In recent years there has been an increasing demand for electric vehicles due to their attractive features including low pollution and increase in efficiency. Electric vehicles use electric motors as primary motion elements and permanent magnet machines found a proven record of use in electric vehicles. Permanent magnet synchronous motor (PMSM) as electric propulsion in electric vehicles supersedes the performance compared to other motor types. However, in order to eliminate the cumbersome mechanical sensors used for feedback, sensorless control of motors has been proposed. This paper proposes the design of sliding mode observer (SMO) based on Lyapunov stability for sensorless control of PMSM. The designed observer is modeled with a simulated PMSM model to evaluate the tracking efficiency of the observer. Further, the SMO is coded using MATLAB/Xilinx block models to investigate the performance at real-time.