Reviews: Neural Lyapunov Control

The topic of this paper is highly relevant, since stability guarantees are often sought after for learned policies. While I'm generally excited about the approach, the paper does not address aspects that might make the technique applicable to domains with non-smooth (e.g. The condition in Eq. 1 is a strong one and I understand the theoretical need for it. However, I'm wondering if there's any value to the proposed technique in case this condition is not met? Will the inclusion of the Lyapunov risk as a term in the cost function yield feedback controllers that are more robust in practice, even for non-smooth systems?