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An adaptive H infin controller is designed for a class of non-linear dynamical systems by using neural networks (NNs) to approximate the unknown system function. It is shown that under bounded initial conditions, the H infin performance from the external disturbance to the controlled output is achieved with a prescribed attenuation level. A systematic design procedure is then developed for the synthesis of the adaptive H infin controller by solving two linear matrix inequalities (LMIs). Finally, a numerical example is included to demonstrate the effectiveness of the proposed controller.