Many practical engineering problems can be modelled as such a class of hybrid dynamic systems, 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. Event feedback strategy is used as the real-time scheduling policy such that one and only one plant among N plants is chosen to be controlled at any time. This paper discuss the asymptotical and exponential stability of this class of hybrid dynamic systems. First, we present the derived discrete-event system for the hybrid dynamic system with event feedback strategy. Then two conjectures on asymptotical and exponential stability are proposed. We show that the conjectures hold in certain special case. Two examples are provided to support the conjectures in general case.