# Small-gain analysis of exponential incremental input/output-to-state stability for large-scale distributed systems

arXiv: https://arxiv.org/abs/2604.07081 · HTML: https://mlsanity.com/paper/2604.07081/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2026.

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

- [A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning](https://mlsanity.com/paper/2604.15238/) (2026)

## Abstract (arXiv)

We provide a detectability analysis for nonlinear large-scale distributed systems in the sense of exponential incremental input/output-to-state stability (i-IOSS). In particular, we prove that the overall system is exponentially i-IOSS if each subsystem is i-IOSS, with interconnections treated as external inputs, and a suitable small-gain condition holds. The analysis is extended to a Lyapunov characterization, resulting in a different quantitative outcome regarding the small-gain condition, which is further analyzed within this work. Moreover, we derive linear matrix inequality conditions posed solely on the local subsystems and their interconnections, which guarantee exponential i-IOSS of the overall distributed system. The results are illustrated on a numerical example.