In this paper, previously developed stability results for open-loop sum-capacitor-voltage control of modular multilevel converters are extended. To give improved damping, circulating-current feedback is included in the control law. With the output-current control loop and a first-order measurement lag taken into account, global asymptotic stability is proven. Careful consideration of the on-line sum-capacitor-voltage reference computation is given, since this is the most critical part of the control system.