# Similarity quantification for linear stochastic systems: A coupling compensator approach

arXiv: https://arxiv.org/abs/2007.09052 · HTML: https://mlsanity.com/paper/2007.09052/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2020.

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

- [Formal Control for Uncertain Systems via Contract-Based Probabilistic Surrogates (Extended Version)](https://mlsanity.com/paper/2506.16971/) (2025)

## Abstract (arXiv)

For the formal verification and design of control systems, abstractions with quantified accuracy are crucial. This is especially the case when considering accurate deviation bounds between a stochastic continuous-state model and its finite (reduced-order) abstraction. In this work, we introduce a coupling compensator to parameterize the set of relevant couplings and we give a comprehensive computational approach and analysis for linear stochastic systems. More precisely, we develop a computational method that characterizes the set of possible simulation relations and gives a trade-off between the error contributions on the systems output and deviations in the transition probability. We show the effect of this error trade-off on the guaranteed satisfaction probability for case studies where a formal specification is given as a temporal logic formula.