A method of decomposition analysis and design is developed for estimating the unmeasurable components of the state vector and external perturbations of a wide class by the methods of design of systems with discontinuous controls in the correction circuit of the dynamic observer. It is helpful in identifying the observable subspace of maximal dimension of the state vector and observable combinations of the components of the state vector, and in solving the estimation problem in a nite time without the need for joint analysis and design of a closed system with an observer.