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 τ and the time delay τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> 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.
Highlights
I T has been known that noise can be used to stabilize a given unstable system or make a stable system even more stable
Mao proposed a new feedback control based on discrete-time state observations in 2013 [7] and later studied the almost sure exponential stabilization for linear and nonlinear systems by discrete-time stochastic feedback control [8]
We aim to explore the stochastic stabilization for an unstable nonlinear system via discrete-time feedback control with a time delay induced by G-Brownian motion
Summary
I T has been known that noise can be used to stabilize a given unstable system or make a stable system even more stable. G-Brownian motion with discrete-time stochastic feedback control was presented to stabilize a given unstable system quasi-sure exponentially in [23]. To our best knowledge, there is little literature on stochastic stabilization of nonlinear systems via discrete-time feedback control with a time delay under the G-expectation framework. We aim to explore the stochastic stabilization for an unstable nonlinear system via discrete-time feedback control with a time delay induced by G-Brownian motion. The discrete-time feedback controls with a time delay were designed in the drift part of hybrid stochastic systems and the moment exponential stability criteria were established in [9], [10]. While here the discrete-time feedback control with a time delay induced by G-Brownian motion can be considered as the diffusion part of the controlled system and the quasisurely exponential stability will be discussed.
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