# Reachability and Controllability Analysis of the State Covariance for Linear Stochastic Systems

arXiv: https://arxiv.org/abs/2406.14740 · HTML: https://mlsanity.com/paper/2406.14740/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2024.

## Built on by (most cited first, 3 of 3)

- [Go With the Flow: Fast Diffusion for Gaussian Mixture Models](https://mlsanity.com/paper/2412.09059/) (2024)
- [Globally Solving Unbalanced Optimal Transport and Density Control for Gaussian Distributions](https://mlsanity.com/paper/2605.04246/) (2026)
- [Mutual Information Optimal Density Control of Linear Systems and Generalized Schr"odinger Bridges with Reference Refinement](https://mlsanity.com/paper/2605.09349/) (2026)

## Abstract (arXiv)

This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete characterization of the set of reachable state covariances is given. For continuous-time systems, we present an upper bound on the set of reachable state covariances. Moreover, for both linear discrete-time and continuous-time systems, necessary and sufficient conditions are provided for the controllability of the state covariance over a finite horizon.