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This paper presents an iterative penalty function method for solving rank-constrained linear matrix inequality (LMI) problems and illustrates its application to reduced-order output feedback stabilization. We propose a penalized objective function to replace the rank condition, so that a solution to the original nonconvex LMI feasibility problem can be obtained by solving a series of convex LMI optimization subproblems. Numerical experiments were performed to demonstrate the proposed method.