Cascaded design of the state observer for nonlinear systems in the presence of external perturbations

Applicability of the block approach to the problem of observation of nonlinear systems in the presence of uncontrollable external perturbations was demonstrated. A block-observable form of the general nonlinear systems was obtained with regard for perturbations. It underlies two types of cascaded procedures for designing the state observers in the class of systems with separable motions: (i) with discontinuous controls and (ii) with high-gain feedbacks. The first procedure relies on the method of equivalent control to restore in a finite time the nonmeasurable components of the state vector and also perturbations. The second procedure e estimates the nonmeasurable components of the state vector in the prelimit situation with a given accuracy and retention of the decomposition of the design procedure.