Adaptive Meshing for CPA Lyapunov Function Synthesis
Abstract
Continuous piecewise affine (CPA) Lyapunov function synthesis is one method to perform Lyapunov stability analysis for nonlinear systems. This method first generates a mesh over the region of interest in the system's state space and then solves a linear program (LP), which enforces constraints on each vertex of the mesh, to synthesize a Lyapunov function. Finer meshes broaden the class of Lyapunov function candidates, but CPA function synthesis is more computationally expensive for finer meshes -- particularly so in higher dimensional systems. This paper explores methods to mesh the region of interest more efficiently so that a Lyapunov function can be synthesized using less computational effort. Three methods are explored -- adaptive meshing, meshing using knowledge of the system model, and a combination of the two. Numerical examples for two and three dimensional nonlinear dynamical systems are used to compare the efficacy of the three methods.
Keywords
Cite
@article{arxiv.2511.20443,
title = {Adaptive Meshing for CPA Lyapunov Function Synthesis},
author = {Amy K. Strong and Samuel Akinwande and Leila Bridgeman},
journal= {arXiv preprint arXiv:2511.20443},
year = {2025}
}