A new statement of the classical problem of stabilizing dynamic system
s which is based on analysis of the problem is proposed. It is based o
n investigating system behavior on a finite time interval. The stabili
zation problem is embedded into special optimal control problems. Algo
rithms for the operation of optimal stabilizers which construct teal-t
ime positional solutions are described for each of these problems. The
stabilization problem is investigated under conditions of complete as
well as incomplete and imprecise information about the current system
states. An example of stabilization under conditions of indeterminacy
is presented.