The paper deals with the problem of stabilizing with a given accuracy for output variables of SISO and MIMO nonlinear systems. A mathematical model of the control plant is represented in block form "input-output" and contains unmatched external disturbances and parametric uncertainties. Within the block approach, decomposition procedures of synthesis of robust control are designed under the uncertainty of the input channels of fictitious and real controls. Using S-shaped, smooth and bounded sigma-functions in local feedbacks allowed us to consider restrictions on state variables at the synthesis stage. For block synthesis of MIMO systems with undetermined and non-singular matrices before fictitious and real control actions, the ideology of the control hierarchy method has been used for calculating lower bounds of amplitudes of sigmoidal controls, ensuring the convergence of the state variables in the defined regions. This approach extends the class of invariant systems by nonlinear systems with non-smooth disturbances, where special requirements for the composition of the state variables in each block are missing.