# SOS Construction of Compatible Control Lyapunov and Barrier Functions

arXiv: https://arxiv.org/abs/2305.01222 · HTML: https://mlsanity.com/paper/2305.01222/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2023.

## Built on by (most cited first, 3 of 3)

- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagation](https://mlsanity.com/paper/2410.16281/) (2024)
- [Barrier Certificates for Unknown Systems with Latent States and Polynomial Dynamics using Bayesian Inference](https://mlsanity.com/paper/2504.01807/) (2025)

## Abstract (arXiv)

We propose a novel approach to certify closed-loop stability and safety of a constrained polynomial system based on the combination of Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs). For polynomial systems that are affine in the control input, both classes of functions can be constructed via Sum Of Squares (SOS) programming. Using two versions of the Positivstellensatz we derive an SOS formulation seeking a rational controller that - if feasible - results in compatible CLF and multiple CBFs.