This paper addresses the problem of controlling wind energy conversion (WEC) systems involving permanent magnet synchronous generator (PMSG) fed by IGBT-based buck-to-buck rectifier-inverter. The prime control objective is to maximize wind energy extraction which cannot be achieved without letting the wind turbine rotor operate in variable-speed mode. Interestingly, the present study features the achievement of the above energetic goal without resorting to sensors of wind velocity, PMSG speed and load torque. To this end, an adaptive output-feedback control strategy devoid of any mechanical sensor is developed (called sensorless), based on the nonlinear model of the whole controlled system and only using electrical variables measurements. This control strategy involves: (i) a sensorless online reference-speed optimizer designed using the turbine power characteristic to meet the maximum power point tracking (MPPT) requirement; (ii) a nonlinear speed regulator designed by using the backstepping technique; (iii) a sensorless interconnected adaptive state observer providing online estimates of the rotor position as well as speed and load/turbine torque. The proposed output-feedback control strategy is backed by a formal analysis showing that all control objectives are actually achieved. Several simulations show that the control strategy enjoys additional robustness properties.