摘要：This paper focuses on a class of highly nonlinear switched stochastic differential delay equations(SDDEs). The key feature is that the switching signal is a semi-Markov process, which is significantly different from most of existing papers where the switching signal is a Markov chain. The infinitesimal generator A acting on the Lyapunov function with respect to the semi Markov modulated SDDEs is established. This useful and important theoretical result will form a foundation for further research on the semi-Markov modulated SDDEs. To demonstrate this point, we will discuss the stabilization of highly nonlinear semi-Markov modulated SDDEs by feedback control based on discrete-time state observations.One more key feature in this paper is that the time varying delay in the given SDDE is no-longer required to be differentiable with the derivative being bounded by a number less than one, which was imposed in most of existing papers.