This paper presents a new switching-cycle state-space model of the modular multilevel converter (MMC), on the basis of which unused switching states of this converter are explored and a corresponding new control method is proposed. This paper begins with a comprehensive summary and analysis on the prior-art modeling approaches of the MMC, where various models used for the MMC are discussed, and their limits in controlling the converter are shown. This is followed by the complete derivation of the proposed state-space switching model, whose mathematical derivation leverages simply on state variable transformations and Kirchhoff's voltage law without losing any circuital characteristics of the converter. As a result, all the possible switching states-many of those not previously used-and operating modes of the converter are effectively unveiled. With it, a switching-cycle control approach is proposed taking advantage of the developed state-space switching model. The new control scheme can greatly reduce the cell capacitance and arm inductance value, as well as enable the MMC to operate at any ac terminal frequency without affecting the voltage ripple of its capacitors. Simulation results are shown to validate the converter operations using the new control scheme.