Quadrotors are a favorite platform amongst academic researchers. Yet there is limited work present on the identification of Linear Time Invariant (LTI) state space models for quadrotors. This thesis focuses on the development of a 70 gram quadrotor with a maximum dimension of less than 6 inches. An MAV this small is extremely agile and in this case, dynamically unstable. Therefore it requires an active control scheme to stabilize the vehicle's attitude. To develop an effective controller using the vast array of available linear control tools, model knowledge is required. The scope of this thesis is to identify an LTI state space model of the 70 gram quadrotor mentioned about hover. Because the quadrotor is unstable, it cannot be flown without some form of feedback control present. To determine the bare airframe dynamics of a closed loop system, the feedback gains must be turned down as low as possible so as to not distort the natural response. Then the bare airframe dynamics can be calculated from the identified closed loop dynamics if the feedback gains and control law are known. Using the derived open loop system this thesis presents options for controller development for both a stabilizing inner loop, and a station keeping outer loop controller.