Stabilization of Stable Manifold of Upright Position of the Spherical Pendulum

Abstract

The stabilization problem of the upright position of the sherical pendulum is treated in detail. This problem is reduced to the stabilization of the stable manifold Omega_st of the upright position of the unforced spherical pendulum. It is shown that for any smooth feedback control derived by the speed-gradient algorithm with the objective to stabilize Omega_st the closed loop system has a limit cycle Gamma, which does not belong to the desired attractor Omega_st. It is shown that Gamma is hyperbolic.

Keywords

• Passivity