Recently, semi-Markovian jump systems (S-MJSs) have received wide attention due to their feasibility in modeling practical systems, for instance, electrical systems, economics and mechanics, that suffer from abrupt structural changes caused by phe- nomena such as random failures or repairs, changes in subsystem interconnections and so on. Nowadays, the analysis and synthesis of S-MJSs is becoming more and more rich, and many important results have been achieved. However, due to the gen- erality that the transition rates in S-MJSs are time-varying and hard to obtain in prac- tice, the fundamental issues of stochastic stability and stabilization of such systems are still challenging. Hence, we make an attempt to tackle the analysis and synthesis of a class of continuous-time S-MJSs with generally uncertain transition rates.