Lyapunov Stability Analysis of a Generated UAV Controller

A Large Language Model-based search for controller synthesis can yield UAV controllers with strong trajectory-tracking performance. However, low tracking error does not necessarily demonstrate closed-loop stability. This study presents a Lyapunov stability assessment of an automatically generated UAV controller produced through a Large Language Model-based search process. The closed-loop system is numerically linearised about the hover equilibrium, yielding a local closed-loop state matrix Ad.Eigenvalue analysis is then used to determine whether Ad is Schur stable, corresponding to all eigenvalues lying inside the unit circle ρ(Ad)<1. A quadratic Lyapunov function is constructed by solving the discrete-time Lyapunov equation AdTPAd−P=−Q. The positive definiteness of the resulting matrix provides a local Lyapunov certificate for the linearised closed-loop system. To connect this local certificate to dynamic flight behaviour, the Lyapunov function is evaluated along trajectory-tracking logs using the tracking-error state. The mean Lyapunov value, maximum Lyapunov value, discrete Lyapunov difference, and mean squared error are used to compare the generated controller with PID, LQR, and PID + DOB baselines. The results show that the generated controller satisfies local Lyapunov stability conditions near hover. Our findings demonstrate that established Lyapunov tools can be applied post hoc to a search-generated UAV controller, providing evidence of local stability.