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PreprintarXiv licencearXiv

Feedback Stabilization for Sampled Linear Systems with Control-linear Noise

  • Cynthia Cheng
  • Xudong Chen
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Abstract

In this paper, we consider linear stochastic systems with control-linear noise and periodically sampled measurements. We address the problem of feedback stabilization in the mean-square sense. The main contribution of the paper is to provide a necessary and sufficient condition for feedback stabilization. In particular, we relate feedback stabilizability of the stochastic system to the existence of a fixed point of a Riccati-type algebraic equation and, further, to the existence of a solution to an infinite-horizon optimal control problem.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026feedback,
  title = {{Feedback Stabilization for Sampled Linear Systems with Control-linear Noise}},
  author = {Cynthia Cheng and Xudong Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30438},
  eprint = {2609.30438},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30438},
}
RIS
TY  - UNPB
TI  - Feedback Stabilization for Sampled Linear Systems with Control-linear Noise
AU  - Cynthia Cheng
AU  - Xudong Chen
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30438
UR  - https://arxiv.org/abs/2609.30438
AB  - In this paper, we consider linear stochastic systems with control-linear noise and periodically sampled measurements. We address the problem of feedback stabilization in the mean-square sense. The main contribution of the paper is to provide a necessary and sufficient condition for feedback stabilization. In particular, we relate feedback stabilizability of the stochastic system to the existence of a fixed point of a Riccati-type algebraic equation and, further, to the existence of a solution to an infinite-horizon optimal control problem.
ER  -