Power-electronic inverters are becoming popular for various industrial drives applications. In recent years also high-power and medium-voltage drive applications have been installed. However, the existing solutions suffer from some important drawbacks. Hybrid asymmetric multi-level inverters promise significant improvements for medium-voltage applications. This dissertation investigates such a hybrid inverter. To simplify the topology, some inverter parts are deprived of their feeding from the net and can only supply reactive power. The non-supplied intermediate-circuit capacitor voltages are inherently unstable and require a suitable control method for converter operation, preferably without influence on the load. Apart from normal operation, also converter start-up is an issue to consider, for which it is desirable to limit additional equipment. In this dissertation, we investigate the behaviour of this new inverter, and develop methods to obtain its reliable operation for the considered applications. These methods include modulation, voltage stabilization and start-up. We establish suitable models for their foundation. The principle achievement of this work is the development of a control method to stabilize a multitude of capacitor voltages which have no equilibrium state. Power balancing is performed by varying the common-mode output voltage, using a non-linear model-predictive controller. This method, which is new to power electronics, is applied to our hybrid asymmetric nine-level inverter driving an asynchronous motor. Computer simulations and measurements on an experimental drive system demonstrate stable behaviour in steady-state and during transients over the whole operating range. The obtained results prove the possible implementation of such a complex control algorithm for fast real-time operation. As second important accomplishment, this thesis proposes a start-up method that charges the non-supplied intermediate-circuit capacitors in parallel with the supplied ones, without additional equipment. Measurements show its successful application in the investigated drive system.