The modeling of high-order converter systems and design of their closed-loop controllers are difficult due to their high nonlinearity, hence high-order systems, large number of zero-poles, and complex frequency-domain characteristics. To ease the design methodologies, this paper studies high-order power converters and proposes a modeling and control method for such converter systems with order reduction. As an example, the 7th-order non-electrolytic capacitor-I-Z-Source converter (NEC-I-ZSC) is employed to implement the proposed design method. Operational analysis and small signal modeling of the NEC-I-ZSC are conducted, and a reduced-order controller is then devised. Experimental verification is conducted, which prove the feasibility and effectiveness of the proposed design method.