Voltage sags are the most prevalent type of power quality disturbances, and the dynamic voltage restorer (DVR) can provide load voltage support with a power rating only a fraction of that of the load. However, most reported control strategies are using open-loop feed forward control, because of the fast voltage compensation requirement, in order to reduce the impact of voltage sags to sensitive loads. It is shown that the open-loop control produces poorly damped response due to the presence of the switching harmonic LC filter. Closed-loop control permits active damping of the LC filter, and a closer tracking of the reference load voltage. Multi-loop feedback PI control has attracted considerable attention, but it has difficulties meeting the fast dynamic response requirement because of the dynamic separation of two cascaded loops. This paper presents a closed-loop state variable control strategy to handle the time varying control references in voltage sag compensation applications. It removes the inner current control loop that is included in the multi-loop control structure, instead, the derivative of the output current is used to increase the dynamic response of the control system. Furthermore, a software based current observer is built to obtain the output current and its derivative, and to minimize the noise effects. The theoretical considerations are verified through simulation and experimental tests.