Robust asymptotic neuro observer with time delay term

This paper concerns the development, of a robust asymptotic neuro observer (NN) for a class of unknown nonlinear systems with noise disturbances in the output. The suggested asymptotic observer has three basic terms: the first one is introduced to approximate the unknown nonlinear dynamics, the second one is related with the innovation (the standard correction term) and the last one is a time delayed term introduced especially to assure the approximation of the unmeasured state derivatives. The Lyapunov-Krasovskii technique is used to proof the robust asymptotic stability “on average” of the obtained estimation error. A special “dead-zone” multiplier is introduced into the learning procedure to guarantee the boundness of the weight matrices of the dynamic NN