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

ABSTRACT Li, X., Lin, X., and Lin, Y. [(2016). Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion. Journal of Mathematicase Analysis and Applications, 439, 235–255] proposed the sufficient conditions for the exponential instability to stochastic differential equations driven by G-Brownian motion (G-SDEs, in short). A natural question is whether we can design a controller to make G-SDEs be stable. By means of the G-Lyapunov function, we design a state-feedback controller to stabilise the system. In addition, applications to stabilisation and synchronisation of Hopfield neural networks driven by G-Brownian motion (G-HNNs, in short) and examples are proposed to illustrate the obtained results.

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