Starting from a data set consisting of input-output measurements of a dynamical process, this paper presents a training procedure for a specifically control-oriented model. The considered dynamic model adopts a particular neural state-space representation: its structure guarantees its linearizability by state feedback. Moreover, the linearizing control law follows trivially from the parameters of the learned model. The method relies on a parameterized continuous-time neural state-space model whose structure is inspired from well-known exact linearization. The feasibility and efficiency of the approach is illustrated on a nonlinear identification benchmark, namely the Silverbox one. The quality of learning and linearizing feature of the control design are validated on two nonlinear models by comparing the input-output behavior of each closed-loop and its best linear approximation.