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This paper presents a continuous approach of sliding-mode current and flux observers for an induction machine. The proposed observer structure both decouples machine equations and makes them completely insensitive to rotor resistance variation. An estimation algorithm based on these observers is proposed to calculate speed and rotor resistance independently. In the proposed algorithm, the speed and rotor resistance are considered to be unknown constants, because the speed and rotor resistance change slowly compared to the electrical variables such as currents and fluxes. The simulation and experimental results demonstrate the good performance of the proposed observer and estimation algorithm and of the overall indirect-field-oriented-controlled system.