# On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems

## TL;DR

This paper investigates conditions under which contracting nonlinear systems admit separable metrics, facilitating scalable stability analysis and control design through convex optimization techniques.

## Contribution

It provides new theoretical results on the existence of separable contraction metrics for monotone nonlinear systems, linking positive linear systems theory with nonlinear stability analysis.

## Key findings

- Established conditions for separable contraction metrics in monotone systems
- Connected positive linear systems theory with nonlinear stability analysis
- Discussed applications to distributed control design via convex optimization

## Abstract

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.