Stochastic Discrete-Time Delay Feedback Stabilization for Nonlinear Systems Under the Sublinear Expectation Framework

This paper is concerned with the stochastic stabilization problem for nonlinear systems by
$G$
-Brownian motion with feedback control based on discrete-time state observations with a time delay. By constructing an auxiliary system, which is a continuous-time stochastic system driven by
$G$
-Brownian motion, we establish a sufficient criterion in terms of the observation gap
$\tau $
and the time delay
$\tau _{0}$
to ensure the quasi-surely exponential stability of the stochastic controlled system. Moreover, implementation of the control strategy is provided. Finally, an example is given to demonstrate the theoretical result.