Stabilisation of SDEs and applications to synchronisation of stochastic neural network driven by G-Brownian motion with state-feedback control

Delay‐dependent stability of a class of stochastic delay systems driven by G‐Brownian motion

“…Based on the stability criteria, the corresponding upper bound of time delay can also be obtained. This is different from [16, 18], where the stability conditions are related to Lyapunov function. In addition, we also reveal that the quadratic variation part may play a positive role in the mean square and quasi‐sure exponential stability.…”

“…In this case, condition (11) is always true, and in condition (12) can be omitted because it is from the quadratic variation part. Hence, the G‐SDDS (6) is mean square and quasi‐surely exponentially stable if there exists a positive definite matrix P such that where . Remark 5 In [16, 18], the sufficient conditions for the stability of stochastic systems driven by G‐Brownian motion were obtained by means of G‐Lyapunov function. In this paper, we no longer give the Lyapunov‐type conditions, but get the explicit sufficient conditions for stability by constructing a concrete Lyapunov functional.…”

“…To make the unstable stochastic systems become stable, Ren et al . [16] investigated the p th moment exponential stabilisation of a class of G‐SDSs under state‐feedback by means of the G‐Lyapunov function. Furthermore, in [17], the stability, asymptotic stability and mean‐square exponential stability of the G‐SDSs with state‐feedback control based on discrete‐time state observation were established by constructing an appropriate G‐Lyapunov function.…”

Stabilization of stochastic differential equations driven by G-Lévy process with discrete-time feedback control

“…The stability has been one of the most important topics in the study of stochastic differential equations (see Mao [13] ). Many authors have discussed the stability for different kinds of stochastic dynamical systems (see, e.g., Hu and Mao [6], Mao [14], Qiu et al [23], Ren et al [27], Ren et al [26], Shao [28], You et al [33], Li et al [8]). Recently, Mao [12] concerned with the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations (also known as stochastic differential equations with the Markovian switching) by discrete-time feedback controls.…”

On boundedness and convergence of solutions for neutral stochastic functional differential equations driven by G-Brownian motion

“…The quasi sure exponential stability for solutions to the stated equations was established by Zhu et al [33]. The mean-square stability of delayed stochastic neural networks driven by G-Brownian motion and stabilization of SDEs driven by G-Brownian motion can be found in [20,28]. For the text on stochastic functional differential equations driven by G-Brownian motion we refer the reader to see [3,5,18].…”