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Model-based Predictive Control (MPC) algorithms popularity grows steadily in industry and academic area as well. Control actions are computed as an optimization problem. Future controlled system behaviour is taken into account - predicted over some horizon. Different methods and mathematical apparatus are utilized to get prediction equations. Diophantine equations and their recursive solving are very neat methods. On the other hand to compute predictions by matrix operations in state-space is easily to program. Paper is focussed on another insightful and compact method based on input-output process model representation and taking advantage of Toeplitz/Hankel matrix algebra.