In this paper, modern control theory is applied to a double inverted pendulum with continuous time control policies based on output variables. Phase variable transformations are used to design the state variable feedback controller. Modal control techniques are employed in the design of the dynamic observer which provides estimates of the complete state. The state estimates are then used in the state feedback control loop. The complete control system consists of the observer and the state feed-back controller. The system was adequately stabilized despite the presence of non-linearities and measurement noise, neither of which were accounted for in the theory.