The stabilization of program motions of balanced gyrostat

We consider program motion of balanced gyrostat. We solve the problem of construction asimptotically stability program motion. The program motion can be any function. Control is received in the form the analytical solution. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunov's functions having constant signs derivatives.