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A finite horizon model predictive control (MPC) algorithm that is robust to modelling uncertainties is developed along with the construction of a moving average system matrix to capture modelling uncertainties and facilitate the future output prediction. The authors' main focus is on the step tracking problem. Using linear matrix inequality techniques, the design is converted into a semi-definite optimisation problem. Closed-loop stability, known to be one of the most challenging topics in finite horizon MPC, is treated by adding extra terminal cost constraints in the semi-definite optimisation. A simulation example demonstrates that the approach can be useful for practical applications.