This paper proposes a convex approach to the design of robust discrete-time observers to the state estimation of induction machines subject to rotor resistance variation and load disturbance. The observer gain is designed in order to minimize these effects on the state estimation in an ℋ∞ sense, while guaranteeing the error dynamics stability. The pro- posed conditions are cast in terms of state-dependent linear matrix inequalities. Simulation results demon- strates the performance of the approach.