PreprintarXiv licencearXiv
High-Probability Sampled-Data Stabilization of General Nonlinear Stochastic Systems
Abstract
In this paper, we study sampled-data stabilization of general nonlinear stochastic systems under a local exponential-type Lyapunov condition for the continuous-time closed-loop system. The coefficients are assumed only locally Lipschitz, with neither linear-growth nor Khasminskii-type conditions. Two counterexamples show that almost-sure stabilization is generally unattainable. Instead, given an initial state, we establish exponential stability with arbitrarily high probability under sufficiently fast sampling. Separate methods are developed for p≥ 2 and 0<p<2, where p is the growth order in the Lyapunov condition. Numerical examples illustrate the results.
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BibTeX
@misc{sun2026highprobability,
title = {{High-Probability Sampled-Data Stabilization of General Nonlinear Stochastic Systems}},
author = {Kele Sun and Yudong Wang and Shijie Zhou and Wei Lin and Xuerong Mao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27345},
eprint = {2609.27345},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27345},
}
RIS
TY - UNPB
TI - High-Probability Sampled-Data Stabilization of General Nonlinear Stochastic Systems
AU - Kele Sun
AU - Yudong Wang
AU - Shijie Zhou
AU - Wei Lin
AU - Xuerong Mao
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27345
UR - https://arxiv.org/abs/2609.27345
AB - In this paper, we study sampled-data stabilization of general nonlinear stochastic systems under a local exponential-type Lyapunov condition for the continuous-time closed-loop system. The coefficients are assumed only locally Lipschitz, with neither linear-growth nor Khasminskii-type conditions. Two counterexamples show that almost-sure stabilization is generally unattainable. Instead, given an initial state, we establish exponential stability with arbitrarily high probability under sufficiently fast sampling. Separate methods are developed for p≥ 2 and 0<p<2, where p is the growth order in the Lyapunov condition. Numerical examples illustrate the results.
ER -