Nonlinear robust control of the top

The synthesizing problem of a restricted control in a stabilizing system of a vertical position of a top axis is considered. The control law is synthesized from the criterion of attaining the maximal region of attraction (MRA-criterion) of stabilizing equilibrium in the phase space of the close system. Without rotation and on the low speeds of one the top is unstable therefore the maximal region of attraction is bounded. In this case the bounds of attracting region are specified by the separatrix set of the unstable equilibrium corresponding to the control restrictions. On the high speeds of rotation the top is stabilized due to gyroscopic effect therefore the maximal region of attraction is unbounded. In this case synthesized control law provides the absolute stability of the close system. The found control is robust one since it admits an uncertainty of the nonlinear control functions in the limits of the Hurwitz angle