On correctness of probabilistic stabilization

Consideration is given to the controlled object with aftereffect under indefinite and stochastic noises. The problem of feedback stabilization with probabilistic actions is discussed. Noises in the form of retarded actions of the motion history are admitted; also, the control of retarded actions of the motion history is tolerated. The paper is based on the Lyapunov stability theory [1] modernized for hereditary and stochastic systems. The approach typical of the control theory in the presence of a conflict or uncertainty is used.