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This paper deals with the problem of predicting the future state ofdiscrete-time input-delayed systems in the presence of unknown disturbancesthat can affect both the state and the output equations of the plant. Since thedisturbance is unknown, computing an exact prediction of the future plantstates is not possible. To circumvent this problem, we propose using ahigh-order extended Luenberger-type observer for the plant states,disturbances, and their finite difference variables, combined with a newequation for computing the prediction based on Newton's series from thecalculus of finite differences. Detailed performance analysis is carried out toshow that, under certain assumptions, both enhanced prediction and improvedattenuation of the unknown disturbances are achieved. Linear matrixinequalities (LMIs) are employed for the observer design to minimize theprediction errors. A stabilization procedure based on an iterative designalgorithm is also presented for the case where the plant is affected bytime-varying uncertainties. Examples from the literature illustrate theadvantages of the scheme.

Newton-series-based observer-predictor control for disturbed input-delayed discrete-time systems