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

Abstract

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.

Keywords

• Discrete-time state observations
• G-Brownian motion%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">G</italic>-Brownian motion
• quasi-surely exponential stability
• time delay