The paper presents a speed sensorless vector control method for an induction motor that is supplied by a PWM inverter through an output LC filter. The system states are estimated by an adaptive full-order observer, and no additional voltage, current or speed measurements are needed. The rotor speed adaptation is based on the estimation error of the inverter output current. Quasi-steady-state analysis is used to illustrate the speed adaptation, and the stability is analyzed using a linearized model. Simulation and experimental results show that it is possible to achieve performance comparable to that of a drive without the LC filter.