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High hydrocarbon emissions during the cold start period is a wellrecognized challenge that has increasing importance in moving towards green vehicles. A model-based controller is a helpful way to reduce cold start hydrocarbon emissions. In our previous work, a model-based controller for a Spark-Ignition engine and an after-treatment system have been developed by using the balanced truncation technique. In this work, the objective was to determine whether balanced truncation surpasses the other model reduction methods. Guyan reduction was selected to compare with balanced truncation for reducing both a linear structural model and the linearized cold start model. An interpretation of the inner domain in Guyan reduction was determined for the linearized cold start model.