# Stability of diffusively coupled linear systems with an invariant cone

## TL;DR

This paper investigates conditions under which diffusive coupling preserves stability in linear systems, identifying specific classes where stability is maintained despite general counterexamples.

## Contribution

It characterizes a class of linear systems for which diffusive coupling guarantees stability, extending understanding beyond known counterexamples.

## Key findings

- Identifies classes of systems with stability-preserving diffusive coupling
- Provides theoretical conditions for stability preservation
- Highlights limitations of diffusive coupling in general

## Abstract

This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a reasonably diverse class of systems for which it is true.