The paper deals with the problem of robust unknown input observer design for the neural-network based models of non-linear discrete-time systems. Authors review the recent development in the area of robust observers for non-linear discrete-time systems and proposes less restrictive procedure for design the H8 observer. The approach guaranties simultaneously the predefined disturbance attenuation level (with respect to state estimation error) and convergence of the observer. The main advantage of the design procedure is its simplicity. The paper presents an unknown input observer design that reduced to a set of linear matrix inequalities. The final part of the paper presents an illustrative example concerning wind turbine.