An Amendment to "Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design"
This is an incremental correction for researchers using Control Contraction Metrics, fixing a gap in a foundational theorem for nonlinear control design.
The paper identifies a missing technical condition in the first theorem of a prior work on Control Contraction Metrics, showing that without it, stabilizability may not hold when the input matrix drops rank. The amendment ensures the theorem's validity under the original assumptions when the input matrix has constant rank or strong CCM conditions hold.
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.