This paper proposes a design of a robust-adaptive full-order observer based on the /spl gamma/-positive real problem for sensorless induction-motor drives. The adaptive full-order observer is known to become unstable in a major part of the regenerating-mode low-speed operation, and this prevents the sensorless vector controller from operating an induction motor successfully. In this paper, a design of the observer gain for both stable speed identification and robust flux phase estimation and an adaptive scheme for stator resistance identification are proposed. First, the error system of the adaptive full-order observer is reconsidered-requirements of this observer with a speed identifier are described, in which a simple robust observer gain design in the sense of H/sub /spl infin// optimization is not useful in reality. Next, in order to satisfy all the requirements of the robust adaptive observer, the design of the observer gain based on the /spl gamma/-positive real problem and the adaptive scheme for stator resistance are described. Finally, several experimental results show the feasibility and effectiveness of the proposed design.