In this paper, the control of a grid-connected wind energy conversion system (WECS), based on an induction machine fed by a matrix converter (MC), is presented. The MC is controlled using a space vector modulation algorithm with zero displacement factor at the input. Stability issues related to the operation of the WECS for the whole power and speed range are fully analyzed in this paper, using a simplified small-signal model. The implementation of a model reference adaptive system (MRAS) observer, for sensorless control of the proposed WECS, is also presented in this paper. The MRAS observer is implemented using the output voltage demand, avoiding the use of voltage transducers to measure the machine voltage. From the speed estimated by the MRAS observer, the electrical torque of the induction generator is regulated in order to drive the WECS to the operating point where the aerodynamic efficiency is maximized. Experimental results obtained with a 2.5-kW prototype are presented and fully discussed in this paper.