Abstract
Given an unstable hybrid neutral stochastic differential equation (NSDE), can we design a delay feedback control to make the controlled hybrid NSDE become stable? It has been proved that this is possible under the linear growth condition. However, there is no answer to the question if the drift and diffusion coefficients of the given unstable NSDE satisfy highly nonlinear growth condition. The aim of this paper is to design delay feedback controls in order to stabilise a class of highly nonlinear hybrid NSDEs whose coefficients satisfy the polynomial growth condition.
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