In the paper linear dynamic systems problem stabilization with account of state variables and controls restrictions synthesis methods are suggested. The suggested approach is based on the block synthesis method and the use of sigma-functions in the feedback chain, which are approximations of discontinuous functions. Besides the procedure decomposition into simple subproblems of lower dimension, the fact that state vector coordinates and a selection in the form of sigma functions are used as fictitious control (restricted in amplitude) provided an opportunity to solve the stabilization problem with account of state variables and controls restrictions.