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This brief addresses the model order reduction problem for linear time invariant (LTI) systems. The problem is to minimize the H infin norm of the error between the original system and the reduced system, which is known to be a nonconvex optimization problem. Based on this, the brief proposes a convex suboptimal solution which is expressed in terms of linear matrix inequalities (LMIs). The performance of the proposed method is assessed through application to several large order systems and compared with the well-known Hankel Norm model order reduction method.