Issues with Lyapunov conditions, Path Following dynamics and inverted pendulum LQR solution

[jlwu002]

Thank you for your interesting work. We have conducted a follow-up study on your research, where we solved for a controller and certified the Lyapunov conditions for arbitrary nonlinear dynamical systems in the discrete-time setting: https://github.com/jlwu002/nlc_discrete (NeurIPS 2023), paper.

We noticed that the controller used in the paper (and code) for Path Following dynamics does not have a bias term, meaning that the controller $u = 0$ at the equilibrium point $(d_e, \theta_e) = 0$. This does not seem feasible for the path-following setting: when the distance error and angle error are both zero (at equilibrium point), we still need the steering angle to ensure the object is following the unit circle target trajectory.