Global Feedback Control for Nonlinear Affine Systems Defined on Time-Varying Parameterized Manifolds

This paper proposes global feedback control for nonlinear affine systems defined on (noncontractible) manifolds parametetrized by time-varying parameter. The proposed global feedback control consists of a coordinate transformation parametetrized by time-varying parameter and sontag-type discontinuous global feedback control. The main theorem illustrates that the proposed control global asymptotic stabilizes the origin of the system, although the time-varying parameter is unbounded. The control performances of the proposed control is confirmed by a simulation.