Many practical engineering problems can be modelled as such a class of hybrid dynamic systems (HDSs), where N plants are controlled by a central controller in sharing time manner. These plants are described by differential equations and the controller works according to the mechanism of discrete event. This paper discuss the controllability and stabilizability of this class of hybrid dynamic systems. First, we define the controllability of this class of HDSs and establish the necessary and sufficient condition for controllability. Furthermore, we define the stabilizability of this class of HDSs and establish the necessary and sufficient condition for stabilizability as well.