In contrast to conventional and classical hybrid electric transmissions, multimode (hybrid electric) transmissions open new perspectives in gear shifting: The tradeoff between avoidance of propulsion torque interruption and dissipation in clutches can be resolved by smart utilization of the second, coequal, propulsion element, and rearrangement of standard shift phases (torque phase and inertia phase). The resulting smooth and lossless gear shifts reach a new level of performance combining comfort and efficiency. Therefore, modeling and control of these gear shifts is an ongoing automotive research topic since several years. However, so far there is no systematic, model-based approach, which would enable broad application in industry. This paper contributes to bridge this gap. The key point is a systematic determination of a consistent set of generalized coordinates, corresponding to a specific gear, i.e., set of locked clutches. This is achieved by exploiting the mechanical peculiarities of drivetrain topologies. Based on this, a straightforward transformation is proposed to derive a comprehensive state-space model for each gear of a given topology. This enables the statement of the control problem for smooth and lossless gear shifting in a novel compact and general form. Finally, a new shift procedure and a generic-model-based feedforward control is proposed and applied to an exemplary multimode transmission. Promising first simulation results confirm the significance of the proposed approach for further investigation and application.