Global stabilization of nonlinear systems with marginally unstable free dynamics by small controls

Presents sufficient conditions under which a fairly large class of single-input nonlinear systems including feedforward systems and the well-known ball-and-beam model, are globally asymptotically and locally exponentially stabilizable by smooth state feedback. A nested saturation controller with the state-dependent saturation levels is constructed explicitly, using a novel design approach which combines the nested saturation strategy for marginally unstable linear systems subject to input saturation, with the low-gain design technique, developed for global asymptotic stabilization of general non-affine systems with marginally stable free dynamics. The power of the proposed low-gain design method is demonstrated by solving a number of nonlinear control problems, particularly, the global stabilization problem of a class of two-dimensional nonlinear systems