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In this paper, a stability theorem of nonlinear fractional-order differential equations is proven theoretically by using the Gronwall-Bellman lemma. According to this theorem, the linear state feedback controller is introduced for stabilizing a class of nonlinear fractional-order systems. And, a new criterion is derived for designing the controller gains for stabilization, in which control parameters can be selected via the pole placement technique of the linear fractional-order control theory. Finally, the theoretical results are further substantiated by simulation results of the fractional-order chaotic Lorenz system with desired design requirements.