Discrete time recurrent neural network observer

State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with the state observation problem when the dynamic model of a plant contains uncertainties or is completely unknown and it is oriented to discrete time nonlinear systems because most of the existent results have been developed for continous time systems. The recurrent neural network (RNN) have shown his advantages to deal with this class problem. The Lyapunov second method is applied to generate a new learning law, containing an adaptive adjustment rate, implying the stability condition for the free parameters of the neural-observer. A numerical example is given using the RNN in the estimation of a mathematical model of HIV infection with three states.