This paper has received mostly positive reviews, although some reviewers pointed out some limitations regarding the controllability of the dynamics and the strength of the comparator class. The author response added some further confusion about the latter issue, direct correspondence with the authors cleared up the misunderstanding. In light of this discussion, it is now clear that the comparator class is rich enough to make the results significant enough to warrant publication. For the final version, the authors are strongly urged to add a detailed discussion about the comparator class that the results actually hold against, and also to emphasize the role of the controllability assumption in their analysis and highlight works that consider weaker assumptions (e.g., stabilizability).