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A method of computing a new model predictive control (MPC) law for linear parameter varying systems with input constraints is proposed. The proposed method improves feasibility and system performance by deriving a new sufficient condition for the cost monotonicity. The control problem is formulated as a minimisation of the upper bound of finite horizon cost function satisfying the sufficient conditions. The relaxation matrices yield less conservative sufficient condition in terms of linear matrix inequalities so that it allows to design a more robust MPC. A numerical example is included to illustrate the effectiveness of the proposed method.