There are given necessary and sufficient conditions of exponential stabilization that are obtained using the direct Lyapunov method. For constructive solution of the stabilization problem generalization of the stabilizing stochastic pair method for stochastic system is used. A numerical method of stabilizing pair construction in some region of phase space is substantiated. The criteria of exponential stabilization of the controlled Markov networks are formulated. The effective algorithms of stabilizing control synthesis are presented.