Reachability and Controllability Analysis of the State Covariance for Linear Stochastic Systems
<|reference_start|>Reachability and Controllability Analysis of the State Covariance for Linear Stochastic Systems: 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.<|reference_end|>
@article{liu2024reachability,
    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={2024},
    archivePrefix={arXiv},
    eprint={2406.14740},
    primaryClass={eess.SY cs.SY}
}