The note presents an \(H_\infty\) control design approach by neural networks (NN). The nonlinear state space models are parametrized by multilayer perceptrons. Then a linear differential inclusion state representation for such a class of multilayer NN is established. Based on this representation, a linear state feedback control is considered. The control design equations are characterized in the form of a set of linear matrix inequalities which allow for the application of convex optimization algorithms. The method is applied to, in a sense, an academic example mimicking a real situation only in a very indirect way. Nevertheless, the realization of the method can suprisingly be implemented on the very elementary level of very simple perceptrons in such a case.