In this paper, previously developed stability results for open-loop sum-capacitor-voltage control of modular multilevel converters are extended. To obtain improved damping, circulating-current feedback is included in the control law. A first-order measurement lag is added to this feedback. With these additions, global asymptotic stability is proven. Careful consideration of the online control-law computation is given, since this is the most critical part of the control system. Experimental results verify the theory.