Given an unstable hybrid stochastic differential equation (SDE), can we design a delay feedback control to make the controlled hybrid SDE become asymptotically stable?  This is possible if the drift and diffusion coefficients of the given SDE satisfy the linear growth condition.  However, many hybrid SDE models in the real world do not fulfil this condition (namely, they are highly nonlinear).  In order to stabilise these highly nonlinear hybrid SDEs, we will need to establish a new theory on the delay dependent stability criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) as almost all existing delay dependent stability criteria require the drift and diffusion coefficients of the SDDEs satisfy the linear growth condition. Making use of our new delay dependent stability, we will demonstrate how to design the delay feedback controls in order to stabilise a class of highly nonlinear hybrid SDEs whose coefficients satisfy the polynomial growth condition.