Power-assisted wheelchairs (PAW) provide an efficient means of transport for disabled persons. In this human-machine interaction, the human-applied torque is a crucial variable to implement the assistive system. The present paper describes a novel scheme to design PAWs without torque sensors. Instead of using a torque sensor, a discrete-time unknown input observer in descriptor form is applied to estimate the human input torque and the angular velocities of the two wheels via the angular position. Using Finsler's lemma, the observer gains are obtained by solving an LMI problem. Based on the estimation, both a torque-assistance system and a speed controller are introduced. In addition, the Input-to-State Stability (ISS) of the interconnected controller-observer system is analysed for the speed controller. Finally, simulation results validate the observer and the power-assisted algorithms. The methodology follows patent WO2015173094 issued in 2015 [20].