High-Probability Sampled-Data Stabilization of General Nonlinear Stochastic Systems

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 $p\ge 2$ and $0<p<2$, where $p$ is the growth order in the Lyapunov condition. Numerical examples illustrate the results.