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This paper is concerned with an iterative linear matrix inequality (LMI) approach to the design of a structurally constrained output feedback controller such as decentralized control. The structured synthesis is formulated as a novel rank-constrained LMI optimization problem, where the controller parameters are explicitly described so as to impose structural constraints on the parameter matrices. An iterative penalty method is discussed to solve the rank-constrained LMI problem. Numerical experiments and comparisons with previous works are performed to illustrate the practicality of the proposed method.