# Contraction Analysis of Discrete-time Stochastic Systems

arXiv: https://arxiv.org/abs/2106.05635 · HTML: https://mlsanity.com/paper/2106.05635/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2021.

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

- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Transfer Learning for a Class of Cascade Dynamical Systems](https://mlsanity.com/paper/2410.06828/) (2024)

## Abstract (arXiv)

In this paper, we develop a novel contraction framework for stability analysis of discrete-time nonlinear systems with parameters following stochastic processes. For general stochastic processes, we first provide a sufficient condition for uniform incremental exponential stability (UIES) in the first moment with respect to a Riemannian metric. Then, focusing on the Euclidean distance, we present a necessary and sufficient condition for UIES in the second moment. By virtue of studying general stochastic processes, we can readily derive UIES conditions for special classes of processes, e.g., i.i.d. processes and Markov processes, which is demonstrated as selected applications of our results.