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Foil-air bearings have presented their advantageous performance due to their different structures when compared to traditional air bearings. However, it is the nonlinear characteristic of this kind of bearing that has drawn studies on dynamic response of the rotor-bearing system, especially rotor stability. In this paper, an improved foil dynamic model with internal bending moment included has been proposed to determine the nominal stiffness of the foil structure. Based on that, the nominal stiffness of the foil structure has been investigated with different geometry parameters of the foil structure. By such means, the stability of the rotor-bearings system has been theoretically studied through an equation system in a common turbocharger structure. The results can be effectively used for designing and suitably selecting some geometry parameters of foil-air bearings to have a good rotor performance in this case.