The paper deals with state observer design for nonlinear quasicanonical systems under the action of external disturbances without entering dynamic model of disturbances. Decomposition synthesis procedure of an observer with continuous smooth S-shaped corrective actions in the form of sigma-functions is designed. This observer provides estimation of unmeasured state variables and external bounded disturbances with any given accuracy. These algorithms are used in the control system of an induction motor under external disturbance with incomplete measurements.