  We provide an amendment to the first theorem of "Control Contraction Metrics:
Convex and Intrinsic Criteria for Nonlinear Feedback Design" by Manchester &
Slotine in the form of an additional technical condition required to show
integrability of differential control signals. This technical condition is
shown to be satisfied under the original assumptions if the input matrix is
constant rank, and also if the strong conditions for a CCM hold. However a
simple counterexample shows that if the input matrix drops rank, then the
weaker conditions of the original theorem may not imply stabilizability of all
trajectories. The remaining claims and illustrative examples of the paper are
shown to remain valid with the new condition.
