controller is designed by means of an optimization procedure. A key step in this procedure is the derivation of a polytopic boundary for the state-space matrices of the IOF linearized system based on the estimated parameters of the neural network and their uncertainty bounds.