# On Compatibility and Region of Attraction for Safe, Stabilizing Control Laws

arXiv: https://arxiv.org/abs/2008.12179 · HTML: https://mlsanity.com/paper/2008.12179/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers](https://mlsanity.com/paper/2504.08249/) (2025)

## Abstract (arXiv)

A novel control method is proposed to ensure compatibility of safe, stabilizing control laws, i.e., simultaneous satisfaction of asymptotic stability and constraint satisfaction for nonlinear affine systems. The results are dependent on an asymptotically stabilizing control law and a zeroing control barrier function (ZCBF), but do not require a control Lyapunov function (CLF). Sufficient conditions for a region of attraction are defined for which the proposed control safely stabilizes the system, while preserving the decrescent Lyapunov function of the original stabilizing control law. The proposed methodology for nonlinear affine systems requires checking conditions of the system dynamics over a substantial portion of the state space, which may be computationally expensive. To facilitate the search for compatibility, we extend the results to a class of nonlinear systems including mechanical systems for which a novel controller is designed to guarantee passivity, safety, and stability. Numerical examples are used to demonstrate the proposed technique.