# Probabilistic reachable and invariant sets for linear systems with correlated disturbance

arXiv: https://arxiv.org/abs/2004.06960 · HTML: https://mlsanity.com/paper/2004.06960/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2020.

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

- [Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift](https://mlsanity.com/paper/2407.11609/) (2024)
- [Probabilistic Robustness Analysis in High Dimensional Space: Application to Semantic Segmentation Network](https://mlsanity.com/paper/2509.11838/) (2025)

## Abstract (arXiv)

In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only a bound on the correlation matrices is supposed to be known. The concept of correlation bound is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given.