In the last decades, many vector control techniques have been developed for induction machine to increase their dynamic performances. But they are based on an accurate estimation of flux variables, which are not measurable in conventional induction machines. So, observer strategies are used in induction machine controls. Complex algorithms have been developed, but their long calculation time does not allow a simple implementation in digital form. For this reason, reduced-order observers are often used when a real-time estimation is implemented. If these structures lead to better flux estimations than in the case of an open-loop model, their convergence gains have to be determined and they are sensitive to the parameters value. The authors present a new analytical method to elaborate a reduced-order observer. The influence of the sampling rate is taken into account and the paper investigates the optimal gain, which minimise the sensitivity to the parameters value. In order to measure the observer robustness, the authors define two criteria, which are computed in steady state: the orientation error and the modulus error of the rotor flux. Some examples illustrate the theory and their calculation results are presented.