This paper concerns the designing of the robust asymptotic state observer f
or the class of unknown nonlinear systems. The Luenberger-type observer is
suggested to be extended in two ways: first, the unknown nonlinear dynamics
is estimated by a dynamic neural network; second, the time delay term is a
dded to compensate the arising differential effects in the Luenberger obser
ver. The Lyapunov-Krasovskii technique is used to prove the robust asymptot
ic stability 'on average' of the neuro observer as well as the boundness of
the observation error. Two examples dealing with the Van Der Pol oscillati
ons and the single-link robot rotation are reported to demonstrate numerica
lly the effectiveness of the suggested approach. Copyright (C) 2000 John Wi
ley & Sons, Ltd.