This paper aims to present an analysis and design of a high-performance speed-sensorless control scheme for a three-phase brushless DC (BLDC) motor drive by means of a novel observer technique in the induced L-infinity norm setting, named robust stochastic L-infinity-induced observer, with the purpose of reducing torque ripple and increasing system robustness. The proposed observer is used for estimating the phase-to-phase trapezoidal back-electromotive-force (back-EMF) for the BLDC motor merely via utilizing measured line stator currents and voltages in such a way that by estimating the back-EMF, position and speed of the rotor is readily obtained. In contrast to the conventional back-EMF sensing methods, this strategy of utilized drive requires no filtering of current and voltage; furthermore, it does not suffer from any sensitivity to switching noises. Owing to that high-speed operation is vital for a motor, the varying input voltage method is used for realizing the minimization of commutation-torque-ripple in a parallel way to the proposed method since drive performance intensely degrades in this mode. Apart from analytic investigation of the proposed method, two other types of observers, namely, the sliding-mode observer and Kalman filter are compared with the proposed method for the aim of determining steady-state accuracy, dynamic performance, parameter and noise sensitivity, low-speed-operation performance, and computational complexity. Finally, the proposed system has been simulated in different operating conditions of the BLDC motor by computer simulation, and the effects of the proposed speed-sensorless control scheme has been assessed by comparative studies and simulation results. Simulation results authenticate that the proposed method is of excellent robustness and high precision estimation in comparison with sliding-mode and Kalman filter methods under different operating conditions in spite of the existence of measurement noise and electric parameter uncertainty. Therefore, the proposed method with its strong robustness makes it possible for the drive to enable the motor to undergo a stable tensionless operation without facing any problem at high-and low-speeds. (C) 2012 Elsevier Ltd. All rights reserved.