  This paper deals with the problem of predicting the future state of
discrete-time input-delayed systems in the presence of unknown disturbances
that can affect both the state and the output equations of the plant. Since the
disturbance is unknown, computing an exact prediction of the future plant
states is not possible. To circumvent this problem, we propose using a
high-order extended Luenberger-type observer for the plant states,
disturbances, and their finite difference variables, combined with a new
equation for computing the prediction based on Newton's series from the
calculus of finite differences. Detailed performance analysis is carried out to
show that, under certain assumptions, both enhanced prediction and improved
attenuation of the unknown disturbances are achieved. Linear matrix
inequalities (LMIs) are employed for the observer design to minimize the
prediction errors. A stabilization procedure based on an iterative design
algorithm is also presented for the case where the plant is affected by
time-varying uncertainties. Examples from the literature illustrate the
advantages of the scheme.
