In this paper an approach for the construction of nonlinear output tracking control on a finite time interval for a class of weakly nonlinear systems with state-dependent coefficients is considered. The proposed method of control synthesis consists of two main stages. On the first stage, a nonlinear state feedback regulator is constructed using a previously proposed control algorithm based on the State-Dependent Riccati Equation (SDRE). On the second stage, the problem of full-order observer construction is formulated and then is reduced to the differential game problem. The form of its solution is obtained with the help of the guaranteed (minimax) control principle, which allows to find the best observer coefficients with respect to a given functional considering the worst-case uncertainty realization. The form of the obtained equations made it possible to use the algorithm from the first stage to determine the observer matrix. The proposed approach is characterized by the nonapplicability of the estimation and control separation principle used for linear systems, since the matrix of observer coefficients turned out to be dependent on the feedback coefficients matrix. The use of numerical-analytical procedures for determination of observer and feedback coefficients matrices significantly reduces the computational complexity of the control algorithm.