The paper is devoted to the problem of the construction of a control which transfers a control system from any point to a given non-equilibrium point in a finite time. The construction of the control is based on the method of controllability function. The ambiguity of the solution of the equation that determines the controllability function is found, which leads to a number of interesting cases. The problem is solved for a linear system. The obtained results are illustrated on a model example.

Mathematics Subject Classification 2010: 93B05, 93B11, 93C10 Key words: controllability function method, linear system, non-equilibrium point