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This paper investigates a robust model predictive control approach for a nonlinear aerodynamic test rig, a twin rotor multi-input-multi-output system (TRMS). A highly nonlinear dynamic model of the system has been used to design the robust controller. According to the nonlinear model a polytopic model has been developed considering the nonlinearities and uncertainties of the plant. To this end, a subset of polytopic model is extracted to cover the necessary dynamics of the system in order to make the optimisation problem more feasible. In other words, the subset of polytopic model mitigates the stringent conditions imposed due to robustness. However, some additional conditions on inputs, outputs and states may need to be imposed in order to prevent any violation from the polytope. When the control system is infeasible, the polytope is redesigned and a new optimisation problem is formulated, accordingly. The robust model predictive control approach based on linear matrix inequalities has been used as a regulator in this study. The responses of the control system show the efficacy and feasibility of the proposed control technique.