# Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimization

arXiv: https://arxiv.org/abs/1406.1256 · HTML: https://mlsanity.com/paper/1406.1256/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2014.

## Built on by (most cited first, 4 of 4)

- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Synthesizing Stable Reduced-Order Visuomotor Policies for Nonlinear Systems via Sums-of-Squares Optimization](https://mlsanity.com/paper/2304.12405/) (2023)
- [Parameter-free Optimal Rates for Nonlinear Semi-Norm Contractions with Applications to Q-Learning](https://mlsanity.com/paper/2508.05984/) (2025)
- [Controller Design for Structured State-space Models via Contraction Theory](https://mlsanity.com/paper/2604.07069/) (2026)

## Abstract (arXiv)

Control contraction metrics (CCMs) are a new approach to nonlinear control design based on contraction theory. The resulting design problems are expressed as pointwise linear matrix inequalities and are and well-suited to solution via convex optimization. In this paper, we extend the theory on CCMs by showing that a pair of "dual" observer and controller problems can be solved using pointwise linear matrix inequalities, and that when a solution exists a separation principle holds. That is, a stabilizing output-feedback controller can be found. The procedure is demonstrated using a benchmark problem of nonlinear control: the Moore-Greitzer jet engine compressor model.