# On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems

arXiv: https://arxiv.org/abs/1704.02676 · HTML: https://mlsanity.com/paper/1704.02676/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2017.

## Built on by (most cited first, 2 of 2)

- [A Contraction Theory Approach to Optimization Algorithms from Acceleration Flows](https://mlsanity.com/paper/2105.08832/) (2021)
- [Distributed Identification of Contracting and/or Monotone Network Dynamics](https://mlsanity.com/paper/2107.14309/) (2021)

## Abstract (arXiv)

Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are exponentially stable, can have that property verified by a separable metric. Making use of recent results in the theory of positive linear systems and separable Lyapunov functions, we prove several new results showing when this is possible, and discuss the application of to nonlinear distributed control design via convex optimization.