In the given paper basic mathematical models and some methods intended for the design and analysis of Cyber-Physical Systems are considered. A semigroup transition system is briefly presented, and some its essential advantages relatively to the timed and time-abstract labeled transition systems designed for a hybrid automaton are outlined. Methods of resolving basic problems of analysis of a weakly initialized hybrid automaton are discussed. It is shown that some of these problems can be resolved by usual methods of Graph Theory. Some method intended to provide the correctness of the customer requirements specifications for the designed hybrid automaton is proposed. Some scheme for resolving two versions of the reachability problem for the designed hybrid automaton is presented.