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

Fengjiao Liu; Panagiotis Tsiotras

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

Systems and Control 2025-09-22 v2 Systems and Control

Authors: Fengjiao Liu , Panagiotis Tsiotras

Abstract

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.

Keywords

state covariance reachability controllability linear stochastic systems finite time horizon

Cite

@article{arxiv.2406.14740,
  title  = {Reachability and Controllability Analysis of the State Covariance for Linear Stochastic Systems},
  author = {Fengjiao Liu and Panagiotis Tsiotras},
  journal= {arXiv preprint arXiv:2406.14740},
  year   = {2025}
}