Optimizing Lyapunov Certificates via Stability-Preserving Quadratization for Polynomial Systems

arXiv:2609.18871 · math.OC, cs.SC, cs.SY, eess.SY · Submitted 2026-09-16 · Read on arXiv

math.OC, cs.SC, cs.SY, eess.SY

Submitted: 2026-09-16

Updated: 2026-09-16

Code: https://github.com/yuanchenyang/SumOfSquares.py

Terminology

• Lyapunov function — 15× in this paper · explained in 2 episodes
• Benchmark — 8× in this paper · explained in 2 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Conference on Decision and Control — 2× in this paper
• Provenance — 2× in this paper · explained in 4 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Alternation — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Ordinary Differential Equations (ODEs) — 1× in this paper · explained in 2 episodes
• Reachability Problems — 1× in this paper
• Region of Attraction (RoA) — 1× in this paper · explained in 2 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Semidefinite Program (SDP) — 1× in this paper · explained in 2 episodes

Sources

• Quadratization of ODEs: Monomial vs. Non-Monomial
• Discovering Polynomial and Quadratic Structure in Nonlinear Ordinary Differential Equations
• Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition

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