IMPROVED RESULTS ON STABILIZATION OF G-SDEs BY FEEDBACK CONTROL BASED ON DISCRETE-TIME OBSERVATIONS

We provide feasible criteria for stabilization of stochastic differential equations driven by G-Brownian motion based on discrete-time observations. We extend the results in Ren, Yin, and Sakthivel [Automatica, 95 (2018), pp. 146-151] substantially by adopting a comparative method rather than the Lyapunov function arguments, for the pth moment and quasi-sure exponential stabilization problems. It seems that our pth moment estimates on the gap between the discretized controlled states and the auxiliary system's states are new. Using tools from the G-Ito stochastic analysis, we first show the exponential stabilization for equations with linear coefficients, then for equations with Lipschitz coefficients. An illustrative example is provided.

Automated summary

This study offers new insights into the stabilization of stochastic differential equations driven by G-Brownian motion, providing specific discussions on pth moment and quasi-sure exponential stabilization problems through a comparative method. The exponential stabilization for equations with linear coefficients and equations with Lipschitz coefficients are demonstrated using tools from G-Ito stochastic analysis, along with an illustrative example.