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In this paper, we propose a novel way to study the GPC closed-loop properties through its eigen polynomial. A coefficient mapping between the eigen polynomials of the plant and the closed-loop GPC system is firstly established. Conditions on the eigen coefficients to be zero are then derived in relationship with the tuning parameters. Based on these conditions, the closed-loop properties of GPC, such as reduced order, deadbeat control and stability are studied and conditions for tuning parameters are given.

GPC Analysis based on a Coefficient Mapping