Stability in Distribution of Highly Nonlinear Hybrid Stochastic Delay Systems by Delay Feedback Control

In this article, the stability in distribution by delay feedback control for a class of hybrid stochastic differential delay equations with highly nonlinear drift and diffusion coefficients is investigated for the first time. Special emphasis should be placed on our success in revealing that the stability of highly nonlinear hybrid stochastic delay systems in distribution can be achieved through more general highly nonlinear delay feedback control (than linear delay feedback control). In order to obtain the asymptotic stability of the system in distribution, three novel $L<^>{p}$-boundedness theorems need to be established. Furthermore, three examples are given to verify the validity of the theoretical analysis.